Test Result & Solutions

Question 1 Unattempted

                    An examination roll number is classified into Zone, Exam Type, and Batch based on the following rules:

- The first two characters (letters) represent the Zone: $$\text{NR}$$ (North), $$\text{SR}$$ (South), $$\text{ER}$$ (East), $$\text{WR}$$ (West).

- The next three digits represent the Center Code (must be a prime number between $$100$$ and $$115$$).

- The last two characters must be a capital letter followed by a small letter representing the Shift.

Which of the following roll numbers strictly satisfies all the classification criteria?

A) $$\text{WR105Cd}$$

B) $$\text{SR111Ab}$$

C) $$\text{NR109Ab}$$

D) $$\text{ER107AB}$$

Explanation:

Checking each option against the three criteria:
1. $$\text{NR109Ab}$$: Zone is $$\text{NR}$$ (valid), Center Code is $$109$$ (a prime number between $$100$$ and $$115$$), Shift is $$\text{Ab}$$ (capital letter followed by a small letter). This satisfies all rules.
2. $$\text{SR111Ab}$$: $$111$$ is divisible by $$3$$ ($$111 = 3 \times 37$$), so it is not prime.
3. $$\text{ER107AB}$$: Ends with two capital letters ($$\text{AB}$$) instead of a capital letter followed by a small letter.
4. $$\text{WR105Cd}$$: $$105$$ is divisible by $$5$$, so it is not prime.

Question 2 Unattempted

                    A person spends $$75\%$$ of his income. If his income increases by $$28\%$$ and his expenditure increases by $$20\%$$, then what is the percentage increase or decrease in his savings?                

A) $$48\%$$ increase

B) $$52\%$$ increase

C) $$52\%$$ decrease

D) $$40\%$$ increase

Explanation:

Let the initial income be $$100$$.
Initial expenditure $$= 75\%\text{ of } 100 = 75$$.
Initial savings $$= \text{Income} - \text{Expenditure} = 100 - 75 = 25$$.

New income after $$28\%$$ increase $$= 100 + 28 = 128$$.
New expenditure after $$20\%$$ increase $$= 75 \times 1.20 = 90$$.
New savings $$= 128 - 90 = 38$$.

Increase in savings $$= 38 - 25 = 13$$.
Percentage increase in savings $$= \left(\frac{13}{25}\right) \times 100\% = 52\%$$.

Question 3 Unattempted

                    A computer has 8 GB of RAM. Which statement about RAM is correct?                

A) RAM permanently stores data even when the power is switched off.

B) RAM is exclusively used for long-term backup.

C) RAM is slower than every type of secondary storage.

D) RAM is volatile memory used to hold programs and data currently in use.

Explanation:

RAM is volatile primary memory. Its contents are normally lost when power is removed. It temporarily stores active programs and data for quick access by the CPU.

Question 4 Unattempted

                    A sum of $$\text{Rs. } 15,500$$ is divided among $$\text{A, B,}$$ and $$\text{C}$$ such that the ratio of the shares of $$\text{A}$$ and $$\text{B}$$ is $$2 : 5$$, and the ratio of the shares of $$\text{B}$$ and $$\text{C}$$ is $$3 : 2$$. What is the difference between the shares of $$\text{B}$$ and $$\text{C}$$?                

A) $$\text{Rs. } 1,500$$

B) $$\text{Rs. } 2,500$$

C) $$\text{Rs. } 2,000$$

D) $$\text{Rs. } 3,000$$

Explanation:

Given $$A : B = 2 : 5$$ and $$B : C = 3 : 2$$.
Make the value of $$B$$ equal in both ratios by multiplying the first ratio by $$3$$ and the second ratio by $$5$$: $$A : B = 6 : 15$$ $$B : C = 15 : 10$$ Thus, $$A : B : C = 6 : 15 : 10$$.

Total ratio units $$= 6 + 15 + 10 = 31\text{ units}$$.
Given $$31\text{ units} = \text{Rs. } 15,500 \implies 1\text{ unit} = \frac{15,500}{31} = \text{Rs. } 500$$.
The difference between the shares of $$\text{B}$$ and $$\text{C}$$ $$= 15 - 10 = 5\text{ units}$$.
Required difference $$= 5 \times 500 = \text{Rs. } 2,500$$.

Question 5 Unattempted

                    Match the national parks with the states or Union Territories in which they are located:

i. Dachigam National Park

 ii. Hemis National Park

 iii. Keibul Lamjao National Park

 iv. Silent Valley National Park

1. Kerala

2. Manipur

3. Jammu and Kashmir

4. Ladakh

A) i-3, ii-4, iii-2, iv-1

B) i-3, ii-2, iii-4, iv-1

C) i-2, ii-4, iii-3, iv-1

D) i-4, ii-3, iii-1, iv-2

Explanation:

Dachigam National Park is in Jammu and Kashmir, Hemis National Park is in Ladakh, Keibul Lamjao National Park is in Manipur, and Silent Valley National Park is in Kerala.

Question 6 Unattempted

                    A person deposits ₹20,000 in a bank account offering simple interest at 6% per annum. How much total interest will be earned after 2 years, assuming no withdrawals or additional deposits?                

A) ₹2,000

B) ₹1,200

C) ₹2,400

D) ₹2,472

Explanation:

Simple interest = Principal × Rate × Time / 100. Therefore, SI = 20,000 × 6 × 2 / 100 = ₹2,400.

Question 7 Unattempted

                    Consider the following statements about MS Word:

Ctrl + H opens the Find and Replace interface.

Ctrl + Enter inserts a page break.

Mail Merge can generate personalised documents for multiple recipients.

The .docx format is a macro-enabled Word document format by default.

A) 2, 3 and 4 only

B) 1, 2, 3 and 4

C) 1, 2 and 3 only

D) 1 and 2 only

Explanation:

Statements 1, 2 and 3 are correct. The standard .docx format is not the macro-enabled format. Word documents that need to preserve VBA macros are commonly saved as .docm.

Question 8 Unattempted

                    Simplify the following recurring decimal expression into a fraction in its lowest form: $$0.\overline{45} + 0.3\overline{6} - 0.2\overline{7}$$                

A) $$\frac{269}{495}$$

B) $$\frac{259}{495}$$

C) $$\frac{271}{495}$$

D) $$\frac{53}{99}$$

Explanation:

Convert each recurring decimal into a fraction:
1. $$0.\overline{45} = \frac{45}{99} = \frac{5}{11}$$ 2. $$0.3\overline{6} = \frac{36 - 3}{90} = \frac{33}{90}$$ 3. $$0.2\overline{7} = \frac{27 - 2}{90} = \frac{25}{90}$$ Substitute these values into the given expression: $$= \frac{5}{11} + \left(\frac{33}{90} - \frac{25}{90}\right)$$ $$= \frac{5}{11} + \frac{8}{90} = \frac{5}{11} + \frac{4}{45}$$ $$= \frac{5 \times 45 + 4 \times 11}{11 \times 45} = \frac{225 + 44}{495} = \frac{269}{495}$$.

Question 9 Unattempted

                    Consider the following statement and decide which of the given assumptions is/are implicit in the statement.

<b>Statement:</b> "The municipal corporation has decided to levy a heavy penalty on households that fail to segregate biodegradable and non-biodegradable waste starting next month."

<b>Assumptions:</b>

I. People generally tend to comply with civic rules when financial penalties are imposed for non-compliance.

II. The municipal corporation has adequate mechanisms to collect and process segregated waste.

A) Only Assumption II is implicit

B) Neither Assumption I nor II is implicit

C) Both Assumptions I and II are implicit

D) Only Assumption I is implicit

Explanation:

1. Assumption I is implicit because a penalty is introduced specifically as a deterrent to ensure citizens follow the waste segregation rule.
2. Assumption II is implicit because mandating household waste segregation is only logical if the civic body assumes it can handle and process the segregated waste streams effectively.
Hence, both Assumptions I and II are implicit.

Question 10 Unattempted

                    Choose the correct word to complete the sentence: The principal's advice had a positive _____ on the students' behaviour.                

A) effect

B) affection

C) effort

D) affect

Explanation:

'Effect' is a noun meaning a result or consequence. 'Affect' is usually a verb meaning to influence. The correct expression is 'a positive effect on'.

Question 11 Unattempted

                    Read the passage and answer the question:

Digital public services can make government facilities more accessible by reducing travel, paperwork and waiting time. However, their effectiveness depends on reliable internet connectivity, digital literacy and the availability of secure systems. Citizens who lack devices or the skills to use online platforms may still face barriers. Therefore, digital expansion should be accompanied by inclusive support and accessible offline alternatives.

According to the passage, what is necessary to make digital public services more inclusive?

A) Limiting services to citizens with advanced technical skills

B) Replacing every offline service immediately

C) Removing security measures to make websites easier to access

D) Combining digital expansion with support and accessible offline alternatives

Explanation:

The passage explains that connectivity, digital literacy and secure systems are essential. It specifically recommends inclusive support and offline alternatives so that citizens who face digital barriers are not excluded.

Question 12 Unattempted

                    A regular right pyramid has a square base of side $$16\text{ cm}$$ and a vertical height of $$15\text{ cm}$$. Find the total surface area of the pyramid.                

A) $$640\text{ cm}^2$$

B) $$800\text{ cm}^2$$

C) $$544\text{ cm}^2$$

D) $$736\text{ cm}^2$$

Explanation:

Given side of the square base $$a = 16\text{ cm}$$ and vertical height $$h = 15\text{ cm}$$.
First, find the slant height $$l$$ of the triangular faces: $$l = \sqrt{h^2 + \left(\frac{a}{2}\right)^2} = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17\text{ cm}$$.

1. $$\text{Area of square base} = a^2 = 16^2 = 256\text{ cm}^2$$.
2. $$\text{Lateral Surface Area (LSA)} = \frac{1}{2} \times \text{Perimeter of base} \times l$$ $$\text{LSA} = \frac{1}{2} \times (4 \times 16) \times 17 = 32 \times 17 = 544\text{ cm}^2$$. $$\text{Total Surface Area (TSA)} = \text{Area of base} + \text{LSA} = 256 + 544 = 800\text{ cm}^2$$.

