Test Result & Solutions

Question 1 Unattempted

                    In symbolic operations, if $$P \Delta Q$$ means $$P > Q$$, $$P \nabla Q$$ means $$P < Q$$, and $$P \odot Q$$ means $$P = Q$$. Given the statements $$A \Delta B$$ and $$B \odot C$$, which of the following conclusions must logically follow?                

A) None of the above

B) $$A \nabla C$$

C) $$A \Delta C$$

D) $$A \odot C$$

Explanation:

From $$A \Delta B$$, we have $$A > B$$. From $$B \odot C$$, we have $$B = C$$. Substituting $$B$$ with $$C$$ in the first inequality gives $$A > C$$, which translates to $$A \Delta C$$.

Question 2 Unattempted

                    Two parallel chords on the same side of the centre of a circle with a radius of $$13\text{ cm}$$ are $$10\text{ cm}$$ and $$24\text{ cm}$$ long. What is the perpendicular distance between the chords?                

A) $$17\text{ cm}$$

B) $$12\text{ cm}$$

C) $$5\text{ cm}$$

D) $$7\text{ cm}$$

Explanation:

Let the distance from the centre to the $$10\text{ cm}$$ chord be $$d_1$$ and to the $$24\text{ cm}$$ chord be $$d_2$$. A perpendicular from the centre bisects the chord. Using Pythagorean theorem: $$d_1 = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = 12\text{ cm}$$. $$d_2 = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = 5\text{ cm}$$. The distance between them is $$d_1 - d_2 = 12 - 5 = 7\text{ cm}$$.

Question 3 Unattempted

                    In a triangle, the point of intersection of the internal angle bisectors is known as its:                

A) Orthocentre

B) Centroid

C) Incentre

D) Circumcentre

Explanation:

The incentre of a triangle is the point where the internal angle bisectors intersect. It serves as the centre of the incircle, which is tangent to all three sides of the triangle.

Question 4 Unattempted

                    Match the following national parks with their respective states or Union Territories:

List I: National ParkList II: State/UT
i. Dachigam National Park1. Assam
ii. Kaziranga National Park2. Jammu and Kashmir
iii. Gir National Park3. Gujarat
iv. Jim Corbett National Park4. Uttarakhand

Choose the correct code.                

List I: National Park	List II: State/UT
i. Dachigam National Park	1. Assam
ii. Kaziranga National Park	2. Jammu and Kashmir
iii. Gir National Park	3. Gujarat
iv. Jim Corbett National Park	4. Uttarakhand

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

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

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

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

Explanation:

Dachigam National Park is in Jammu and Kashmir, Kaziranga is in Assam, Gir is in Gujarat, and Jim Corbett National Park is in Uttarakhand.

Question 5 Unattempted

                    In Windows File Explorer, a user selects a file and presses Shift + Delete. Which statement is generally correct?                

A) The file is renamed automatically.

B) The file is copied to the clipboard.

C) The file is compressed and moved to the Recycle Bin.

D) The file is permanently deleted without normally passing through the Recycle Bin.

Explanation:

Shift + Delete generally deletes a selected file without sending it to the Recycle Bin. Recovery may still be possible in some circumstances, so the shortcut should not be treated as a secure data-erasure method.

Question 6 Unattempted

                    Find the missing term in the Semantic Alphabet Series: $$B, E, H, K, ?$$                

A) $$M$$

B) $$O$$

C) $$P$$

D) $$N$$

Explanation:

The positional values of the letters are $$B=2$$, $$E=5$$, $$H=8$$, $$K=11$$. The series follows an arithmetic progression with a common difference of $$+3$$. The next value is $$11 + 3 = 14$$, which corresponds to the letter $$N$$.

Question 7 Unattempted

                    Simplify the elementary surd expression: $$\frac{3}{\sqrt{5} - \sqrt{2}}$$.                

A) $$3(\sqrt{5} + \sqrt{2})$$

B) $$\sqrt{5} - \sqrt{2}$$

C) $$\sqrt{5} + \sqrt{2}$$

D) $$\frac{\sqrt{5} + \sqrt{2}}{3}$$

Explanation:

To rationalize the denominator, multiply the numerator and denominator by the conjugate, $$\sqrt{5} + \sqrt{2}$$. The expression becomes $$\frac{3(\sqrt{5} + \sqrt{2})}{(\sqrt{5})^2 - (\sqrt{2})^2} = \frac{3(\sqrt{5} + \sqrt{2})}{5 - 2} = \frac{3(\sqrt{5} + \sqrt{2})}{3} = \sqrt{5} + \sqrt{2}$$.

Question 8 Unattempted

                    A pipe can fill a tank in $$15$$ hours. Due to a leak at the bottom, it takes $$20$$ hours to fill the tank. If the tank is completely full, how much time will the leak alone take to empty it?                

A) $$30$$ hours

B) $$50$$ hours

C) $$45$$ hours

D) $$60$$ hours

Explanation:

Let the leak empty the tank in $$x$$ hours. Work done by the inlet pipe in $$1$$ hour = $$\frac{1}{15}$$. Work done by the leak in $$1$$ hour = $$-\frac{1}{x}$$. Net work done in $$1$$ hour when both are open = $$\frac{1}{20}$$. Therefore, $$\frac{1}{15} - \frac{1}{x} = \frac{1}{20} \implies \frac{1}{x} = \frac{1}{15} - \frac{1}{20} = \frac{4 - 3}{60} = \frac{1}{60}$$. Thus, the leak will empty the tank in $$60$$ hours.

Question 9 Unattempted

                    Choose the grammatically correct improvement for the underlined portion: 'No sooner did the train arrive when the passengers rushed towards the exit.'                

A) No sooner the train arrived than the passengers rushed towards the exit.

B) No sooner did the train arrive than the passengers rushed towards the exit.

C) No sooner had the train arrive than the passengers rushed towards the exit.

D) No sooner did the train arrived when the passengers rushed towards the exit.

Explanation:

The correct correlative construction is 'no sooner...than'. After 'did', the base form 'arrive' is required. Therefore, option A is correct.

Question 10 Unattempted

                    With reference to Jammu and Kashmir, consider the following statements:

1. Wular Lake is associated with the Jhelum River system.

2. The Karewa formations are important for saffron cultivation in parts of Kashmir.

3. The Pir Panjal Range separates the Kashmir Valley from the Jammu region in the broad physiographic sense.

Which statements are correct?

A) 1, 2 and 3

B) 1 and 3 only

C) 1 and 2 only

D) 2 and 3 only

Explanation:

All three statements are correct. Wular Lake is linked to the Jhelum River system, Karewa deposits support saffron cultivation in parts of Kashmir, and the Pir Panjal Range forms a major mountain barrier between the Kashmir Valley and the Jammu region.

Question 11 Unattempted

                    In October 2026, the Union Government announced that 11 crore Farmer IDs had been created ahead of schedule. This milestone is most directly associated with which initiative?                

A) Ayushman Bharat Digital Mission

B) PM Vishwakarma

C) Digital India Land Records Modernization Programme alone

D) Digital Agriculture initiatives

Explanation:

The Ministry of Agriculture and Farmers Welfare reported on 24 October 2026 that 11 crore Farmer IDs had been created five months ahead of schedule as part of the Digital Agriculture initiative. Farmer IDs support digital identification and integration of farmers' agricultural information. Source: Press Information Bureau, Government of India, 24 October 2026.

Question 12 Unattempted

                    Simplify the mathematical expression: $$\frac{0.8 \times 0.8 \times 0.8 - 0.5 \times 0.5 \times 0.5}{0.8 \times 0.8 + 0.8 \times 0.5 + 0.5 \times 0.5}$$                

A) $$0.3$$

B) $$1.3$$

C) $$0.13$$

D) $$0.4$$

Explanation:

The given expression is in the form of $$\frac{a^3 - b^3}{a^2 + ab + b^2}$$, where $$a = 0.8$$ and $$b = 0.5$$. According to algebraic identities, $$\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b$$. Substituting the values, we get $$0.8 - 0.5 = 0.3$$.