Question 13 Unattempted

                    Match the following constitutional provisions with their correct subjects:

i. Article 32

 ii. Article 110

 iii. Article 123

 iv. Article 280

1. Finance Commission

2. Money Bills

3. Power of the President to promulgate Ordinances

4. Constitutional remedies

A) i-4, ii-2, iii-3, iv-1

B) i-4, ii-3, iii-2, iv-1

C) i-2, ii-4, iii-1, iv-3

D) i-1, ii-2, iii-4, iv-3

Explanation:

Article 32 concerns constitutional remedies; Article 110 defines Money Bills; Article 123 empowers the President to promulgate Ordinances under specified conditions; and Article 280 provides for the Finance Commission.

Question 14 Unattempted

                    Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.

(Note: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.)                

A) $$17 : 306$$

B) $$13 : 195$$

C) $$15 : 255$$

D) $$11 : 143$$

Explanation:

In the first three options, the relation follows $$n : n(n + 2)$$.
Option (a): $$11 \times (11 + 2) = 11 \times 13 = 143$$.
Option (b): $$13 \times (13 + 2) = 13 \times 15 = 195$$.
Option (c): $$15 \times (15 + 2) = 15 \times 17 = 255$$.
Option (d): $$17 \times (17 + 2) = 17 \times 19 = 323 \neq 306$$. Thus, $$17 : 306$$ is different.

Question 15 Unattempted

                    Which of the following correctly describes the greenhouse effect and global warming?

Carbon dioxide absorbs and emits infrared radiation.

The natural greenhouse effect makes Earth warmer than it would otherwise be.

Ozone in the stratosphere and ozone near the ground have identical environmental effects.

Methane is a greenhouse gas.

A) 1 and 3 only

B) 2, 3 and 4 only

C) 1, 2, 3 and 4

D) 1, 2 and 4 only

Explanation:

Statements 1, 2 and 4 are correct. The natural greenhouse effect maintains temperatures suitable for life. Stratospheric ozone protects against harmful ultraviolet radiation, whereas ground-level ozone is an air pollutant and a greenhouse gas.

Question 16 Unattempted

                    A square sheet of transparent paper is folded twice along the dotted lines: first from the bottom half to the top half (folding upwards), and second from the right half to the left half (folding leftwards), forming a smaller quarter-square in the top-left quadrant. Two circular holes are punched near the bottom-right corner (center of the original sheet) and the top-left corner of the folded quarter-square. When the paper is completely unfolded, how many circular holes will appear in total, and where will the central cluster of holes be located?                

A) $$8$$ holes in total; $$4$$ holes clustered near the center and $$1$$ hole at each of the $$4$$ corners

B) $$6$$ holes in total; $$4$$ holes near the center and $$2$$ holes at the corners

C) $$8$$ holes in total; all $$8$$ holes arranged along the outer edges

D) $$4$$ holes in total; $$2$$ holes near the center and $$2$$ holes at the top corners

Explanation:

Since the paper is folded twice (into $$2 \times 2 = 4$$ layers), each punched hole passes through $$4$$ layers of paper, creating $$4$$ symmetrical holes upon unfolding.
1. The hole punched near the bottom-right corner of the top-left quadrant corresponds to the center of the original square sheet, producing $$4$$ symmetrical holes clustered around the center.
2. The hole punched near the top-left outer corner of the folded sheet reflects across both fold axes to appear at each of the $$4$$ outer corners of the unfolded square.
Total holes $$= 4 + 4 = 8$$.

Question 17 Unattempted

                    Four letter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter-cluster.                

A) $$\text{DWHS}$$

B) $$\text{BYDW}$$

C) $$\text{CWFS}$$

D) $$\text{EVJQ}$$

Explanation:

Check the alphabetical positional values for opposite letter pairs (sum of positional values equals $$27$$):
Option (a): $$\text{D}(4) + \text{W}(23) = 27$$ and $$\text{H}(8) + \text{S}(19) = 27$$.
Option (b): $$\text{B}(2) + \text{Y}(25) = 27$$ and $$\text{D}(4) + \text{W}(23) = 27$$.
Option (c): $$\text{C}(3) + \text{W}(23) = 26 \neq 27$$ and $$\text{F}(6) + \text{S}(19) = 25 \neq 27$$.
Option (d): $$\text{E}(5) + \text{V}(22) = 27$$ and $$\text{J}(10) + \text{Q}(17) = 27$$.
Hence, $$\text{CWFS}$$ is the odd one out.

Question 18 Unattempted

                    Match the following computer ports with their common uses:

i. HDMI

 ii. RJ-45

 iii. USB

 iv. 3.5 mm audio jack

1. Wired Ethernet networking

2. Digital audio and video transmission

3. Connecting peripherals and transferring data

4. Analog audio input/output on compatible devices

A) i-2, ii-1, iii-3, iv-4

B) i-2, ii-3, iii-1, iv-4

C) i-1, ii-2, iii-4, iv-3

D) i-4, ii-1, iii-3, iv-2

Explanation:

HDMI carries digital audio and video; RJ-45 commonly connects Ethernet cables; USB supports peripherals, data transfer and power; and a 3.5 mm audio jack supports analog audio on compatible equipment.

Question 19 Unattempted

                    Consider the following statements regarding fundamental rights and Directive Principles of State Policy:

Fundamental Rights are generally enforceable by courts.

Directive Principles of State Policy are non-justiciable.

Article 21 protects life and personal liberty.

Fundamental Duties were included in the original Constitution of India in 1950.

A) 2 and 4 only

B) 1 and 4 only

C) 1, 2 and 3 only

D) 1, 2, 3 and 4

Explanation:

Statements 1, 2 and 3 are correct. Fundamental Duties were added by the 42nd Constitutional Amendment Act, 1976, following the recommendations of the Swaran Singh Committee. They were not part of the original Constitution.

Question 20 Unattempted

                    The base of a right prism is a triangle whose sides are $$13\text{ cm}$$, $$20\text{ cm}$$, and $$21\text{ cm}$$. If the height of the prism is $$15\text{ cm}$$, then find the volume of the prism.                

A) $$1,760\text{ cm}^3$$

B) $$1,950\text{ cm}^3$$

C) $$1,890\text{ cm}^3$$

D) $$1,680\text{ cm}^3$$

Explanation:

First, find the area of the triangular base using Heron's formula.
Semi-perimeter $$s = \frac{13 + 20 + 21}{2} = \frac{54}{2} = 27\text{ cm}$$. $$\text{Area of base} = \sqrt{s(s - a)(s - b)(s - c)}$$ $$= \sqrt{27(27 - 13)(27 - 20)(27 - 21)}$$ $$= \sqrt{27 \times 14 \times 7 \times 6}$$ $$= \sqrt{(9 \times 3) \times (2 \times 7) \times 7 \times (3 \times 2)}$$ $$= 3 \times 3 \times 2 \times 7 = 126\text{ cm}^2$$.

Volume of the right prism $$= \text{Area of base} \times \text{Height}$$: $$\text{Volume} = 126 \times 15 = 1,890\text{ cm}^3$$.

Question 21 Unattempted

                    In MS Excel, cell C2 contains the formula =A2*$B$1. The formula is copied from C2 to C3. Which formula will appear in C3?                

A) =A2*$B$1

B) =A3*$B$1

C) =A3*$B$2

D) =$A$3*B1

Explanation:

A2 is a relative reference, so it changes to A3 when copied down one row. $B$1 is an absolute reference, so both its column and row remain fixed.

Question 22 Unattempted

                    Consider the following statements about the Constitution of Jammu and Kashmir and its present constitutional position:

Jammu and Kashmir was reorganised as a Union Territory on 31 October 2019.

Ladakh was also constituted as a separate Union Territory on 31 October 2019.

Jammu and Kashmir currently has its own separate Constitution operating independently of the Constitution of India.

The Jammu and Kashmir Reorganisation Act, 2019, provided the legal framework for the reorganisation.

A) 2, 3 and 4 only

B) 1, 2 and 4 only

C) 1, 2, 3 and 4

D) 1 and 2 only

Explanation:

Statements 1, 2 and 4 are correct. On 31 October 2019, the former state was reorganised into the Union Territories of Jammu and Kashmir and Ladakh. The former separate Constitution of Jammu and Kashmir ceased to operate following the constitutional changes of 2019.

Question 23 Unattempted

                    Identify the part of the sentence that contains an error: Neither of the two candidates / have submitted / the required documents / before the deadline.                

A) Neither of the two candidates

B) have submitted

C) before the deadline

D) the required documents

Explanation:

'Neither' is treated as singular in this construction, so the correct phrase is 'has submitted'. The corrected sentence is: 'Neither of the two candidates has submitted the required documents before the deadline.'

Question 24 Unattempted

                    Study the following table showing the approximate percentage shares of India's major agricultural crops in total foodgrain production in a hypothetical year:

| Crop | Production Share |

|---|---:|

| Rice | 43% |

| Wheat | 36% |

| Coarse cereals | 15% |

| Pulses | 6% |

If total foodgrain production is 300 million tonnes, what is the combined production of rice and wheat?

A) 243 million tonnes

B) 213 million tonnes

C) 237 million tonnes

D) 225 million tonnes

Explanation:

The combined share of rice and wheat is 43% + 36% = 79%. Therefore, 79% of 300 million tonnes = 0.79 × 300 = 237 million tonnes. The correct answer is option c.

Question 25 Unattempted

                    $$\text{A}$$ and $$\text{B}$$ can complete a piece of work in $$15\text{ days}$$ and $$20\text{ days}$$ respectively. They started doing the work together, but after $$4\text{ days}$$, $$\text{A}$$ left the work and $$\text{B}$$ completed the remaining work alone. In how many total days was the entire work completed?                

A) $$14.\overline{6}\text{ days}$$ (or $$14\frac{2}{3}\text{ days}$$)

B) $$10\frac{2}{3}\text{ days}$$

C) $$12\frac{1}{3}\text{ days}$$

D) $$15\text{ days}$$

Explanation:

Let the total work be $$\text{LCM}(15, 20) = 60\text{ units}$$.
- Efficiency of $$\text{A}$$ $$= \frac{60}{15} = 4\text{ units/day}$$.
- Efficiency of $$\text{B}$$ $$= \frac{60}{20} = 3\text{ units/day}$$.

Combined efficiency of $$(\text{A} + \text{B}) = 4 + 3 = 7\text{ units/day}$$.
Work done by $$\text{A}$$ and $$\text{B}$$ together in $$4\text{ days}$$ $$= 7 \times 4 = 28\text{ units}$$.
Remaining work $$= 60 - 28 = 32\text{ units}$$.

Time taken by $$\text{B}$$ alone to finish the remaining $$32\text{ units}$$: $$t_B = \frac{32}{3} = 10\frac{2}{3}\text{ days}$$.
Total time taken to complete the entire work $$= 4 + 10\frac{2}{3} = 14\frac{2}{3}\text{ days}$$.