Question 13 Unattempted

                    Match the following keyboard shortcuts with their standard Windows or Microsoft Office functions:

ShortcutFunction
i. Ctrl + Shift + Esc1. Open Task Manager
ii. Win + E2. Open File Explorer
iii. Ctrl + H in MS Word3. Open Find and Replace
iv. F12 in MS Word4. Open Save As

Choose the correct code.                

Shortcut	Function
i. Ctrl + Shift + Esc	1. Open Task Manager
ii. Win + E	2. Open File Explorer
iii. Ctrl + H in MS Word	3. Open Find and Replace
iv. F12 in MS Word	4. Open Save As

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

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

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

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

Explanation:

Ctrl + Shift + Esc opens Task Manager, Win + E opens File Explorer, Ctrl + H opens Find and Replace in MS Word, and F12 opens the Save As dialog in desktop Word.

Question 14 Unattempted

                    The angle of elevation of the top of a tower from a point on the ground, which is $$30\text{ m}$$ away from the foot of the tower, is $$30^\circ$$. Find the height of the tower.                

A) $$10\sqrt{3}\text{ m}$$

B) $$15\sqrt{3}\text{ m}$$

C) $$10\text{ m}$$

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

Explanation:

Let the height of the tower be $$h$$. Using the tangent ratio, $$\tan(30^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{30}$$. Since $$\tan(30^\circ) = \frac{1}{\sqrt{3}}$$, we have $$\frac{1}{\sqrt{3}} = \frac{h}{30}$$. Solving for $$h$$, $$h = \frac{30}{\sqrt{3}} = \frac{30\sqrt{3}}{3} = 10\sqrt{3}\text{ m}$$.

Question 15 Unattempted

                    Evaluate the following trigonometric expression involving complementary angles: $$\frac{\sin(35^\circ)}{\cos(55^\circ)} + \frac{\sec(20^\circ)}{\text{cosec}(70^\circ)}$$.                

A) $$4$$

B) $$2$$

C) $$1$$

D) $$0$$

Explanation:

Using the complementary angle identities, $$\cos(55^\circ) = \cos(90^\circ - 35^\circ) = \sin(35^\circ)$$, so $$\frac{\sin(35^\circ)}{\cos(55^\circ)} = 1$$. Similarly, $$\text{cosec}(70^\circ) = \text{cosec}(90^\circ - 20^\circ) = \sec(20^\circ)$$, so $$\frac{\sec(20^\circ)}{\text{cosec}(70^\circ)} = 1$$. The sum is $$1 + 1 = 2$$.

Question 16 Unattempted

                    Change into indirect speech: He said to me, 'Why did you not inform me about the meeting yesterday?'                

A) He asked me why I had not informed him about the meeting the previous day.

B) He told me why I did not inform him about the meeting the previous day.

C) He asked me why had I not informed him about the meeting yesterday.

D) He asked me why I have not informed him about the meeting yesterday.

Explanation:

In indirect questions, normal statement word order is used. 'Did not inform' changes to 'had not informed', 'you' becomes 'I', 'me' becomes 'him', and 'yesterday' changes to 'the previous day' when the reporting context requires backshift.

Question 17 Unattempted

                    Read the passage and answer the question.

'Public reports on urban air quality increasingly emphasise that pollution is not caused by a single source. Transport emissions, construction dust, industrial activity and seasonal weather conditions may interact to worsen exposure. Experts therefore recommend combining reliable monitoring with targeted emission controls and public communication. A short-term improvement in air quality, they caution, does not necessarily demonstrate that the underlying sources have been permanently addressed.'

Which conclusion is best supported by the passage?

A) Public communication can replace emission controls and monitoring.

B) Transport is the sole cause of urban air pollution.

C) A single day of cleaner air proves that pollution-control policies have permanently succeeded.

D) Effective air-quality management requires multiple measures and sustained assessment.

Explanation:

The passage identifies multiple pollution sources and recommends monitoring, targeted controls and communication. It also warns against treating a temporary improvement as proof of lasting success. Therefore, sustained, multi-pronged action is the best-supported conclusion.

Question 18 Unattempted

                    A train $$150$$ m long passes a stationary pole in $$15$$ seconds. It passes another train of the same length travelling in the opposite direction in $$12$$ seconds. What is the speed of the second train?                

A) $$72$$ km/hr

B) $$54$$ km/hr

C) $$45$$ km/hr

D) $$36$$ km/hr

Explanation:

Speed of the first train = $$\frac{\text{Distance}}{\text{Time}} = \frac{150}{15} = 10$$ m/s. When the two trains cross each other in opposite directions, relative distance = $$150 + 150 = 300$$ m. Relative speed = $$\frac{300}{12} = 25$$ m/s. Since they move in opposite directions, relative speed = $$S_1 + S_2$$. So, $$10 + S_2 = 25 \implies S_2 = 15$$ m/s. Converting to km/hr: $$15 \times \frac{18}{5} = 54$$ km/hr.

Question 19 Unattempted

                    Consider the following statements regarding operating systems, memory management and computer architecture:

1. A process in a blocked state is generally waiting for an event, such as completion of an I/O operation, rather than actively executing on the CPU.

2. A page fault necessarily indicates that a program has attempted to access an illegal memory address.

3. DMA (Direct Memory Access) allows certain I/O devices to transfer data to or from main memory with reduced continuous CPU involvement.

4. In a system using virtual memory, two processes can use the same virtual address while the corresponding addresses map to different physical memory locations.

Which of the statements given above are correct?

A) 2, 3 and 4 only

B) 1, 2, 3 and 4

C) 1 and 2 only

D) 1, 3 and 4 only

Explanation:

Statements 1, 3 and 4 are correct. A blocked process waits for an event or resource; DMA enables data transfers with less continuous CPU involvement; and virtual memory allows different processes to map identical virtual addresses to different physical locations. Statement 2 is incorrect because a page fault can occur during a valid memory access when the required page is not currently mapped in physical memory. The operating system may resolve the fault without terminating the program.

Question 20 Unattempted

                    Consider the following statements regarding the Central Processing Unit (CPU):

1. The Control Unit directs the operations of the processor but does not normally perform arithmetic calculations itself.

2. The Arithmetic Logic Unit (ALU) performs arithmetic and logical operations.

3. Registers generally have lower access latency than main memory.

4. Cache memory is always slower than RAM because it is located closer to the CPU.

Which statements are correct?

A) 2, 3 and 4 only

B) 1, 2 and 3 only

C) 1 and 2 only

D) 1, 2, 3 and 4

Explanation:

Statements 1, 2 and 3 are correct. The Control Unit coordinates processor operations, the ALU performs arithmetic and logical operations, and registers provide very fast storage within the CPU. Statement 4 is false because cache memory is generally faster than RAM and is designed to reduce average memory-access time.

Question 21 Unattempted

                    How many meaningful three-letter English words can be formed using the letters in the set $$S = \{A, R, T\}$$ exactly once?                

A) $$3$$

B) $$4$$

C) $$2$$

D) $$5$$

Explanation:

The permutations of the set $$S$$ are ART, ATR, RAT, RTA, TAR, TRA. The meaningful English words among these are ART, RAT, and TAR. Thus, there are $$3$$ meaningful words.

Question 22 Unattempted

                    A malicious program appears to be a legitimate utility, but after the user installs it, it secretly performs unauthorized actions. Unlike a typical computer worm, it does not need to self-replicate to spread. What type of malware best fits this description?                

A) Trojan horse

B) Boot sector virus

C) Worm

D) Adware only

Explanation:

A Trojan horse disguises itself as legitimate or useful software while carrying out unauthorized actions. A worm is characterized by its ability to self-replicate and spread, often across networks, without needing to attach itself to another program.

Question 23 Unattempted

                    A tradesman marks his goods $$25$$% above the cost price and allows a discount of $$12$$% on the marked price. Find his overall profit percentage.                

A) $$13$$%

B) $$10$$%

C) $$12$$%

D) $$15$$%

Explanation:

Let the Cost Price (CP) be $$100$$. The Marked Price (MP) becomes $$100 + 25 = 125$$. A discount of $$12$$% is given on the MP, so Discount = $$12$$% of $$125 = 15$$. The Selling Price (SP) = $$125 - 15 = 110$$. The profit is $$110 - 100 = 10$$. The profit percentage is $$10$$%.

Question 24 Unattempted

                    The National Social Assistance Programme (NSAP), whose continuation for five years from 2026–27 to 2030–31 was approved by the Union Cabinet in October 2026, primarily aims to provide social assistance to which groups?                

A) Only government employees after retirement

B) Only farmers owning more than five hectares of land

C) Only students enrolled in central universities

D) Eligible elderly persons, widows and persons with disabilities from vulnerable households

Explanation:

The NSAP provides social assistance through schemes targeting eligible vulnerable groups, including elderly persons, widows and persons with disabilities, subject to scheme conditions. The Union Cabinet approved its continuation for 2026–27 to 2030–31 on 14 October 2026. Source: Press Information Bureau, Government of India.

Question 25 Unattempted

                    Choose the correct pair of words to complete the sentence: 'The scientist's findings were initially dismissed as ______, but subsequent experiments provided ______ evidence in their favour.'                

A) irrefutable; tentative

B) conclusive; contradictory

C) speculative; compelling

D) credible; negligible

Explanation:

'Speculative' describes claims based on conjecture rather than sufficient evidence, while 'compelling' describes evidence that is convincing. The contrast between initial dismissal and later experimental support makes option B correct.

Question 26 Unattempted

                    Consider the following statements in syllogistic reasoning:<br>1. All $$X$$ are $$Y$$.<br>2. Some $$Y$$ are $$Z$$.<br>Conclusions:<br>I. Some $$Z$$ are $$X$$.<br>II. Some $$Y$$ are $$X$$.<br>Which conclusion logically follows?                

A) Neither Conclusion follows

B) Only Conclusion I follows

C) Both Conclusions I and II follow

D) Only Conclusion II follows

Explanation:

Since 'All $$X$$ are $$Y$$', its conversion 'Some $$Y$$ are $$X$$' is strictly true, validating Conclusion II. However, there is no direct relationship established between $$X$$ and $$Z$$ (the intersection of $$Y$$ and $$Z$$ might not overlap with $$X$$), so Conclusion I does not follow.

Question 27 Unattempted

                    Consider the following statements about Internet protocols and networking:

1. DNS translates domain names into information such as IP addresses used for network communication.

2. HTTPS uses TLS to protect HTTP communication in modern deployments.

3. SMTP is commonly used to send or relay email.

4. IMAP is designed primarily to assign IP addresses automatically to hosts.

Which statements are correct?

A) 1, 2, 3 and 4

B) 1, 2 and 3 only

C) 2, 3 and 4 only

D) 1 and 2 only

Explanation:

Statements 1, 2 and 3 are correct. DNS resolves domain names, HTTPS protects HTTP communication using TLS in modern deployments, and SMTP is used to send or relay email. DHCP, not IMAP, is commonly used to assign IP configuration automatically. IMAP is an email-access protocol.

Question 28 Unattempted

                    The average of $$11$$ numbers is $$50$$. If the average of the first $$6$$ numbers is $$49$$ and that of the last $$6$$ numbers is $$52$$, find the $$6^{\text{th}}$$ number.                

A) $$60$$

B) $$54$$

C) $$56$$

D) $$48$$

Explanation:

The sum of all $$11$$ numbers is $$11 \times 50 = 550$$. The sum of the first $$6$$ numbers is $$6 \times 49 = 294$$. The sum of the last $$6$$ numbers is $$6 \times 52 = 312$$. The $$6^{\text{th}}$$ number is counted twice in these two sums. Therefore, the $$6^{\text{th}}$$ number = $$(294 + 312) - 550 = 606 - 550 = 56$$.

Question 29 Unattempted

                    Solve the Number Analogy: $$0.16 : 0.0016 :: 1.02 : ?$$                

A) $$1.002$$

B) $$0.00102$$

C) $$0.102$$

D) $$0.0102$$

Explanation:

The relationship between the first pair is a division by $$100$$, or moving the decimal point two places to the left: $$\frac{0.16}{100} = 0.0016$$. Applying the same operation to the second term: $$\frac{1.02}{100} = 0.0102$$.

Question 30 Unattempted

                    $$A$$ and $$B$$ invest in a partnership business in the ratio $$3:2$$. If $$5$$% of the total profit goes to a charity and $$A$$'s share of the remaining profit is ₹ $$855$$, find the total profit.                

A) ₹ $$1400$$

B) ₹ $$1500$$

C) ₹ $$1600$$

D) ₹ $$1200$$

Explanation:

Let the total profit be $$100x$$. After giving $$5$$% to charity, the remaining profit is $$95x$$. This remaining profit is shared between $$A$$ and $$B$$ in the ratio $$3:2$$. $$A$$'s share = $$\frac{3}{5} \times 95x = 57x$$. Given that $$A$$'s share is ₹ $$855$$, we have $$57x = 855 \implies x = 15$$. The total profit = $$100x = 100 \times 15 =$$ ₹ $$1500$$.

Question 31 Unattempted

                    The sum of the ages of a father and his son is $$45$$ years. Five years ago, the product of their ages was $$34$$. What is the father's current age?                

A) $$42$$ years

B) $$40$$ years

C) $$36$$ years

D) $$39$$ years

Explanation:

Let the father's age be $$F$$ and son's age be $$S$$. $$F + S = 45 \implies S = 45 - F$$. Five years ago: $$(F - 5)(S - 5) = 34$$. Substitute $$S$$: $$(F - 5)(40 - F) = 34$$. Expanding gives $$40F - F^2 - 200 + 5F = 34 \implies F^2 - 45F + 234 = 0$$. Factoring yields $$(F - 39)(F - 6) = 0$$. Since the father must be older, $$F = 39$$.

Question 32 Unattempted

                    Consider the following statements about the Comptroller and Auditor General of India (CAG):

1. The CAG is appointed by the President of India.

2. The CAG audits government expenditure as provided under the constitutional and statutory framework.

3. The CAG can be removed in the same manner and on the same grounds as a Supreme Court judge.

Which statements are correct?

A) 1 only

B) 1 and 2 only

C) 1, 2 and 3

D) 2 and 3 only

Explanation:

All three statements are correct. The President appoints the CAG. The CAG audits public accounts and government expenditure within the prescribed framework. Removal follows the same manner and grounds as removal of a Supreme Court judge.

Question 33 Unattempted

                    Which of the following best describes the repo rate?                

A) The rate at which commercial banks lend money to customers

B) The rate at which banks lend money to one another without RBI involvement

C) The rate of interest paid by the government on all tax refunds

D) The rate at which the RBI lends short-term funds to banks under the repo arrangement

Explanation:

The repo rate is the rate associated with the Reserve Bank of India's lending of funds to banks against eligible securities under a repurchase agreement. It is an important monetary policy instrument used to influence liquidity and borrowing costs.

Question 34 Unattempted

                    In a specific coding system, the word $$CAT$$ is coded as $$24$$ and $$DOG$$ is coded as $$26$$. How will the word $$TIGER$$ be coded?                

A) $$59$$

B) $$58$$

C) $$60$$

D) $$57$$

Explanation:

The code is the sum of the alphabetical positions of the letters. For $$CAT$$: $$C(3) + A(1) + T(20) = 24$$. For $$DOG$$: $$D(4) + O(15) + G(7) = 26$$. For $$TIGER$$: $$T(20) + I(9) + G(7) + E(5) + R(18) = 59$$.