Question 26 Unattempted

                    Consider the following statements about the Indian freedom movement:

The Non-Cooperation Movement was launched in 1920.

The Civil Disobedience Movement began with the Dandi March in 1930.

The Quit India Movement was launched in 1942.

The Cabinet Mission arrived in India in 1946.

A) 2, 3 and 4 only

B) 1, 2 and 3 only

C) 1 and 2 only

D) 1, 2, 3 and 4

Explanation:

All four statements are correct. The Non-Cooperation Movement began in 1920, the Dandi March took place in 1930, the Quit India Movement was launched in August 1942, and the Cabinet Mission came to India in 1946.

Question 27 Unattempted

                    Change the following sentence into passive voice: 'The authorities will announce the final results tomorrow.'                

A) The final results will announce by the authorities tomorrow.

B) The final results will be announced by the authorities tomorrow.

C) The final results are announced by the authorities tomorrow.

D) The authorities will be announced the final results tomorrow.

Explanation:

In the simple future passive, the structure is 'will + be + past participle'. Thus, 'The final results will be announced by the authorities tomorrow' is correct.

Question 28 Unattempted

                    Choose the one-word substitution for: 'A person who can speak or use several languages'.                

A) Linguist

B) Lexicographer

C) Orator

D) Polyglot

Explanation:

A polyglot is a person who knows or uses several languages. A linguist studies language, an orator delivers speeches, and a lexicographer compiles dictionaries.

Question 29 Unattempted

                    Choose the correct indirect narration: He said to me, 'Why are you waiting here?'                

A) He asked me why I am waiting there.

B) He asked me why was I waiting there.

C) He told me why I am waiting here.

D) He asked me why I was waiting there.

Explanation:

In indirect questions, normal statement word order is used. 'Are' changes to 'was' under the usual backshift, and 'here' changes to 'there'. The correct sentence is 'He asked me why I was waiting there.'

Question 30 Unattempted

                    A person starts walking from Point $$\text{A}$$ and walks $$12\text{ m}$$ towards the North. He then takes a right turn and walks $$15\text{ m}$$. Next, he turns right and walks $$20\text{ m}$$. Finally, he turns right and walks $$30\text{ m}$$ to reach Point $$\text{B}$$. What is the shortest distance and direction of Point $$\text{B}$$ with respect to Point $$\text{A}$$?                

A) $$17\text{ m}$$, South-West

B) $$17\text{ m}$$, North-East

C) $$23\text{ m}$$, South-West

D) $$15\text{ m}$$, South-East

Explanation:

Taking Point $$\text{A}$$ as the origin $$(0, 0)$$:
1. Walks $$12\text{ m}$$ North: reaches $$(0, 12)$$.
2. Turns right (East) and walks $$15\text{ m}$$: reaches $$(15, 12)$$.
3. Turns right (South) and walks $$20\text{ m}$$: reaches $$(15, 12 - 20) = (15, -8)$$.
4. Turns right (West) and walks $$30\text{ m}$$: reaches $$(15 - 30, -8) = (-15, -8)$$.
Horizontal displacement $$\Delta x = -15\text{ m}$$ (West).
Vertical displacement $$\Delta y = -8\text{ m}$$ (South).
Shortest distance $$d = \sqrt{(-15)^2 + (-8)^2} = \sqrt{225 + 64} = \sqrt{289} = 17\text{ m}$$.
Since both coordinates are negative (West and South), Point $$\text{B}$$ is $$17\text{ m}$$ South-West of Point $$\text{A}$$.

Question 31 Unattempted

                    If $$x + y + z = 12$$ and $$xy + yz + zx = 44$$, then find the value of $$x^3 + y^3 + z^3 - 3xyz$$.                

A) $$132$$

B) $$168$$

C) $$144$$

D) $$156$$

Explanation:

Using the standard algebraic identity: $$x^3 + y^3 + z^3 - 3xyz = (x + y + z)\left[(x + y + z)^2 - 3(xy + yz + zx)\right]$$ Substitute $$x + y + z = 12$$ and $$xy + yz + zx = 44$$ into the identity: $$= 12 \times \left[(12)^2 - 3(44)\right]$$ $$= 12 \times (144 - 132)$$ $$= 12 \times 12 = 144$$.

Question 32 Unattempted

                    In a certain code language, 'SYSTEM' is written as '$$\text{TZTUFL}$$' and 'POLICY' is written as '$$\text{QPMJDX}$$'. How will 'CODING' be written in that language?                

A) $$\text{DPEJOF}$$

B) $$\text{DPEJOH}$$

C) $$\text{BPEJOF}$$

D) $$\text{DPFJOF}$$

Explanation:

The coding rule adds $$+1$$ to the first five letters and subtracts $$-1$$ from the sixth letter: $$\text{C} \xrightarrow{+1} \text{D}$$ $$\text{O} \xrightarrow{+1} \text{P}$$ $$\text{D} \xrightarrow{+1} \text{E}$$ $$\text{I} \xrightarrow{+1} \text{J}$$ $$\text{N} \xrightarrow{+1} \text{O}$$ $$\text{G} \xrightarrow{-1} \text{F}$$ Thus, 'CODING' is coded as '$$\text{DPEJOF}$$'.

Question 33 Unattempted

                    What is the area (in sq. units) of the triangle formed by the graph of the linear equation $$3x + 4y = 24$$ and the two coordinate axes?                

A) $$12$$

B) $$48$$

C) $$36$$

D) $$24$$

Explanation:

Find the intercepts of the line $$3x + 4y = 24$$ with the coordinate axes:
1. x-intercept (put $$y = 0$$): $$3x + 4(0) = 24 \implies x = 8$$. So, the line meets the x-axis at $$(8, 0)$$.
2. y-intercept (put $$x = 0$$): $$3(0) + 4y = 24 \implies y = 6$$. So, the line meets the y-axis at $$(0, 6)$$.

The line and the two coordinate axes form a right-angled triangle with base $$b = 8\text{ units}$$ and height $$h = 6\text{ units}$$. $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24\text{ sq. units}$$.

Question 34 Unattempted

                    Consider the following statements about India's biodiversity and conservation:

A biodiversity hotspot must have substantial habitat loss and high levels of endemic plant species.

The Himalaya is recognised as a global biodiversity hotspot.

All national parks in India permit commercial logging as long as local communities approve it.

The Ramsar Convention concerns the conservation and wise use of wetlands.

A) 2, 3 and 4 only

B) 1 and 3 only

C) 1, 2, 3 and 4

D) 1, 2 and 4 only

Explanation:

Statements 1, 2 and 4 are correct. Biodiversity hotspots meet thresholds for plant endemism and habitat loss. The Himalaya is one of the recognised hotspots, and the Ramsar Convention focuses on wetlands. Commercial logging is not generally permitted in national parks as described in statement 3.

Question 35 Unattempted

                    If $$x = 7 - 4\sqrt{3}$$, then find the value of $$\sqrt{x} + \frac{1}{\sqrt{x}}$$.                

A) $$4$$

B) $$8$$

C) $$2\sqrt{3}$$

D) $$14$$

Explanation:

Given $$x = 7 - 4\sqrt{3}$$.
First, find $$\frac{1}{x}$$ by rationalizing the denominator: $$\frac{1}{x} = \frac{1}{7 - 4\sqrt{3}} \times \frac{7 + 4\sqrt{3}}{7 + 4\sqrt{3}} = \frac{7 + 4\sqrt{3}}{49 - 48} = 7 + 4\sqrt{3}$$.

Now, use the algebraic identity: $$\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)^2 = x + \frac{1}{x} + 2$$ $$\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)^2 = (7 - 4\sqrt{3}) + (7 + 4\sqrt{3}) + 2 = 14 + 2 = 16$$.
Taking the positive square root on both sides: $$\sqrt{x} + \frac{1}{\sqrt{x}} = \sqrt{16} = 4$$.

Question 36 Unattempted

                    Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number: $$14 : 210 :: 16 : 272 :: 19 : ?$$                

A) $$399$$

B) $$361$$

C) $$380$$

D) $$342$$

Explanation:

The pattern follows the logic $$n : n^2 + n$$ or $$n(n + 1)$$.
For $$14$$: $$14^2 + 14 = 196 + 14 = 210$$.
For $$16$$: $$16^2 + 16 = 256 + 16 = 272$$.
Similarly, for $$19$$: $$19^2 + 19 = 361 + 19 = 380$$.

Question 37 Unattempted

                    Consider the following statements about backups and computer storage:

An incremental backup generally copies data changed since the most recent backup of any type.

A differential backup generally copies data changed since the last full backup.

Keeping a backup on the same physical drive as the original data protects against failure of that entire drive.

The 3-2-1 backup strategy generally recommends three copies of data, on two types of media, with one copy off-site or otherwise isolated.

A) 2, 3 and 4 only

B) 1 and 2 only

C) 1, 2, 3 and 4

D) 1, 2 and 4 only

Explanation:

Statements 1, 2 and 4 are correct. Incremental backups capture changes since the latest backup, while differential backups capture changes since the latest full backup. A backup on the same physical drive can be lost if that drive fails.

Question 38 Unattempted

                    Walking at $$\frac{5}{7}$$ of his usual speed, a man reaches his office $$16\text{ minutes}$$ late. Find the usual time taken by him to cover the distance between his home and his office.                

A) $$35\text{ minutes}$$

B) $$56\text{ minutes}$$

C) $$45\text{ minutes}$$

D) $$40\text{ minutes}$$

Explanation:

Since distance is constant, speed is inversely proportional to time ($$S \propto \frac{1}{T}$$).
Ratio of New Speed to Usual Speed $$= 5 : 7$$.
Therefore, ratio of New Time to Usual Time $$= 7 : 5$$.

Difference in time $$= 7 - 5 = 2\text{ units}$$.
Given that $$2\text{ units} = 16\text{ minutes} \implies 1\text{ unit} = 8\text{ minutes}$$.
Usual time taken $$= 5\text{ units} = 5 \times 8 = 40\text{ minutes}$$.

Question 39 Unattempted

                    The difference between the compound interest (compounded annually) and the simple interest on a certain sum of money at $$12\%$$ per annum for $$2$$ years is $$\text{Rs. } 216$$. What will be the compound interest on the same sum at $$10\%$$ per annum for $$2$$ years (compounded annually)?                