Question 35 Unattempted

                    Consider the following statements about e-banking and secure Internet use:

1. A one-time password (OTP) should not be disclosed to an unsolicited caller claiming to be a bank employee.

2. HTTPS alone guarantees that a website is legitimate and cannot be fraudulent.

3. Multifactor authentication can add a layer of security beyond a password alone.

4. Public Wi-Fi should be used cautiously for sensitive financial transactions, particularly on untrusted networks.

Which statements are correct?

A) 1 and 3 only

B) 1, 2, 3 and 4

C) 1, 3 and 4 only

D) 1 and 2 only

Explanation:

Statements 1, 3 and 4 are correct. Never disclose OTPs to unsolicited callers, use multifactor authentication where available, and be cautious with sensitive transactions on untrusted public Wi-Fi. HTTPS encrypts the connection to a domain but does not by itself prove that the site is trustworthy; fraudulent websites can also use HTTPS.

Question 36 Unattempted

                    For a moderately skewed statistical distribution, if the mean is $$24$$ and the median is $$26$$, find the mode using the empirical relationship.                

A) $$28$$

B) $$32$$

C) $$34$$

D) $$30$$

Explanation:

The empirical relationship between the measures of central tendency is given by $$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$$. Substituting the given values: $$\text{Mode} = 3(26) - 2(24) = 78 - 48 = 30$$.

Question 37 Unattempted

                    $$A$$ can do a piece of work in $$15$$ days and $$B$$ can do it in $$20$$ days. If they work on it together for $$4$$ days, then what fraction of the total work is left?                

A) $$\frac{1}{4}$$

B) $$\frac{7}{15}$$

C) $$\frac{8}{15}$$

D) $$\frac{1}{2}$$

Explanation:

Work done by $$A$$ in $$1$$ day = $$\frac{1}{15}$$. Work done by $$B$$ in $$1$$ day = $$\frac{1}{20}$$. Work done by both in $$1$$ day = $$\frac{1}{15} + \frac{1}{20} = \frac{4 + 3}{60} = \frac{7}{60}$$. Work done in $$4$$ days = $$4 \times \frac{7}{60} = \frac{28}{60} = \frac{7}{15}$$. Fraction of work left = $$1 - \frac{7}{15} = \frac{8}{15}$$.

Question 38 Unattempted

                    Which of the following correctly represents the general order of the memory hierarchy from fastest access 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 typical order from fastest to slower access is CPU registers, cache, RAM, and secondary storage such as an SSD. Actual performance varies by technology and configuration, but registers and cache are designed for much faster access than main memory and storage.

Question 39 Unattempted

                    Change the sentence into passive voice: 'The authorities will have completed the investigation before the deadline.'                

A) The investigation has been completed by the authorities before the deadline.

B) The investigation will have completed by the authorities before the deadline.

C) The investigation will have been completed by the authorities before the deadline.

D) The investigation would have been completed by the authorities before the deadline.

Explanation:

The future perfect passive is formed using 'will have been + past participle'. Thus, 'will have completed' becomes 'will have been completed'.

Question 40 Unattempted

                    In a Venn Diagram representing two sets $$A$$ and $$B$$ inside a universal set $$U$$, you are given: $$n(U) = 100$$, $$n(A) = 50$$, $$n(B) = 30$$, and $$n(A \cap B) = 10$$. Find the cardinality of the complement of their union, $$n((A \cup B)')$$.                

A) $$30$$

B) $$40$$

C) $$20$$

D) $$50$$

Explanation:

Using the principle of inclusion-exclusion, $$n(A \cup B) = n(A) + n(B) - n(A \cap B) = 50 + 30 - 10 = 70$$. The complement is $$n(U) - n(A \cup B) = 100 - 70 = 30$$.

Question 41 Unattempted

                    Choose the grammatically correct sentence.                

A) Neither the principal or the teachers were willing to accept responsibility.

B) Neither the principal nor the teachers were willing to accept responsibility.

C) Neither the principal nor the teachers was willing to accept responsibility.

D) Neither the principal nor the teachers is willing to accepted responsibility.

Explanation:

With 'neither...nor', the verb generally agrees with the subject nearer to it. Here, 'teachers' is plural, so 'were' is correct.

Question 42 Unattempted

                    A person is standing on a platform when a moving train suddenly starts. The person tends to fall backward. Which scientific principle best explains this observation?                

A) Archimedes' principle

B) Inertia of rest

C) Newton's law of gravitation

D) Conservation of electric charge

Explanation:

Due to inertia of rest, the person's body tends to remain at rest when the train starts moving forward. The feet move with the train while the upper body tends to remain at rest momentarily, causing the person to lean or fall backward.

Question 43 Unattempted

                    Which of the following numbers does NOT belong to the classification set $$S = \{27, 64, 125, 144, 216\}$$?                

A) $$64$$

B) $$125$$

C) $$216$$

D) $$144$$

Explanation:

The numbers $$27, 64, 125$$, and $$216$$ are all perfect cubes ($$3^3, 4^3, 5^3, 6^3$$ respectively). However, $$144$$ is a perfect square ($$12^2$$) but not a perfect cube. Therefore, $$144$$ is the odd one out.

Question 44 Unattempted

                    In October 2026, the Union Government approved a Productivity Linked Bonus for railway employees equivalent to 78 days. Which is the primary purpose of such a bonus?                

A) To replace the basic salary of railway employees

B) To pay only employees who have completed 40 years of service

C) To provide a performance-linked or productivity-related financial benefit under the applicable scheme

D) To provide a permanent increase in pension to every railway employee

Explanation:

A Productivity Linked Bonus is a financial benefit provided to eligible employees under the applicable scheme, linked to productivity-related criteria. The Union Cabinet approved a 78-day bonus for railway employees in October 2026. Source: Press Information Bureau, Government of India, 14 October 2026.

Question 45 Unattempted

                    Which of the following fractions is the largest: $$\frac{7}{8}, \frac{13}{16}, \frac{31}{40}, \frac{63}{80}$$?                

A) $$\frac{31}{40}$$

B) $$\frac{13}{16}$$

C) $$\frac{63}{80}$$

D) $$\frac{7}{8}$$

Explanation:

To compare the fractions, convert them to a common denominator. The LCM of $$8, 16, 40$$, and $$80$$ is $$80$$. $$\frac{7}{8} = \frac{70}{80}$$. $$\frac{13}{16} = \frac{65}{80}$$. $$\frac{31}{40} = \frac{62}{80}$$. $$\frac{63}{80}$$ remains the same. Comparing the numerators ($$70 > 65 > 63 > 62$$), the largest fraction is $$\frac{70}{80}$$, which corresponds to $$\frac{7}{8}$$.

Question 46 Unattempted

                    Match the following Indian rivers with the water bodies into which they drain:

List I: RiverList II: Water body
i. Narmada1. Bay of Bengal
ii. Godavari2. Arabian Sea
iii. Mahanadi3. Arabian Sea
iv. Tapi4. Bay of Bengal

Choose the correct code, noting that rivers sharing the same destination may have the same number.                

List I: River	List II: Water body
i. Narmada	1. Bay of Bengal
ii. Godavari	2. Arabian Sea
iii. Mahanadi	3. Arabian Sea
iv. Tapi	4. Bay of Bengal

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

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

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

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

Explanation:

The Narmada and Tapi drain into the Arabian Sea. The Godavari and Mahanadi drain into the Bay of Bengal. In the given list, 1 denotes the Bay of Bengal and 2 denotes the Arabian Sea; the duplicated labels in List II represent the same destinations.

Question 47 Unattempted

                    Consider the following statements about Microsoft Excel:

1. COUNT counts cells containing numeric values.

2. COUNTA counts non-empty cells, including cells containing text.

3. COUNTBLANK counts blank cells in a specified range.

4. The formula =SUM(A1:A5) adds the values in cells A1 through A5, inclusive.

Which statements are correct?

A) 1, 2, 3 and 4

B) 1, 3 and 4 only

C) 1 and 2 only

D) 2 and 3 only

Explanation:

All four statements are correct. COUNT counts numeric entries, COUNTA counts non-empty cells, COUNTBLANK counts blank cells, and SUM(A1:A5) adds the values across the inclusive range A1 to A5.

Question 48 Unattempted

                    Which of the following pairs is incorrectly matched?                

A) Lal Ded — Kashmiri mystic poet

B) Kalhana — Rajatarangini

C) Habba Khatoon — Kashmiri poetess

D) Abhinavagupta — Author of Ain-i-Akbari

Explanation:

Abhinavagupta was a major Kashmiri philosopher and scholar associated with Kashmir Shaivism and aesthetics. Ain-i-Akbari was written by Abu'l-Fazl during the reign of Akbar. Kalhana authored Rajatarangini, an important historical chronicle of Kashmir.

Question 49 Unattempted

                    Select the most appropriate word to fill in the blank: 'The judge's remarks were so ______ that neither party could interpret them as an unequivocal endorsement.'                

A) Explicit

B) Dogmatic

C) Ambiguous

D) Conclusive

Explanation:

'Ambiguous' means open to more than one interpretation. Since neither party could interpret the remarks as a clear endorsement, 'ambiguous' is the best fit.

Question 50 Unattempted

                    Which of the following pairs relating to Indian sports is correctly matched?                

A) Thomas Cup — Men's team badminton

B) Ranji Trophy — Football

C) Santosh Trophy — International cricket

D) Davis Cup — Men's international team hockey

Explanation:

The Thomas Cup is an international men's team badminton championship. The Davis Cup is men's international team tennis, the Santosh Trophy is an Indian football competition, and the Ranji Trophy is a domestic first-class cricket competition.

Question 51 Unattempted

                    In Microsoft Excel, cell A1 contains 15, B1 contains 4, and C1 contains the formula =A1/B1. If C1 is formatted to display two decimal places, what will normally be displayed?                

A) 3.8

B) 3.75

C) 4

D) 3.7500

Explanation:

15 divided by 4 equals 3.75. Formatting a cell to display two decimal places changes the displayed precision, not the underlying calculated value. In this case, the displayed value is 3.75.

Question 52 Unattempted

                    A boat can travel at a speed of $$13$$ km/hr in still water. If the speed of the stream is $$4$$ km/hr, find the time taken by the boat to go $$68$$ km downstream.                

A) $$3$$ hours

B) $$6$$ hours

C) $$5$$ hours

D) $$4$$ hours

Explanation:

Speed of the boat in still water = $$13$$ km/hr. Speed of the stream = $$4$$ km/hr. Downstream speed = $$\text{Speed of boat} + \text{Speed of stream} = 13 + 4 = 17$$ km/hr. Time taken to travel $$68$$ km downstream = $$\frac{\text{Distance}}{\text{Speed}} = \frac{68}{17} = 4$$ hours.

Question 53 Unattempted

                    In a problem-solving scenario testing combinatorial logic, there is a tournament with $$n = 10$$ teams. If every team plays exactly one match against every other team, what is the total number of matches played?                

A) $$90$$

B) $$50$$

C) $$100$$

D) $$45$$

Explanation:

The total number of matches is equal to the number of ways to choose $$2$$ teams from $$10$$. This is given by the combination formula: $$\binom{n}{2} = \frac{n(n-1)}{2}$$. Substituting $$n = 10$$, we get $$\frac{10 \times 9}{2} = 45$$ matches.

Question 54 Unattempted

                    If the radius of a sphere is doubled, what is the percentage increase in its surface area?                

A) $$400\%$$

B) $$200\%$$

C) $$100\%$$

D) $$300\%$$

Explanation:

Original surface area $$A_1 = 4 \pi r^2$$. If the new radius is $$R = 2r$$, the new surface area is $$A_2 = 4 \pi (2r)^2 = 16 \pi r^2$$. Note that $$A_2 = 4 A_1$$. The increase in area is $$A_2 - A_1 = 4A_1 - A_1 = 3A_1$$. The percentage increase is $$\frac{3A_1}{A_1} \times 100\% = 300\%$$.

Question 55 Unattempted

                    If person $$A$$'s salary is $$25$$% more than person $$B$$'s salary, then by what percentage is $$B$$'s salary less than $$A$$'s salary?                

A) $$20$$%

B) $$30$$%

C) $$33.33$$%

D) $$25$$%

Explanation:

Let $$B$$'s salary be $$100$$. Then $$A$$'s salary is $$125$$. The difference in their salaries is $$25$$. To find how much percent $$B$$'s salary is less than $$A$$'s, we calculate based on $$A$$'s salary: $$\frac{25}{125} \times 100 = \frac{1}{5} \times 100 = 20$$%.

Question 56 Unattempted

                    Consider the following statements about the ozone layer:

1. The stratospheric ozone layer absorbs much of the Sun's harmful ultraviolet radiation.

2. Chlorofluorocarbons can contribute to ozone depletion.

3. The ozone layer is located mainly in the troposphere, closest to Earth's surface.

Which statements are correct?

A) 1, 2 and 3

B) 2 and 3 only

C) 1 and 2 only

D) 1 only

Explanation:

Statements 1 and 2 are correct. The ozone layer is concentrated in the stratosphere, where it absorbs much of the Sun's harmful ultraviolet radiation. Certain chlorine-containing compounds released from CFCs contribute to ozone depletion.

Question 57 Unattempted

                    Consider the following statements about the 73rd Constitutional Amendment:

1. It gave constitutional status to Panchayati Raj institutions.

2. It introduced provisions for reservation of seats for Scheduled Castes and Scheduled Tribes in Panchayats.

3. It inserted Part IX into the Constitution.

Which statements are correct?

A) 1 and 2 only

B) 1, 2 and 3

C) 1 and 3 only

D) 2 and 3 only

Explanation:

All three statements are correct. The 73rd Constitutional Amendment Act, 1992, gave constitutional status to Panchayati Raj institutions, provided for reservations including for SCs and STs, and inserted Part IX, covering Articles 243 to 243-O, into the Constitution.

Question 58 Unattempted

                    Find the missing number in the Number Analogy: $$68 : 130 :: 222 : ?$$                

A) $$350$$

B) $$360$$

C) $$343$$

D) $$352$$

Explanation:

The relationship relies on cubes of consecutive numbers: $$68 = 4^3 + 4$$ and $$130 = 5^3 + 5$$. Similarly, $$222 = 6^3 + 6$$. The next number will follow $$7^3 + 7 = 343 + 7 = 350$$.

Question 59 Unattempted

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

A) Magnanimous

B) Placable

C) Intransigent

D) Capricious

Explanation:

'Obdurate' means stubbornly refusing to change one's opinion or course of action. 'Intransigent' means unwilling to compromise, making it the closest synonym.

Question 60 Unattempted

                    Choose the correctly spelt word.                

A) Consciencious

B) Conscientious

C) Conscientous

D) Conscienciousness

Explanation:

'Conscientious' is the correct spelling. It means careful, diligent and guided by a sense of duty.

Question 61 Unattempted

                    If the symbol $$+$$ means $$\times$$, $$-$$ means $$+$$, $$\times$$ means $$\div$$, and $$\div$$ means $$-$$, then find the value of the expression: $$6 - 9 + 8 \times 3 \div 20$$                

A) $$8$$

B) $$14$$

C) $$10$$

D) $$12$$

Explanation:

By substituting the symbols according to the given rules, the expression becomes: $$6 + 9 \times 8 \div 3 - 20$$. Using BODMAS rule: $$8 \div 3 = \frac{8}{3}$$. Then, $$9 \times \left(\frac{8}{3}\right) = 24$$. Now, addition and subtraction: $$6 + 24 - 20 = 30 - 20 = 10$$.

Question 62 Unattempted

                    Read the passage and answer the question.

'A young librarian noticed that many children visited the library but rarely borrowed books. Instead of reprimanding them, she began reading short stories aloud every Friday. Gradually, the children started asking questions, recommending stories to one another, and borrowing books to read at home. She discovered that curiosity, when encouraged patiently, often produces better results than criticism.'