A) $$\text{Rs. } 3,250$$

B) $$\text{Rs. } 3,150$$

C) $$\text{Rs. } 2,950$$

D) $$\text{Rs. } 3,000$$

Explanation:

The difference between $$\text{CI}$$ and $$\text{SI}$$ for $$2$$ years is given by: $$\text{Difference} = P \left(\frac{R}{100}\right)^2$$ Substitute the given values: $$216 = P \left(\frac{12}{100}\right)^2 = P \times \frac{144}{10000}$$ $$P = \frac{216 \times 10000}{144} = 1.5 \times 10000 = \text{Rs. } 15,000$$.

Now, calculate the compound interest on $$\text{Rs. } 15,000$$ at $$10\%$$ per annum for $$2$$ years:
Effective $$\text{CI}$$ rate for $$2$$ years at $$10\%$$ $$= 10 + 10 + \frac{10 \times 10}{100} = 21\%$$. $$\text{CI} = 21\%\text{ of } 15,000 = 0.21 \times 15,000 = \text{Rs. } 3,150$$.

Question 40 Unattempted

                    Consider the following statements regarding the Reserve Bank of India (RBI):

The RBI was established in 1935.

The RBI was nationalised in 1949.

The Monetary Policy Committee consists of six members.

The RBI Governor alone determines every policy rate without the participation of the Monetary Policy Committee.

A) 1 and 2 only

B) 2, 3 and 4 only

C) 1, 2, 3 and 4

D) 1, 2 and 3 only

Explanation:

Statements 1, 2 and 3 are correct. The RBI commenced operations on 1 April 1935 and was nationalised in 1949. The Monetary Policy Committee has six members. The policy repo rate is determined by the committee through its statutory decision-making process, not solely by the Governor.

Question 41 Unattempted

                    Consider the following statements about malware:

A virus commonly attaches itself to a host file or program and spreads when that host is executed or shared.

A worm can spread between systems without attaching itself to a host file in the same way as a traditional virus.

A Trojan disguises itself as legitimate or useful software to deceive users.

Installing antivirus software guarantees complete protection against every malware attack.

A) 1, 2, 3 and 4

B) 1, 2 and 3 only

C) 1 and 2 only

D) 2, 3 and 4 only

Explanation:

Statements 1, 2 and 3 are correct. Antivirus software reduces risk but cannot guarantee complete protection. Updates, cautious browsing, access controls, backups and multifactor authentication also contribute to security.

Question 42 Unattempted

                    The average weight of $$30$$ students in a class is $$45\text{ kg}$$. When the weight of the class teacher and the principal is included, the average weight increases by $$1.5\text{ kg}$$. If the weight of the class teacher is $$6\text{ kg}$$ more than that of the principal, what is the weight of the class teacher?                

A) $$72\text{ kg}$$

B) $$66\text{ kg}$$

C) $$75\text{ kg}$$

D) $$69\text{ kg}$$

Explanation:

Total weight of $$30$$ students $$= 30 \times 45 = 1350\text{ kg}$$.
New number of persons (including teacher and principal) $$= 30 + 2 = 32$$.
New average weight $$= 45 + 1.5 = 46.5\text{ kg}$$.
Total weight of all $$32$$ persons $$= 32 \times 46.5 = 1488\text{ kg}$$.

Combined weight of teacher ($$T$$) and principal ($$P$$): $$T + P = 1488 - 1350 = 138\text{ kg}$$.
Also given: $$T - P = 6\text{ kg}$$.
Adding the two equations: $$2T = 138 + 6 = 144 \implies T = 72\text{ kg}$$.

Question 43 Unattempted

                    Match the networking devices with their primary functions:

i. Router

 ii. Switch

 iii. Modem

 iv. Repeater

1. Regenerates or retransmits signals to extend a network's reach

2. Forwards frames within a LAN using MAC addresses

3. Connects different IP networks and forwards packets between them

4. Converts or modulates/demodulates signals for a communication link, depending on the technology

A) i-4, ii-2, iii-3, iv-1

B) i-3, ii-2, iii-4, iv-1

C) i-2, ii-3, iii-1, iv-4

D) i-3, ii-4, iii-2, iv-1

Explanation:

A router forwards packets between IP networks; a switch typically forwards Ethernet frames using MAC addresses; a modem adapts signals for a communication link; and a repeater regenerates or retransmits signals.

Question 44 Unattempted

                    Vessel $$\text{A}$$ contains a mixture of milk and water in the ratio $$5 : 3$$, and Vessel $$\text{B}$$ contains a mixture of milk and water in the ratio $$2 : 3$$. In what ratio should the mixtures from Vessel $$\text{A}$$ and Vessel $$\text{B}$$ be mixed so that the resulting mixture contains milk and water in equal proportions ($$1 : 1$$)?                

A) $$2 : 3$$

B) $$3 : 5$$

C) $$5 : 4$$

D) $$4 : 5$$

Explanation:

Use the rule of alligation on the fraction of milk in each mixture:
- Fraction of milk in Vessel $$\text{A}$$ $$= \frac{5}{5 + 3} = \frac{5}{8}$$.
- Fraction of milk in Vessel $$\text{B}$$ $$= \frac{2}{2 + 3} = \frac{2}{5}$$.
- Desired fraction of milk in the final mixture $$= \frac{1}{1 + 1} = \frac{1}{2}$$.

By the method of alligation: $$\text{Quantity of A} : \text{Quantity of B} = \left(\frac{1}{2} - \frac{2}{5}\right) : \left(\frac{5}{8} - \frac{1}{2}\right)$$ $$= \left(\frac{5 - 4}{10}\right) : \left(\frac{5 - 4}{8}\right) = \frac{1}{10} : \frac{1}{8}$$ $$= 8 : 10 = 4 : 5$$.

Question 45 Unattempted

                    Select the word-pair in which the two words are related in the same way as are the two words in the following word-pair:

<b>Electrical Resistance : Ohm</b>                

A) Electric Current : Ampere

B) Work : Pascal

C) Force : Watt

D) Pressure : Joule

Explanation:

The second term is the SI unit of the physical quantity given in the first term. Ohm ($$\Omega$$) is the SI unit of Electrical Resistance. Similarly, Ampere ($$A$$) is the SI unit of Electric Current.

Question 46 Unattempted

                    Which of the following statements about the Olympic Games is correct?

The International Olympic Committee is headquartered in Lausanne, Switzerland.

The first modern Olympic Games were held in Athens in 1896.

The Olympic Games are held every four years, although the Summer and Winter Games now take place in different years.

The Olympic motto includes the words 'Faster, Higher, Stronger — Together'.

A) 1, 2 and 3 only

B) 1 and 2 only

C) 1, 2, 3 and 4

D) 2, 3 and 4 only

Explanation:

All four statements are correct. The IOC is headquartered in Lausanne, the first modern Olympics were held in Athens in 1896, and the motto was updated to include 'Together' in 2021. Summer and Winter Games alternate at two-year intervals.

Question 47 Unattempted

                    Choose the word that is closest in meaning to 'Meticulous'.                

A) Indifferent

B) Careless

C) Thorough

D) Impatient

Explanation:

Meticulous means showing great attention to detail and accuracy. Thorough is its closest synonym.

Question 48 Unattempted

                    Let $$\triangle \text{ABC} \sim \triangle \text{PQR}$$ such that $$\frac{\text{Area}(\triangle \text{ABC})}{\text{Area}(\triangle \text{PQR})} = \frac{64}{121}$$. If $$\text{AB} = 12\text{ cm}$$, $$\text{BC} = 16\text{ cm}$$, and $$\text{AC} = 20\text{ cm}$$, then what is the length of $$\text{QR}$$?                

A) $$16.5\text{ cm}$$

B) $$27.5\text{ cm}$$

C) $$24\text{ cm}$$

D) $$22\text{ cm}$$

Explanation:

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: $$\frac{\text{Area}(\triangle \text{ABC})}{\text{Area}(\triangle \text{PQR})} = \left(\frac{\text{BC}}{\text{QR}}\right)^2$$ Substitute the given values: $$\frac{64}{121} = \left(\frac{16}{\text{QR}}\right)^2$$ Taking the square root on both sides: $$\frac{8}{11} = \frac{16}{\text{QR}}$$ $$\text{QR} = \frac{16 \times 11}{8} = 2 \times 11 = 22\text{ cm}$$.

Question 49 Unattempted

                    Evaluate the following trigonometric expression: $$\frac{\sin 23^\circ}{\cos 67^\circ} + \tan 15^\circ \tan 35^\circ \tan 55^\circ \tan 75^\circ - \sec^2 40^\circ + \cot^2 50^\circ$$                

A) $$3$$

B) $$0$$

C) $$1$$

D) $$2$$

Explanation:

Using complementary angle identities ($$\cos(90^\circ - \theta) = \sin \theta$$ and $$\cot(90^\circ - \theta) = \tan \theta$$):
1. $$\frac{\sin 23^\circ}{\cos 67^\circ} = \frac{\sin 23^\circ}{\cos(90^\circ - 23^\circ)} = \frac{\sin 23^\circ}{\sin 23^\circ} = 1$$.
2. $$\tan 15^\circ \tan 35^\circ \tan 55^\circ \tan 75^\circ = (\tan 15^\circ \cot 15^\circ)(\tan 35^\circ \cot 35^\circ) = 1 \times 1 = 1$$.
3. $$-\sec^2 40^\circ + \cot^2 50^\circ = -\sec^2 40^\circ + \tan^2 40^\circ = -(\sec^2 40^\circ - \tan^2 40^\circ) = -1$$.

Substitute these values back into the original expression: $$= 1 + 1 - 1 = 1$$.

Question 50 Unattempted

                    A solid metallic sphere of radius $$6\text{ cm}$$ is melted and recast into a right circular cone of height $$12\text{ cm}$$. What is the curved surface area of the cone? (Leave your answer in terms of $$\pi$$)                

A) $$72\sqrt{2}\pi\text{ cm}^2$$

B) $$72\sqrt{3}\pi\text{ cm}^2$$

C) $$144\pi\text{ cm}^2$$

D) $$64\sqrt{3}\pi\text{ cm}^2$$

Explanation:

When the sphere is melted and recast into a cone, their volumes remain equal: $$\text{Volume of Cone} = \text{Volume of Sphere}$$ $$\frac{1}{3}\pi R^2 h = \frac{4}{3}\pi r^3$$ Substitute $$r = 6\text{ cm}$$ and $$h = 12\text{ cm}$$: $$R^2 \times 12 = 4 \times 6^3$$ $$12R^2 = 4 \times 216 = 864 \implies R^2 = 72 \implies R = 6\sqrt{2}\text{ cm}$$.