What is the central lesson of the passage?

A) Criticism is the most effective method of improving reading habits.

B) Libraries are useful only when books are read aloud.

C) Patient encouragement can nurture curiosity and change behaviour.

D) Children should be compelled to borrow books regularly.

Explanation:

The librarian encourages children through storytelling rather than criticism. Their growing interest in reading illustrates that patient encouragement can foster curiosity and positive behavioural change.

Question 63 Unattempted

                    A custom symbolic operation is defined as $$a \star b = a^2 + b^2 - a b$$. Determine the value of $$5 \star 3$$.                

A) $$19$$

B) $$20$$

C) $$18$$

D) $$17$$

Explanation:

Substitute $$a = 5$$ and $$b = 3$$ into the defined function: $$5 \star 3 = 5^2 + 3^2 - (5 \times 3)$$. Calculating the terms: $$25 + 9 - 15 = 34 - 15 = 19$$.

Question 64 Unattempted

                    What is the next term in the number series: $$2, 10, 30, 68, ?$$                

A) $$125$$

B) $$140$$

C) $$130$$

D) $$135$$

Explanation:

The series follows the pattern $$n^3 + n$$. For $$n=1$$, $$1^3+1 = 2$$. For $$n=2$$, $$2^3+2 = 10$$. For $$n=3$$, $$3^3+3 = 30$$. For $$n=4$$, $$4^3+4 = 68$$. Therefore, the next term for $$n=5$$ is $$5^3+5 = 125+5 = 130$$.

Question 65 Unattempted

                    The lengths of the diagonals of a regular rhombus are $$16\text{ cm}$$ and $$12\text{ cm}$$. Find the perimeter of the rhombus.                

A) $$60\text{ cm}$$

B) $$48\text{ cm}$$

C) $$28\text{ cm}$$

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

Explanation:

The diagonals of a rhombus bisect each other at right angles $$(90^\circ)$$. The half-diagonals are $$8\text{ cm}$$ and $$6\text{ cm}$$. By the Pythagorean theorem, the side $$s$$ of the rhombus is $$s = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\text{ cm}$$. The perimeter is $$4s = 4 \times 10 = 40\text{ cm}$$.

Question 66 Unattempted

                    Two unbiased six-sided dice are rolled simultaneously. What is the simple probability of getting a sum of exactly $$8$$?                

A) $$\frac{5}{36}$$

B) $$\frac{1}{6}$$

C) $$\frac{7}{36}$$

D) $$\frac{1}{9}$$

Explanation:

The total number of possible outcomes when two dice are rolled is $$6 \times 6 = 36$$. The favorable outcomes that result in a sum of $$8$$ are $$(2,6), (3,5), (4,4), (5,3),$$ and $$(6,2)$$. There are $$5$$ favorable outcomes. Therefore, the probability $$P(E) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{5}{36}$$.

Question 67 Unattempted

                    The graphs of the linear equations $$2x + 3y = 6$$ and $$4x + 6y = 18$$ represent lines that are:                

A) Parallel

B) Intersecting exactly at one point

C) Intersecting at two points

D) Coincident

Explanation:

For linear equations $$a_1x + b_1y = c_1$$ and $$a_2x + b_2y = c_2$$, if $$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$, the lines are parallel. Checking the ratios: $$\frac{2}{4} = \frac{1}{2}$$, $$\frac{3}{6} = \frac{1}{2}$$, and $$\frac{6}{18} = \frac{1}{3}$$. Since $$\frac{1}{2} = \frac{1}{2} \neq \frac{1}{3}$$, the lines are parallel.

Question 68 Unattempted

                    In Date Matching and Modular Arithmetic: If $$1^{\text{st}}$$ January $$2004$$ was a Thursday, what day of the week was $$1^{\text{st}}$$ January $$2005$$?                

A) Saturday

B) Monday

C) Friday

D) Sunday

Explanation:

The year $$2004$$ is a leap year, containing $$366$$ days. Since $$366 \equiv 2 \pmod{7}$$, a leap year offsets the calendar by exactly $$2$$ days. Therefore, the day shifts from Thursday to Saturday.

Question 69 Unattempted

                    Which vitamin deficiency is most directly associated with scurvy?                

A) Vitamin D

B) Vitamin C

C) Vitamin B12

D) Vitamin A

Explanation:

Scurvy results from vitamin C deficiency. Vitamin C is required for collagen synthesis, and its deficiency can cause bleeding gums, poor wound healing and other connective-tissue problems.

Question 70 Unattempted

                    Two numbers are in the ratio $$3:5$$. If $$9$$ is subtracted from each number, the new numbers are in the ratio $$12:23$$. What is the smaller number?                

A) $$27$$

B) $$39$$

C) $$33$$

D) $$45$$

Explanation:

Let the numbers be $$3x$$ and $$5x$$. According to the given condition, $$\frac{3x - 9}{5x - 9} = \frac{12}{23}$$. Cross-multiplying gives $$23(3x - 9) = 12(5x - 9)$$. This simplifies to $$69x - 207 = 60x - 108$$. Solving for $$x$$, we get $$9x = 99$$, which means $$x = 11$$. The smaller number is $$3x = 3 \times 11 = 33$$.

Question 71 Unattempted

                    A shopkeeper sells an article at a profit of $$20$$%. If he had bought it at $$10$$% less and sold it for ₹ $$18$$ less, he would have made a $$30$$% profit. Find the original cost price of the article.                

A) ₹ $$450$$

B) ₹ $$500$$

C) ₹ $$600$$

D) ₹ $$750$$

Explanation:

Let the original Cost Price (CP) be $$100x$$. Original Selling Price (SP) = $$120x$$. New CP = $$90x$$ (since bought at $$10$$% less). New SP to make $$30$$% profit = $$90x + (30$$% of $$90x) = 90x + 27x = 117x$$. The difference in selling prices is $$120x - 117x = 3x$$. Given that the difference is ₹ $$18$$, we have $$3x = 18 \implies x = 6$$. Original CP = $$100 \times 6 =$$ ₹ $$600$$.

Question 72 Unattempted

                    Choose the antonym of 'Ephemeral'.                

A) Fleeting

B) Momentary

C) Transient

D) Perennial

Explanation:

'Ephemeral' means lasting for a very short time. 'Perennial' means lasting for a long time or recurring indefinitely, making it the appropriate antonym.

Question 73 Unattempted

                    If $$x + \frac{1}{x} = 5$$, find the value of $$x^3 + \frac{1}{x^3}$$.                

A) $$125$$

B) $$140$$

C) $$110$$

D) $$115$$

Explanation:

Using the algebraic identity $$a^3 + b^3 = (a + b)^3 - 3ab(a + b)$$, we have $$x^3 + \frac{1}{x^3} = \left(x + \frac{1}{x}\right)^3 - 3\left(x\right)\left(\frac{1}{x}\right)\left(x + \frac{1}{x}\right)$$. Substituting the given value gives $$5^3 - 3(1)(5) = 125 - 15 = 110$$.

Question 74 Unattempted

                    Consider the following statements about the Indian monsoon:

1. Differential heating of land and sea contributes to monsoon circulation.

2. The Himalayas influence the distribution and movement of monsoon systems.

3. The southwest monsoon generally reaches Kerala before most other parts of mainland India.

Which statements are correct?

A) 1 and 2 only

B) 1, 2 and 3

C) 2 and 3 only

D) 1 and 3 only

Explanation:

All three statements are correct. Differential heating helps establish seasonal pressure differences, the Himalayas influence atmospheric circulation and rainfall distribution, and the southwest monsoon normally makes its initial landfall over Kerala before advancing across India.

Question 75 Unattempted

                    A mechanism dictates that an object ascends a $$12\text{ m}$$ vertical shaft. In the first minute, it ascends $$2\text{ m}$$, but in the subsequent minute, it slips down $$1\text{ m}$$. How many minutes will it take for the object to exactly reach the top at $$12\text{ m}$$?                

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

B) $$20\text{ mins}$$

C) $$21\text{ mins}$$

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

Explanation:

The object has an effective upward movement of $$1\text{ m}$$ every $$2$$ minutes. It will continue this alternating pattern until it reaches $$10\text{ m}$$, which will take $$2 \times 10 = 20$$ minutes. In the $$21^{\text{st}}$$ minute, it will ascend $$2\text{ m}$$ and reach exactly $$12\text{ m}$$ without needing to slip back down.

Question 76 Unattempted

                    The difference between simple interest and compound interest on a certain principal amount for $$2$$ years at $$10$$% per annum is ₹ $$40$$. Find the principal amount.                

A) ₹ $$5000$$

B) ₹ $$4000$$

C) ₹ $$3000$$

D) ₹ $$6000$$

Explanation:

The formula for the difference between CI and SI for $$2$$ years is $$D = P \left(\frac{R}{100}\right)^2$$. Substituting the given values: $$40 = P \left(\frac{10}{100}\right)^2$$. This gives $$40 = P \times \left(\frac{1}{10}\right)^2 = P \times \frac{1}{100}$$. Solving for $$P$$, we get $$P = 40 \times 100 =$$ ₹ $$4000$$.

Question 77 Unattempted

                    Match the following networking devices with their principal functions:

DeviceFunction
i. Router1. Forwards packets between networks
ii. Switch2. Forwards Ethernet frames within a LAN using MAC addresses
iii. Repeater3. Regenerates or retransmits signals to extend a link
iv. Firewall4. Enforces traffic-security rules

Choose the correct matching code.                

Device	Function
i. Router	1. Forwards packets between networks
ii. Switch	2. Forwards Ethernet frames within a LAN using MAC addresses
iii. Repeater	3. Regenerates or retransmits signals to extend a link
iv. Firewall	4. Enforces traffic-security rules

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

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

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

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

Explanation:

A router forwards packets between networks, a switch commonly forwards Ethernet frames using MAC addresses, a repeater extends a link by regenerating or retransmitting signals, and a firewall applies security rules to network traffic.

Question 78 Unattempted

                    Which of the following statements about the Indus River system is correct?

1. The Chenab is formed by the confluence of the Chandra and Bhaga rivers.

2. The Jhelum originates from Verinag in Jammu and Kashmir.

3. The Ravi flows through the Kashmir Valley before entering Pakistan.

Select the correct answer.

A) 2 and 3 only

B) 1 and 3 only

C) 1 and 2 only

D) 1, 2 and 3

Explanation:

Statements 1 and 2 are correct. The Chenab is formed by the confluence of the Chandra and Bhaga rivers near Tandi in Himachal Pradesh. The Jhelum originates at Verinag in Kashmir. The Ravi does not flow through the Kashmir Valley.

Question 79 Unattempted

                    Testing space orientation: A particle starts at the origin $$(0,0)$$, translates $$4$$ units along the positive x-axis to $$(4,0)$$, rotates $$90^{\circ}$$ counter-clockwise, and translates $$3$$ units straight. What is the shortest straight-line distance from its final position to the origin?                

A) $$8$$

B) $$6$$

C) $$7$$

D) $$5$$

Explanation:

The final coordinates of the particle are $$(4,3)$$. The shortest distance to the origin is calculated using the Pythagorean theorem: $$d = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$.

Question 80 Unattempted

                    Which statement correctly distinguishes GDP at market prices from GDP at factor cost in the traditional national-income framework?                

A) GDP at market prices equals GDP at factor cost plus indirect taxes minus subsidies.

B) GDP at market prices excludes indirect taxes entirely.

C) GDP at factor cost always exceeds GDP at market prices.

D) GDP at market prices equals GDP at factor cost minus indirect taxes plus subsidies.

Explanation:

In the traditional framework, GDP at market prices is obtained by adding indirect taxes and subtracting subsidies from GDP at factor cost. Thus, GDP at market prices = GDP at factor cost + indirect taxes − subsidies.

Question 81 Unattempted

                    Given the compound inequality statement: $$M \ge N > O = P \le Q$$. <br>Conclusions:<br>I. $$M > P$$<br>II. $$O \le Q$$<br>Which of the conclusions are definitively true?                

A) Neither I nor II follows

B) Both I and II follow

C) Only I follows

D) Only II follows

Explanation:

From the statement $$M \ge N > O$$, we can deduce $$M > O$$. Since $$O = P$$, substituting $$P$$ gives $$M > P$$, so Conclusion I is true. From $$O = P \le Q$$, we directly read $$O \le Q$$, making Conclusion II true. Both follow.

Question 82 Unattempted

                    A right circular cone and a right circular cylinder have the same base radius $$r$$ and the same height $$h$$. What is the ratio of the volume of the cylinder to the volume of the cone?                

A) $$1:1$$

B) $$3:1$$

C) $$4:3$$

D) $$1:3$$

Explanation:

The volume of a cylinder is given by $$V_{\text{cyl}} = \pi r^2 h$$. The volume of a cone is $$V_{\text{cone}} = \frac{1}{3} \pi r^2 h$$. The ratio $$\frac{V_{\text{cyl}}}{V_{\text{cone}}} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h} = \frac{1}{\frac{1}{3}} = 3$$. Therefore, the ratio is $$3:1$$.

Question 83 Unattempted

                    Which of the following correctly describes the role of the Finance Commission of India?                

A) It determines the repo rate for the RBI.

B) It appoints the Chief Ministers of states.

C) It conducts elections to Parliament and state legislatures.

D) It recommends the distribution of certain tax revenues between the Union and the states.

Explanation:

Under Article 280 of the Constitution, the President constitutes a Finance Commission to make recommendations on matters including the distribution of tax proceeds between the Union and states and grants-in-aid to states.

Question 84 Unattempted

                    Arrange the following parts to form a meaningful sentence:

P. despite repeated warnings from experts

Q. many communities continue to ignore

R. the long-term consequences of water scarcity

S. and postpone essential conservation measures

A) P-Q-R-S

B) Q-R-S-P

C) R-Q-P-S

D) S-P-Q-R

Explanation:

The intended sequence is P-Q-R-S: 'Despite repeated warnings from experts, many communities continue to ignore the long-term consequences of water scarcity and postpone essential conservation measures.'

Question 85 Unattempted

                    Identify the part of the sentence containing an error: 'Hardly had the committee reached a decision / than the chairman / announced the result / to the waiting candidates.'                

A) to the waiting candidates

B) Hardly had the committee reached a decision

C) than the chairman

D) announced the result

Explanation:

'Hardly' is conventionally followed by 'when' or 'before', not 'than', in this correlative construction. The correct sentence is: 'Hardly had the committee reached a decision when the chairman announced the result to the waiting candidates.'

Question 86 Unattempted

                    With reference to the Revolt of 1857, consider the following statements:

1. Mangal Pandey was associated with the events at Barrackpore.

2. Begum Hazrat Mahal led the resistance against the British in Lucknow.

3. Bahadur Shah II was proclaimed the leader of the revolt by the rebels in Delhi.

Which of the statements given above are correct?

A) 1 and 3 only

B) 1 and 2 only

C) 1, 2 and 3

D) 2 and 3 only

Explanation:

All three statements are correct. Mangal Pandey was associated with Barrackpore in 1857, Begum Hazrat Mahal led resistance in Lucknow, and Bahadur Shah II was proclaimed the symbolic leader of the revolt in Delhi.

Question 87 Unattempted

                    If $$\tan(\theta) = \frac{3}{4}$$, what is the value of the expression $$\frac{\sin(\theta) + \cos(\theta)}{\sin(\theta) - \cos(\theta)}$$?                