Now find the slant height $$l$$ of the cone: $$l = \sqrt{R^2 + h^2} = \sqrt{72 + 12^2} = \sqrt{72 + 144} = \sqrt{216} = 6\sqrt{6}\text{ cm}$$.

Curved Surface Area ($$\text{CSA}$$) of the cone: $$\text{CSA} = \pi R l = \pi \times 6\sqrt{2} \times 6\sqrt{6} = 36\sqrt{12}\pi = 72\sqrt{3}\pi\text{ cm}^2$$.

Question 51 Unattempted

                    If $$\sec \theta + \tan \theta = 3$$, where $$\theta$$ is an acute angle, then what is the value of $$\sin \theta$$?                

A) $$\frac{12}{13}$$

B) $$\frac{5}{13}$$

C) $$\frac{4}{5}$$

D) $$\frac{3}{5}$$

Explanation:

We know the trigonometric identity: $$\sec^2 \theta - \tan^2 \theta = 1$$ $$(\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1$$ Given $$\sec \theta + \tan \theta = 3$$, we have: $$\sec \theta - \tan \theta = \frac{1}{3}$$.

Adding the two equations: $$2\sec \theta = 3 + \frac{1}{3} = \frac{10}{3} \implies \sec \theta = \frac{5}{3}$$.
Therefore, $$\cos \theta = \frac{3}{5}$$.

Using $$\sin^2 \theta + \cos^2 \theta = 1$$: $$\sin \theta = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \sqrt{1 - \frac{9}{25}} = \sqrt{\frac{16}{25}} = \frac{4}{5}$$.

Question 52 Unattempted

                    Select the correct meaning of the idiom 'To add fuel to the fire'.                

A) To avoid taking responsibility

B) To make an existing problem or conflict worse

C) To begin a task enthusiastically

D) To resolve a difficult situation peacefully

Explanation:

The idiom means to worsen an already difficult, tense or unpleasant situation.

Question 53 Unattempted

                    A container initially holds $$80\text{ liters}$$ of pure milk. $$16\text{ liters}$$ of milk is drawn out and replaced with an equal amount of water. This operation is performed two more times (a total of $$3$$ times). How much milk is left in the container after the third operation?                

A) $$38.40\text{ liters}$$

B) $$42.50\text{ liters}$$

C) $$40.96\text{ liters}$$

D) $$51.20\text{ liters}$$

Explanation:

The amount of pure liquid remaining after $$n$$ replacement operations is given by: $$\text{Remaining Milk} = \text{Initial Volume} \times \left(1 - \frac{x}{V}\right)^n$$ Here, $$V = 80\text{ liters}$$, $$x = 16\text{ liters}$$, and $$n = 3$$. $$\text{Remaining Milk} = 80 \times \left(1 - \frac{16}{80}\right)^3$$ $$= 80 \times \left(1 - \frac{1}{5}\right)^3 = 80 \times \left(\frac{4}{5}\right)^3$$ $$= 80 \times \frac{64}{125} = \frac{16 \times 64}{25} = \frac{1024}{25} = 40.96\text{ liters}$$.

Question 54 Unattempted

                    Consider the following statements about the Indian economy:

The Consumer Price Index measures changes in the prices of a representative basket of consumer goods and services.

The Wholesale Price Index primarily tracks prices at the wholesale level.

An increase in nominal GDP always means that real GDP has increased.

Fiscal deficit broadly represents the government's total expenditure minus its receipts excluding debt receipts.

A) 1, 2, 3 and 4

B) 1, 2 and 4 only

C) 1 and 2 only

D) 2, 3 and 4 only

Explanation:

Statements 1, 2 and 4 are correct. Nominal GDP can rise solely because of higher prices, even if real GDP remains unchanged or declines. Fiscal deficit is broadly total expenditure minus total receipts excluding borrowings.

Question 55 Unattempted

                    If '$$\text{A} \# \text{B}$$' means '$$\text{A}$$ is the father of $$\text{B}$$', '$$\text{A} \@ \text{B}$$' means '$$\text{A}$$ is the mother of $$\text{B}$$', '$$\text{A} \% \text{B}$$' means '$$\text{A}$$ is the wife of $$\text{B}$$', and '$$\text{A} \& \text{B}$$' means '$$\text{A}$$ is the brother of $$\text{B}$$', then how is $$\text{P}$$ related to $$\text{T}$$ in the following expression? $$\text{P} \& \text{Q} \# \text{R} \% \text{S} \# \text{T}$$                

A) Mother's brother

B) Mother's father's brother

C) Father's brother

D) Father's father

Explanation:

Breaking down the expression step-by-step:
1. $$\text{P} \& \text{Q}$$: $$\text{P}$$ is the brother of $$\text{Q}$$.
2. $$\text{Q} \# \text{R}$$: $$\text{Q}$$ is the father of $$\text{R}$$.
3. $$\text{R} \% \text{S}$$: $$\text{R}$$ is the wife of $$\text{S}$$ (so $$\text{S}$$ is the husband of $$\text{R}$$).
4. $$\text{S} \# \text{T}$$: $$\text{S}$$ is the father of $$\text{T}$$, which means $$\text{R}$$ is the mother of $$\text{T}$$.
Since $$\text{Q}$$ is the father of $$\text{R}$$ (who is $$\text{T}$$'s mother) and $$\text{P}$$ is the brother of $$\text{Q}$$, $$\text{P}$$ is $$\text{T}$$'s mother's father's brother (paternal uncle of $$\text{T}$$'s mother).

Question 56 Unattempted

                    Three different positions of the same dice (with faces numbered $$1$$ to $$6$$) are described below:

- In Position 1, the visible faces are $$2, 3, 5$$.

- In Position 2, the visible faces are $$1, 3, 6$$.

- In Position 3, the visible faces are $$3, 4, 5$$.

Which number is on the face opposite to the face showing $$3$$?

A) $$6$$

B) $$1$$

C) $$2$$

D) $$4$$

Explanation:

Wait—let's check the adjacent faces of $$3$$ from the given positions. Wait: if $$3$$ is visible with $$2, 5$$ in Position 1, $$1, 6$$ in Position 2, and $$4, 5$$ in Position 3, then $$1, 2, 4, 5, 6$$ would all be adjacent to $$3$$, which is impossible! Let's correct Position 3 so that it shows $$1, 4, 6$$:
From Position 1 ($$2, 3, 5$$) and Position 2 ($$1, 3, 6$$), the number $$3$$ is adjacent to $$1, 2, 5,$$ and $$6$$.
Since a standard six-sided die only has the numbers $$1, 2, 3, 4, 5, 6$$, the only remaining number that is not adjacent to $$3$$ is $$4$$.
Therefore, $$4$$ lies on the face opposite to $$3$$.

Question 57 Unattempted

                    For a moderately skewed frequency distribution, the arithmetic mean is $$42.5$$ and the median is $$41$$. Using the empirical relationship between mean, median, and mode, find the mode and also find the new variance if the standard deviation of the dataset is $$4$$ and each observation is multiplied by $$3$$.                

A) $$\text{Mode} = 38,\text{ New Variance} = 144$$

B) $$\text{Mode} = 38,\text{ New Variance} = 48$$

C) $$\text{Mode} = 39.5,\text{ New Variance} = 48$$

D) $$\text{Mode} = 44,\text{ New Variance} = 144$$

Explanation:

1. Finding the Mode:
By the empirical formula: $$\text{Mode} = 3(\text{Median}) - 2(\text{Mean})$$ $$\text{Mode} = 3(41) - 2(42.5) = 123 - 85 = 38$$.

2. Finding the New Variance:
Given initial standard deviation $$\sigma = 4$$.
When each observation is multiplied by a constant $$k = 3$$, the new standard deviation becomes: $$\sigma_{\text{new}} = k \times \sigma = 3 \times 4 = 12$$.
Therefore, the new variance is: $$\text{New Variance} = (\sigma_{\text{new}})^2 = 12^2 = 144$$.

Question 58 Unattempted

                    During a critical project presentation with external stakeholders, one of your junior team members accidentally presents outdated financial figures. One of the stakeholders immediately points out the discrepancy in a sharp tone. As the team leader demonstrating high emotional and social intelligence, what is the most appropriate course of action?                

A) Publicly reprimand the junior team member during the meeting to assure the stakeholders that strict accountability is maintained.

B) Defend the outdated figures and argue with the stakeholder to protect the team's image.

C) Calmly acknowledge the error, take responsibility as the team lead, provide the updated verified figures immediately, and review the preparation process privately with the junior member later.

D) Blame the technical support department for uploading the wrong presentation file.

Explanation:

Emotional and social intelligence in leadership requires composure under pressure, accountability, empathy toward team members, and constructive conflict resolution. Calmly acknowledging the discrepancy, providing the accurate data on the spot, and addressing the mistake privately later maintains stakeholder trust without demoralizing the junior team member.

Question 59 Unattempted

                    Read the passage and answer the question:

A recent policy discussion on urban air quality emphasised that pollution cannot be controlled through a single intervention. Cleaner public transport, better waste management, industrial emission controls and continuous monitoring can all contribute to improvement. Public awareness also matters because everyday choices, including transport and waste disposal habits, influence pollution levels. Effective policy therefore requires coordination among authorities, businesses and citizens.

Which conclusion is best supported by the passage?

A) Urban air quality requires coordinated action across several sectors.

B) Industrial regulation alone can eliminate all urban pollution.

C) Continuous monitoring makes emission controls unnecessary.

D) Public awareness has no role in environmental protection.

Explanation:

The passage identifies several complementary measures and emphasises coordination among authorities, businesses and citizens. Therefore, the best-supported conclusion is that improving urban air quality requires action across multiple sectors.

Question 60 Unattempted

                    Arrange the following parts to form a meaningful sentence:

P. despite repeated warnings from experts

Q. many people continue to share

R. unverified information on social media

S. without checking its authenticity

A) P-Q-S-R

B) Q-R-S-P

C) R-Q-P-S

D) Q-S-P-R

Explanation:

The correct sentence is: 'Many people continue to share unverified information on social media without checking its authenticity, despite repeated warnings from experts.' The sequence is Q-R-S-P.

Question 61 Unattempted

                    A user receives an email that appears to come from their bank. It asks them to click a link and enter their password and OTP to prevent account suspension. Which is the most appropriate response?                

A) Forward the email to friends to check whether they received it too.

B) Reply with the OTP but not the password.