A) $$\frac{1}{7}$$

B) $$-\frac{1}{7}$$

C) $$7$$

D) $$-7$$

Explanation:

Divide the numerator and the denominator by $$\cos(\theta)$$. The expression becomes $$\frac{\tan(\theta) + 1}{\tan(\theta) - 1}$$. Substituting $$\tan(\theta) = \frac{3}{4}$$, we get $$\frac{\frac{3}{4} + 1}{\frac{3}{4} - 1} = \frac{\frac{7}{4}}{-\frac{1}{4}}$$. The $$4$$ cancels out, leaving $$\frac{7}{-1} = -7$$.

Question 88 Unattempted

                    In two similar triangles $$\Delta ABC$$ and $$\Delta PQR$$, the ratio of their corresponding sides is $$3:5$$. What is the ratio of their areas?                

A) $$27:125$$

B) $$9:25$$

C) $$3:5$$

D) $$6:10$$

Explanation:

According to the property of similar triangles, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, the ratio of their areas is $$\left(\frac{3}{5}\right)^2 = \frac{9}{25}$$ or $$9:25$$.

Question 89 Unattempted

                    Find the missing variable $$x$$ in the following number classification grid represented by rows: Row 1 is $$[3, 5, 34]$$, Row 2 is $$[6, 8, 100]$$, and Row 3 is $$[4, 7, x]$$.                

A) $$63$$

B) $$64$$

C) $$66$$

D) $$65$$

Explanation:

The logic in each row follows $$a^2 + b^2 = c$$. For Row 1: $$3^2 + 5^2 = 9 + 25 = 34$$. For Row 2: $$6^2 + 8^2 = 36 + 64 = 100$$. For Row 3: $$4^2 + 7^2 = 16 + 49 = 65$$. Therefore, $$x = 65$$.

Question 90 Unattempted

                    Match the following computer ports and interfaces with their typical functions:

List IList II
i. HDMI1. Wired Ethernet networking
ii. RJ-45 Ethernet port2. Digital audio and video transmission
iii. USB3. Peripheral connection and data transfer
iv. PS/24. Legacy keyboard or mouse connection

Select the correct matching code.                

List I	List II
i. HDMI	1. Wired Ethernet networking
ii. RJ-45 Ethernet port	2. Digital audio and video transmission
iii. USB	3. Peripheral connection and data transfer
iv. PS/2	4. Legacy keyboard or mouse connection

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

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

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

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

Explanation:

HDMI carries digital audio and video, RJ-45 is commonly used for Ethernet, USB connects peripherals and supports data transfer, and PS/2 is a legacy interface for keyboards and mice.

Question 91 Unattempted

                    Find the missing term $$x$$ in the alternating number series: $$3, 7, 6, 10, 9, 13, x, 16$$                

A) $$15$$

B) $$14$$

C) $$12$$

D) $$11$$

Explanation:

This is a blended alternating series. The odd-positioned sequence is $$3, 6, 9, x$$, which increases by $$+3$$, meaning $$x = 9 + 3 = 12$$. The even-positioned sequence is $$7, 10, 13, 16$$, which also increases by $$+3$$ correctly.

Question 92 Unattempted

                    Consider the following statements about computer memory and storage:

1. SRAM does not require periodic refresh in the same way that DRAM does.

2. DRAM is commonly used to implement a computer's main memory.

3. ROM is necessarily impossible to modify under all circumstances.

4. Virtual memory allows an operating system to use secondary storage to support the illusion of a larger address space than physical RAM alone provides.

Which statements are correct?

A) 2, 3 and 4 only

B) 1, 2 and 4 only

C) 1 and 2 only

D) 1, 2, 3 and 4

Explanation:

Statements 1, 2 and 4 are correct. SRAM does not need periodic refresh, DRAM is widely used for main memory, and virtual memory can use storage to back portions of a process's address space. Statement 3 is false because some ROM-family technologies, such as EEPROM and flash memory, can be erased and reprogrammed.

Question 93 Unattempted

                    Which statement about Microsoft PowerPoint is correct?                

A) The Notes pane is used exclusively to insert formulas into slides.

B) Transitions control the spelling and grammar of slide text.

C) Animations can only be applied to entire presentations, not individual objects.

D) Slide Master can control recurring design elements and layouts across a presentation.

Explanation:

Slide Master is used to manage common design elements, formatting and layouts across slides. Transitions control how one slide moves to the next, while animations apply effects to objects such as text, shapes and images.

Question 94 Unattempted

                    What does the idiom 'To throw down the gauntlet' mean?                

A) To surrender without resistance

B) To conceal one's intentions

C) To withdraw from a competition secretly

D) To issue a challenge

Explanation:

'To throw down the gauntlet' means to issue a challenge or invite someone to a contest or confrontation.

Question 95 Unattempted

                    Consider the following statements regarding the Constitution of India:

1. Article 19 guarantees certain freedoms to citizens.

2. Article 21 protects life and personal liberty.

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

Which statements are correct?

A) 1, 2 and 3

B) 1 only

C) 2 and 3 only

D) 1 and 2 only

Explanation:

Statements 1 and 2 are correct. Article 19 provides specified freedoms to citizens, while Article 21 protects life and personal liberty. Fundamental Duties were added by the 42nd Constitutional Amendment Act, 1976, and were not part of the original Constitution.

Question 96 Unattempted

                    In what ratio must a grocer mix two varieties of tea costing ₹ $$60$$ per kg and ₹ $$65$$ per kg so that by selling the mixed variety at ₹ $$68.20$$ per kg, he may gain $$10$$%?                

A) $$3:2$$

B) $$2:1$$

C) $$5:4$$

D) $$4:3$$

Explanation:

Selling Price (SP) of $$1$$ kg mixture = ₹ $$68.20$$, Gain = $$10$$%. Cost Price (CP) of $$1$$ kg mixture = $$\frac{100}{110} \times 68.20 =$$ ₹ $$62$$. By the rule of alligation: Cost of cheaper ($$60$$) and cost of dearer ($$65$$). Mean price = $$62$$. Ratio = $$(65 - 62) : (62 - 60) = 3 : 2$$.

Question 97 Unattempted

                    Choose the correct one-word substitution: 'A person who deliberately sets fire to property, especially maliciously, is called a/an ______.'                

A) Defaulter

B) Extortionist

C) Embezzler

D) Arsonist

Explanation:

An 'arsonist' is a person who deliberately and unlawfully sets fire to property. An extortionist obtains something through coercion, while an embezzler misappropriates entrusted funds.

Question 98 Unattempted

                    A user receives an email that imitates their bank and asks them to click a link to verify their password. The link leads to a fake login page. Which security threat is most directly involved, and what is the best preventive measure?                

A) Phishing; independently open the bank's official app or type its verified address rather than using the email link

B) DDoS; increase the screen resolution

C) Worm infection; disable all keyboard shortcuts

D) Defragmentation; run a disk defragmenter before logging in

Explanation:

This is phishing: an attacker impersonates a trusted organization to steal credentials or sensitive information. Avoid clicking unexpected login links, verify the sender and domain, access the bank through its official app or verified address, and use multifactor authentication where available.

Question 99 Unattempted

                    If the variance $$\sigma^2$$ of a given data set is $$144$$, what is its standard deviation $$\sigma$$?                

A) $$14$$

B) $$72$$

C) $$12$$

D) $$16$$

Explanation:

The standard deviation is defined as the positive square root of the variance. Therefore, $$\sigma = \sqrt{144} = 12$$.

Question 100 Unattempted

                    Evaluate the nested square root: $$\sqrt{248 + \sqrt{52 + \sqrt{144}}}$$                

A) $$14$$

B) $$24$$

C) $$18$$

D) $$16$$

Explanation:

Start evaluating from the innermost square root: $$\sqrt{144} = 12$$. Substitute this back: $$\sqrt{52 + 12} = \sqrt{64} = 8$$. Substitute this back into the outermost square root: $$\sqrt{248 + 8} = \sqrt{256} = 16$$.

Unlock your test result

YOUR SCORE

Leaderboard Hidden

Detailed Solutions