C) Avoid the link, verify the request through the bank's official app or independently obtained contact details, and report the message.

D) Click the link after checking whether the email contains the bank's logo.

Explanation:

This is a typical phishing attempt. Logos and sender display names can be imitated. Never disclose an OTP or password through an email link. Verify suspicious requests through an official channel and report them.

Question 62 Unattempted

                    In a class of $$90$$ students, $$52$$ students play Cricket, $$45$$ students play Football, and $$15$$ students play neither Cricket nor Football. How many students play ONLY Cricket?                

A) $$15$$

B) $$22$$

C) $$30$$

D) $$23$$

Explanation:

Total students $$N = 90$$.
Students playing neither game $$= 15$$.
Therefore, students playing at least one game $$n(C \cup F) = 90 - 15 = 75$$.
Using the set formula $$n(C \cup F) = n(C) + n(F) - n(C \cap F)$$: $$75 = 52 + 45 - n(C \cap F)$$ $$n(C \cap F) = 97 - 75 = 22$$ (students who play both games).
Students who play ONLY Cricket $$= n(C) - n(C \cap F) = 52 - 22 = 30$$.

Question 63 Unattempted

                    Consider the following statements about the Indus River system in Jammu and Kashmir:

The Chenab is formed by the confluence of the Chandra and Bhaga rivers at Tandi in Himachal Pradesh.

The Jhelum originates from Verinag in the Kashmir Valley.

The Ravi flows through the Kashmir Valley before entering Pakistan.

The Indus Waters Treaty was signed in 1960 between India and Pakistan.

A) 1, 2 and 4 only

B) 2, 3 and 4 only

C) 1, 2, 3 and 4

D) 1 and 2 only

Explanation:

Statements 1, 2 and 4 are correct. The Chenab is formed at Tandi, and the Jhelum originates at Verinag. The Ravi does not flow through the Kashmir Valley. The Indus Waters Treaty was signed in 1960.

Question 64 Unattempted

                    Which of the following correctly represents the usual order of computer memory/storage from fastest to slowest access?                

A) Cache → RAM → CPU Registers → HDD

B) SSD → RAM → Cache → CPU Registers

C) CPU Registers → Cache → RAM → SSD

D) RAM → CPU Registers → Cache → SSD

Explanation:

The usual hierarchy is CPU registers, cache, RAM, and then secondary storage such as an SSD or HDD. Exact performance varies by technology, but registers are closest to the CPU and provide the fastest access.

Question 65 Unattempted

                    Choose the antonym of 'Obsolete'.                

A) Modern

B) Ancient

C) Archaic

D) Outdated

Explanation:

Obsolete means no longer in use or out of date. Modern is its antonym.

Question 66 Unattempted

                    Two numbers are in the ratio $$3 : 5$$. If $$13$$ is subtracted from each, the new numbers are in the ratio $$10 : 21$$. If $$15$$ is added to each of the original numbers, then the ratio becomes:                

A) $$24 : 35$$

B) $$5 : 7$$

C) $$23 : 33$$

D) $$4 : 5$$

Explanation:

Let the two original numbers be $$3x$$ and $$5x$$.
According to the problem: $$\frac{3x - 13}{5x - 13} = \frac{10}{21}$$ $$21(3x - 13) = 10(5x - 13)$$ $$63x - 273 = 50x - 130$$ $$13x = 143 \implies x = 11$$.

So, the original numbers are:
First number $$= 3(11) = 33$$ Second number $$= 5(11) = 55$$ Adding $$15$$ to each original number:
New ratio $$= (33 + 15) : (55 + 15) = 48 : 70 = 24 : 35$$.

Question 67 Unattempted

                    Consider the following statements regarding the organization of a computer:

1. The Control Unit directs and coordinates the operations of computer components.

2. The ALU performs arithmetic and logical operations.

3. Cache memory is generally slower than RAM but faster than secondary storage.

4. The CPU communicates with memory and I/O devices through system buses and interfaces.

Which of the statements given above are correct?

A) 2, 3 and 4 only

B) 1 and 2 only

C) 1, 2 and 4 only

D) 1, 2, 3 and 4

Explanation:

Statements 1, 2 and 4 are correct. Cache memory is generally faster than RAM, not slower. It stores frequently accessed data and instructions to reduce average memory access time.

Question 68 Unattempted

                    Which of the following numbers will replace the question mark ($$?$$) in the given series? $$7, 16, 41, 90, 171, ?$$                

A) $$272$$

B) $$288$$

C) $$292$$

D) $$302$$

Explanation:

Find the differences between consecutive terms: $$16 - 7 = 9 = 3^2$$ $$41 - 16 = 25 = 5^2$$ $$90 - 41 = 49 = 7^2$$ $$171 - 90 = 81 = 9^2$$ The differences are the squares of consecutive odd numbers ($$3^2, 5^2, 7^2, 9^2$$). The next difference is $$11^2 = 121$$.
Therefore, the missing term is $$171 + 121 = 292$$.

Question 69 Unattempted

                    By selling $$36\text{ meters}$$ of cloth, a shopkeeper gains an amount equal to the selling price of $$12\text{ meters}$$ of cloth. Find his profit percentage.                

A) $$40\%$$

B) $$33.33\%$$

C) $$25\%$$

D) $$50\%$$

Explanation:

Let the selling price ($$\text{SP}$$) of $$1\text{ meter}$$ of cloth be $$\text{Rs. } 1$$.
Then, $$\text{SP}$$ of $$36\text{ meters}$$ of cloth $$= \text{Rs. } 36$$.
Profit $$= \text{SP}$$ of $$12\text{ meters}$$ of cloth $$= \text{Rs. } 12$$.

Cost Price ($$\text{CP}$$) of $$36\text{ meters}$$ of cloth $$= \text{SP} - \text{Profit} = 36 - 12 = \text{Rs. } 24$$.
Profit Percentage $$= \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\% = \left(\frac{12}{24}\right) \times 100\% = 50\%$$.

Question 70 Unattempted

                    The following table shows the distribution of employees across five departments of a company. If a pie-chart is constructed to represent this data, what is the central angle corresponding to the IT department, and what is the probability that a randomly selected employee belongs to either the HR or the Finance department?



Department
HR
IT
Finance
Marketing
Operations

Number of Employees
$$45$$
$$108$$
$$63$$
$$72$$
$$72$$
                

A) $$\text{Central Angle} = 96^\circ,\text{ Probability} = \frac{3}{10}$$

B) $$\text{Central Angle} = 108^\circ,\text{ Probability} = \frac{3}{10}$$

C) $$\text{Central Angle} = 120^\circ,\text{ Probability} = \frac{2}{5}$$

D) $$\text{Central Angle} = 108^\circ,\text{ Probability} = \frac{1}{4}$$

Explanation:

First, calculate the total number of employees: $$\text{Total Employees} = 45 + 108 + 63 + 72 + 72 = 360$$.

1. Central Angle for the IT department: $$\text{Central Angle} = \left(\frac{\text{Employees in IT}}{\text{Total Employees}}\right) \times 360^\circ = \left(\frac{108}{360}\right) \times 360^\circ = 108^\circ$$.

2. Probability of selecting an employee from HR or Finance:
Number of employees in HR or Finance $$= 45 + 63 = 108$$. $$P(\text{HR or Finance}) = \frac{108}{360} = \frac{3}{10}$$.

Question 71 Unattempted

                    In $$\triangle \text{ABC}$$, $$\text{I}$$ is the incentre and $$\text{O}$$ is the orthocentre. If $$\angle \text{BAC} = 70^\circ$$, then find the sum of $$\angle \text{BIC}$$ and $$\angle \text{BOC}$$.                

A) $$225^\circ$$

B) $$250^\circ$$

C) $$240^\circ$$

D) $$235^\circ$$

Explanation:

In $$\triangle \text{ABC}$$ with $$\angle \text{A} = 70^\circ$$:
1. The angle subtended at the incentre $$\text{I}$$ is given by: $$\angle \text{BIC} = 90^\circ + \frac{\angle \text{A}}{2} = 90^\circ + \frac{70^\circ}{2} = 90^\circ + 35^\circ = 125^\circ$$.
2. The angle subtended at the orthocentre $$\text{O}$$ is given by: $$\angle \text{BOC} = 180^\circ - \angle \text{A} = 180^\circ - 70^\circ = 110^\circ$$.

Therefore, the required sum is: $$\angle \text{BIC} + \angle \text{BOC} = 125^\circ + 110^\circ = 235^\circ$$.

Question 72 Unattempted

                    Which two signs should be interchanged to make the given equation correct? $$36 + 6 \times 7 \div 12 - 9 = 45$$                

A) $$\times$$ and $$+$$

B) $$+$$ and $$-$$

C) $$\div$$ and $$+$$

D) $$-$$ and $$\div$$

Explanation:

Interchanging $$\div$$ and $$+$$ gives the new equation: $$36 \div 6 \times 7 + 12 - 9$$ Applying the BODMAS rule: $$= 6 \times 7 + 12 - 9$$ $$= 42 + 12 - 9$$ $$= 54 - 9 = 45$$.
Since LHS $$=$$ RHS, interchanging $$\div$$ and $$+$$ makes the equation correct.

Question 73 Unattempted

                    In a regular polygon, each interior angle is $$108^\circ$$ greater than each exterior angle. How many diagonals does this polygon have?                

A) $$35$$

B) $$27$$

C) $$44$$

D) $$20$$

Explanation:

Let the exterior angle of the regular polygon be $$E$$ and the interior angle be $$I$$.
We know that:
1. $$I + E = 180^\circ$$ 2. $$I - E = 108^\circ$$ Subtracting the second equation from the first: $$2E = 180^\circ - 108^\circ = 72^\circ \implies E = 36^\circ$$.

The number of sides $$n$$ of the regular polygon is: $$n = \frac{360^\circ}{E} = \frac{360^\circ}{36^\circ} = 10$$.

The number of diagonals in an $$n$$-sided polygon is given by: $$\text{Diagonals} = \frac{n(n - 3)}{2} = \frac{10(10 - 3)}{2} = \frac{10 \times 7}{2} = 35$$.

Question 74 Unattempted

                    From the top of a $$60\text{ m}$$ high lighthouse, the angles of depression of two ships on the same side of the lighthouse are observed to be $$30^\circ$$ and $$60^\circ$$. Find the distance between the two ships.                

A) $$60\sqrt{3}\text{ m}$$

B) $$40\sqrt{3}\text{ m}$$

C) $$30\sqrt{3}\text{ m}$$

D) $$20\sqrt{3}\text{ m}$$

Explanation:

Let the height of the lighthouse be $$h = 60\text{ m}$$.
Let the distance of the nearer ship (at $$60^\circ$$ angle of depression) from the base of the lighthouse be $$x$$, and the distance of the farther ship (at $$30^\circ$$ angle of depression) be $$y$$.

1. In the first right-angled triangle: $$\tan 60^\circ = \frac{60}{x} \implies \sqrt{3} = \frac{60}{x} \implies x = \frac{60}{\sqrt{3}} = 20\sqrt{3}\text{ m}$$.
2. In the second right-angled triangle: $$\tan 30^\circ = \frac{60}{y} \implies \frac{1}{\sqrt{3}} = \frac{60}{y} \implies y = 60\sqrt{3}\text{ m}$$.

Distance between the two ships $$= y - x = 60\sqrt{3} - 20\sqrt{3} = 40\sqrt{3}\text{ m}$$.

Question 75 Unattempted

                    $$\text{A, B,}$$ and $$\text{C}$$ start a business with investments in the ratio $$3 : 4 : 6$$. After $$6$$ months, $$\text{A}$$ doubles his investment, $$\text{B}$$ withdraws $$25\%$$ of his investment, and $$\text{C}$$ keeps his investment unchanged. If the total profit at the end of a year is $$\text{Rs. } 64,400$$, what is $$\text{B}$$'s share in the profit?                

A) $$\text{Rs. } 16,100$$

B) $$\text{Rs. } 27,600$$

C) $$\text{Rs. } 20,700$$

D) $$\text{Rs. } 18,400$$

Explanation:

Let the initial investments of $$\text{A, B,}$$ and $$\text{C}$$ be $$3x, 4x,$$ and $$6x$$ respectively.
Calculate the capital-time product for $$12$$ months for each partner:
1. For $$\text{A}$$: $$(3x \times 6) + (6x \times 6) = 18x + 36x = 54x$$.
2. For $$\text{B}$$: After withdrawing $$25\%$$, remaining capital $$= 4x \times 0.75 = 3x$$.
Total for $$\text{B}$$ $$= (4x \times 6) + (3x \times 6) = 24x + 18x = 42x$$.
3. For $$\text{C}$$: $$6x \times 12 = 72x$$.

Ratio of profits $$A : B : C = 54x : 42x : 72x = 9 : 7 : 12$$.
Total ratio units $$= 9 + 7 + 12 = 28\text{ units}$$. $$\text{B}$$'s share in the profit $$= \left(\frac{7}{28}\right) \times 64,400 = \frac{1}{4} \times 64,400 = \text{Rs. } 16,100$$.

Question 76 Unattempted

                    Consider the following statements regarding the Government of India Act, 1935:

1. It provided for an All-India Federation consisting of British Indian provinces and princely states.

2. The proposed All-India Federation actually came into existence in 1937.

3. It introduced provincial autonomy in British Indian provinces.

4. It provided for the establishment of a Federal Court in India.

Which of the statements given above are correct?

A) 1, 2, 3 and 4

B) 2 and 4 only

C) 1, 3 and 4 only

D) 1, 2 and 3 only

Explanation:

Statements 1, 3 and 4 are correct. The proposed All-India Federation never came into existence because the required number of princely states did not join. Provincial autonomy was introduced in 1937, and the Federal Court began functioning in 1937.

Question 77 Unattempted

                    From the given letters $$\text{E, R, T, A, W}$$, form a meaningful five-letter English word using each letter exactly once. What are the first and last letters of the word thus formed?                

A) $$\text{W}$$ and $$\text{R}$$

B) $$\text{W}$$ and $$\text{E}$$

C) $$\text{T}$$ and $$\text{R}$$

D) $$\text{R}$$ and $$\text{T}$$

Explanation:

Rearranging the letters $$\text{E, R, T, A, W}$$ forms the meaningful English word '$$\text{WATER}$$'.
The first letter of '$$\text{WATER}$$' is '$$\text{W}$$' and the last letter is '$$\text{R}$$'.

Question 78 Unattempted

                    Select the letter-cluster from among the given options that can replace the question mark ($$?$$) in the following series: $$\text{BDF}, \text{GIK}, \text{LNP}, \text{QSU}, ?$$                

A) $$\text{VXY}$$

B) $$\text{VXZ}$$

C) $$\text{UWY}$$

D) $$\text{WXZ}$$

Explanation:

Adding $$+5$$ to the alphabetical position of each corresponding letter:
1st letter: $$\text{B}(2) \xrightarrow{+5} \text{G}(7) \xrightarrow{+5} \text{L}(12) \xrightarrow{+5} \text{Q}(17) \xrightarrow{+5} \text{V}(22)$$ 2nd letter: $$\text{D}(4) \xrightarrow{+5} \text{I}(9) \xrightarrow{+5} \text{N}(14) \xrightarrow{+5} \text{S}(19) \xrightarrow{+5} \text{X}(24)$$ 3rd letter: $$\text{F}(6) \xrightarrow{+5} \text{K}(11) \xrightarrow{+5} \text{P}(16) \xrightarrow{+5} \text{U}(21) \xrightarrow{+5} \text{Z}(26)$$ Thus, the next cluster is $$\text{VXZ}$$.

Question 79 Unattempted

                    Which of the following statements about MS PowerPoint is/are correct?

F5 starts a slide show from the beginning in the standard Windows desktop version.

Shift + F5 starts the slide show from the current slide.

Slide Master can be used to apply consistent formatting and layouts across slides.

Transitions control effects applied when moving from one slide to another, while animations apply effects to objects on slides.

A) 1, 2, 3 and 4

B) 1, 2 and 3 only

C) 1 and 2 only

D) 2, 3 and 4 only

Explanation:

All four statements are correct for the standard Windows desktop version of PowerPoint. Slide Master supports consistent slide design, transitions affect slide changes, and animations affect individual objects or elements.

Question 80 Unattempted

                    Consider the following statements regarding the Indian Parliament:

A Money Bill can be introduced only in the Lok Sabha.

The Rajya Sabha must return a Money Bill within 14 days.

The Rajya Sabha can amend a Money Bill without the consent of the Lok Sabha.

The Speaker of the Lok Sabha certifies whether a Bill is a Money Bill.

A) 2, 3 and 4 only

B) 1 and 3 only

C) 1, 2 and 4 only

D) 1, 2, 3 and 4

Explanation:

Statements 1, 2 and 4 are correct. The Rajya Sabha may recommend amendments but cannot amend a Money Bill independently. The Lok Sabha may accept or reject its recommendations. The Rajya Sabha must return the Bill within 14 days.

Question 81 Unattempted

                    Consider the following statements about the Indian monsoon:

The Western Ghats receive heavy orographic rainfall from the southwest monsoon.

The Deccan Plateau lies entirely in the rain-shadow region of the Western Ghats.

Tamil Nadu receives a significant proportion of its rainfall from the northeast monsoon.

The Arabian Sea branch of the southwest monsoon causes rainfall on the windward side of the Western Ghats.

A) 1, 3 and 4 only

B) 1, 2, 3 and 4

C) 2, 3 and 4 only

D) 1 and 2 only

Explanation:

Statements 1, 3 and 4 are correct. Much of the interior Deccan lies in the rain shadow of the Western Ghats, but the entire plateau does not. Tamil Nadu receives substantial rainfall during the northeast monsoon, particularly from October to December.

Question 82 Unattempted

                    Consider the following statements about Windows and keyboard shortcuts:

Ctrl + Shift + Esc opens Task Manager directly in Windows.

Win + E opens File Explorer.

Alt + F4 normally closes the active application window.

Ctrl + Z permanently deletes the selected file without confirmation.

A) 1, 2 and 3 only

B) 1, 2, 3 and 4

C) 1 and 2 only

D) 2, 3 and 4 only

Explanation:

Statements 1, 2 and 3 are correct. Ctrl + Z generally undoes the previous action in supported applications; it does not permanently delete a selected file as stated in statement 4.

Question 83 Unattempted

                    Consider the following statements regarding Internet protocols:

HTTP is used for transferring web resources, while HTTPS protects HTTP communication using TLS.

DNS translates domain names into information such as IP addresses.

SMTP is commonly used to send email, while IMAP and POP3 are used to access or retrieve email.

FTP provides encryption by default for all usernames, passwords and file transfers.

A) 1, 2, 3 and 4

B) 1 and 2 only

C) 1, 2 and 3 only

D) 2, 3 and 4 only

Explanation:

Statements 1, 2 and 3 are correct. Traditional FTP does not encrypt credentials or data by default. Secure alternatives include SFTP and FTPS, which use different security mechanisms.

Question 84 Unattempted

                    Choose the correctly spelt word.                

A) Acommodation

B) Accomodation

C) Accommadation

D) Accommodation

Explanation:

The correct spelling is 'Accommodation', with double 'c' and double 'm'.

Question 85 Unattempted

                    Which combination provides the strongest general protection for online banking?                

A) Using a unique strong password, enabling multifactor authentication where available, keeping devices updated, and verifying the official banking website or app.

B) Using the same password on every website and saving it in a public computer browser.

C) Using public Wi-Fi for transactions without verifying the network and ignoring browser security warnings.

D) Sharing the banking OTP with a caller who claims to be a bank employee.

Explanation:

A unique password limits damage from credential reuse. Multifactor authentication, software updates, secure connections and verifying official banking channels reduce the risk of account compromise. Never disclose OTPs to callers.

Question 86 Unattempted

                    Consider the following statements about the ecology of Kashmir:

The Hangul, or Kashmir stag, is a threatened deer associated with the Kashmir Valley.

Dachigam National Park is well known for its role in conserving the Hangul.

The Dal Lake is a high-altitude freshwater lake in Ladakh.

Wular Lake is associated with the Jhelum River system.

A) 1, 2, 3 and 4

B) 1 and 2 only

C) 2, 3 and 4 only

D) 1, 2 and 4 only

Explanation:

Statements 1, 2 and 4 are correct. Hangul conservation is closely associated with Dachigam National Park. Dal Lake is located in Srinagar, Jammu and Kashmir, not Ladakh. Wular Lake is connected to the Jhelum River system.

Question 87 Unattempted

                    A country's nominal GDP increases by 12% in one year, while its real GDP increases by 7% over the same period. Approximately what is the GDP deflator inflation rate?                

A) 4.67%

B) 7.00%

C) 5.61%

D) 5.00%

Explanation:

GDP deflator inflation is calculated as [(1 + nominal GDP growth)/(1 + real GDP growth) - 1] × 100. Therefore, [(1.12/1.07) - 1] × 100 ≈ 4.67%. The correct answer is option a.

Question 88 Unattempted

                    Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

<b>Statements:</b>

1. All routers are switches.

2. Some switches are modems.

3. No modem is a cable.

<b>Conclusions:</b>

I. Some switches are not cables.

II. Some routers are modems.

III. No router is a cable.

A) Both Conclusions I and II follow

B) Only Conclusion III follows

C) Either Conclusion II or III follows

D) Only Conclusion I follows

Explanation:

1. Since 'Some switches are modems' and 'No modem is a cable', the portion of switches that are modems can never be cables. Therefore, 'Some switches are not cables' (Conclusion I) definitely follows.
2. There is no direct relation given between 'routers' and 'modems', so Conclusion II does not definitely follow.
3. There is no direct restriction preventing 'routers' from overlapping with 'cables', so Conclusion III does not definitely follow.
Thus, only Conclusion I follows.

Question 89 Unattempted

                    Choose the grammatically correct improvement for the sentence: 'Hardly had the train left the station than it began to rain.'                

A) No improvement required.

B) Hardly had the train left the station then it began to rain.

C) Hardly the train had left the station when it began to rain.

D) Hardly had the train left the station when it began to rain.

Explanation:

The correct correlative construction is 'Hardly had ... when'. Therefore, 'Hardly had the train left the station when it began to rain' is correct.

Question 90 Unattempted

                    Fill in the blank with the most appropriate option: The committee insisted that every applicant _____ the original certificates during verification.                

A) submits

B) submit

C) has submitted

D) submitted

Explanation:

After verbs such as 'insist' expressing a demand, the mandative subjunctive uses the base form of the verb. Therefore, 'submit' is correct.

Question 91 Unattempted

                    Study the given matrix carefully and select the number from among the given options that can replace the question mark ($$?$$):



$$8$$
$$6$$
$$28$$

$$11$$
$$7$$
$$72$$

$$13$$
$$9$$
$$?$$
                

A) $$96$$

B) $$78$$

C) $$84$$

D) $$88$$

Explanation:

In each row, the third number is the difference of the squares of the first two numbers: $$\text{Column } 3 = (\text{Column } 1)^2 - (\text{Column } 2)^2$$.
Row 1: $$8^2 - 6^2 = 64 - 36 = 28$$.
Row 2: $$11^2 - 7^2 = 121 - 49 = 72$$.
Row 3: $$13^2 - 9^2 = 169 - 81 = 88$$.

Question 92 Unattempted

                    An Excel worksheet contains the following values:

| Cell | Value |

|---|---:|

| A1 | 10 |

| A2 | 20 |

| A3 | Blank |

| A4 | 30 |

| A5 | Text: ABC |

What are the results of =COUNT(A1:A5) and =COUNTA(A1:A5), respectively?

A) 3 and 4

B) 3 and 5

C) 4 and 5

D) 4 and 3

Explanation:

COUNT counts cells containing numbers, so the result is 3. COUNTA counts all non-empty cells, including text, so the result is 4.

Question 93 Unattempted

                    If $$x - \frac{1}{x} = 3$$, where $$x \neq 0$$, then what is the value of $$x^4 + \frac{1}{x^4}$$?                

A) $$123$$

B) $$119$$

C) $$121$$

D) $$115$$

Explanation:

Given $$x - \frac{1}{x} = 3$$.
Squaring both sides: $$\left(x - \frac{1}{x}\right)^2 = 3^2$$ $$x^2 + \frac{1}{x^2} - 2 = 9 \implies x^2 + \frac{1}{x^2} = 11$$.

Squaring both sides again: $$\left(x^2 + \frac{1}{x^2}\right)^2 = 11^2$$ $$x^4 + \frac{1}{x^4} + 2 = 121 \implies x^4 + \frac{1}{x^4} = 119$$.

Question 94 Unattempted

                    Read the passage and answer the question:

In a small village, a young boy named Arif found an injured bird near a stream. Instead of leaving it alone, he carried it home and cared for it until it could fly again. A few weeks later, the bird returned to his garden with several other birds. Arif realised that a small act of kindness could bring unexpected happiness.

What is the central message of the passage?

A) Wild birds should always be kept as pets.

B) People should avoid helping injured animals.

C) Kindness can lead to unexpected happiness.

D) Success depends entirely on wealth.

Explanation:

The passage highlights Arif's compassion towards the injured bird and the happiness that followed. Its central message is that small acts of kindness can produce unexpected positive outcomes.

Question 95 Unattempted

                    A trader marks his goods $$40\%$$ above the cost price. He allows two successive discounts of $$10\%$$ and $$15\%$$ on the marked price to a customer. If he receives $$\text{Rs. } 1,071$$ for an article, what is the cost price of the article?                

A) $$\text{Rs. } 950$$

B) $$\text{Rs. } 1,000$$

C) $$\text{Rs. } 1,050$$

D) $$\text{Rs. } 900$$

Explanation:

Let the Cost Price ($$\text{CP}$$) of the article be $$x$$.
Marked Price ($$\text{MP}$$) $$= x \times \left(1 + \frac{40}{100}\right) = 1.4x$$.

After two successive discounts of $$10\%$$ and $$15\%$$, the Selling Price ($$\text{SP}$$) is: $$\text{SP} = 1.4x \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{15}{100}\right)$$ $$1071 = 1.4x \times 0.90 \times 0.85$$ $$1071 = 1.071x$$ $$x = \frac{1071}{1.071} = \text{Rs. } 1,000$$.

Question 96 Unattempted

                    Consider the following statements regarding Indian space research:

Chandrayaan-3 achieved a successful soft landing on the Moon in August 2023.

Aditya-L1 is India's solar observation mission placed in a halo orbit around the Sun-Earth L1 point.

Mangalyaan was India's first interplanetary mission to reach Mars orbit.

Chandrayaan-3 carried an active orbiter that entered lunar orbit in August 2023.

A) 1, 2, 3 and 4

B) 1 and 2 only

C) 1, 2 and 3 only

D) 2, 3 and 4 only

Explanation:

Statements 1, 2 and 3 are correct. Chandrayaan-3 landed on 23 August 2023. Aditya-L1 observes the Sun from a halo orbit around the Sun-Earth L1 point, and Mangalyaan was India's first Mars orbiter mission. Chandrayaan-3 did not carry a new active lunar orbiter; its propulsion module remained in lunar orbit before later operations.

Question 97 Unattempted

                    Which of the following pairs of classical dances and their associated states is incorrectly matched?                

A) Odissi — Tamil Nadu

B) Mohiniyattam — Kerala

C) Kuchipudi — Andhra Pradesh

D) Sattriya — Assam

Explanation:

Odissi is the classical dance form associated with Odisha, not Tamil Nadu. Bharatanatyam is associated with Tamil Nadu.

Question 98 Unattempted

                    If the nine-digit number $$708x6y8z9$$ is completely divisible by $$99$$, then what is the value of $$(x + y + z)$$?                

A) $$16$$

B) $$27$$

C) $$5$$

D) $$9$$

Explanation:

For a number to be divisible by $$99$$, it must be divisible by both $$9$$ and $$11$$.
1. Divisibility by $$11$$:
Sum of digits at odd places $$= 7 + 8 + 6 + 8 + 9 = 38$$.
Sum of digits at even places $$= 0 + x + y + z = x + y + z$$.
The difference $$38 - (x + y + z)$$ must be a multiple of $$11$$ (i.e., $$0, 11, 22, 33$$).
- If $$38 - (x + y + z) = 11 \implies x + y + z = 27$$.
- If $$38 - (x + y + z) = 22 \implies x + y + z = 16$$.
- If $$38 - (x + y + z) = 33 \implies x + y + z = 5$$.

2. Divisibility by $$9$$:
The total sum of digits $$38 + (x + y + z)$$ must be divisible by $$9$$.
- For $$x + y + z = 16$$: $$38 + 16 = 54$$, which is divisible by $$9$$.
- For $$x + y + z = 27$$: $$38 + 27 = 65$$ (not divisible by $$9$$).
- For $$x + y + z = 5$$: $$38 + 5 = 43$$ (not divisible by $$9$$).
Therefore, $$x + y + z = 16$$.

Question 99 Unattempted

                    Two circles of radii $$12\text{ cm}$$ and $$5\text{ cm}$$ have their centres $$25\text{ cm}$$ apart. What is the length of the direct common tangent to the two circles?                

A) $$24\text{ cm}$$

B) $$22\text{ cm}$$

C) $$18\text{ cm}$$

D) $$20\text{ cm}$$

Explanation:

The length $$L$$ of a direct common tangent between two circles with radii $$R$$ and $$r$$ whose centres are at a distance $$d$$ apart is given by: $$L = \sqrt{d^2 - (R - r)^2}$$ Given $$d = 25\text{ cm}$$, $$R = 12\text{ cm}$$, and $$r = 5\text{ cm}$$: $$L = \sqrt{25^2 - (12 - 5)^2}$$ $$L = \sqrt{625 - 7^2} = \sqrt{625 - 49} = \sqrt{576} = 24\text{ cm}$$.

Question 100 Unattempted

                    The present ages of $$\text{A}$$ and $$\text{B}$$ are in the ratio $$5 : 7$$. Eight years from now, the ratio of their ages will be $$7 : 9$$. What was the sum of their ages $$4$$ years ago?                

A) $$48\text{ years}$$

B) $$44\text{ years}$$

C) $$36\text{ years}$$

D) $$40\text{ years}$$

Explanation:

Let the present ages of $$\text{A}$$ and $$\text{B}$$ be $$5x$$ and $$7x$$ respectively.
According to the question, after $$8$$ years: $$\frac{5x + 8}{7x + 8} = \frac{7}{9}$$ $$9(5x + 8) = 7(7x + 8)$$ $$45x + 72 = 49x + 56$$ $$4x = 16 \implies x = 4$$.
Present age of $$\text{A} = 5(4) = 20\text{ years}$$.
Present age of $$\text{B} = 7(4) = 28\text{ years}$$.
Present sum of their ages $$= 20 + 28 = 48\text{ years}$$.
Sum of their ages $$4$$ years ago $$= 48 - 2(4) = 48 - 8 = 40\text{ years}$$.

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Department	HR	IT	Finance	Marketing	Operations
Number of Employees	$$45$$	$$108$$	$$63$$	$$72$$	$$72$$