SSC CGL 2024 PYQs

Question 1

If 2cosec2θ + 3cot2θ = 17, then the value of 'θ' when 0° ≤ θ ≤ 90° is:

Accepted Answer

Use the identity cosec²θ = 1 + cot²θ. Substitute this into the equation to get a quadratic in cot²θ. Solve for cot²θ, then find cotθ and subsequently θ.

Question 2

A grocer professes to sell rice at the cost price, but uses a fake weight of 870 g for 1 kg. Find his profit percentage (correct to two decimal places).

Accepted Answer

The grocer sells 1000g but delivers only 870g. Profit is (1000-870) = 130g. Profit percentage = (130/870) * 100 = 14.94%.

Question 3

If the sum of three numbers is 18 and the sum of their squares is 36, then find the difference between the sum of their cubes and three times of their product.

Accepted Answer

Use the identity a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca). First, find (ab+bc+ca) using (a+b+c)² = a²+b²+c²+2(ab+bc+ca). Substitute values to get the result.

Question 4

Simplify 21 - [6 + 7 - {3.22 - (1.1 × 0.2)}].

Accepted Answer

Follow BODMAS: first solve the innermost parenthesis (1.1 × 0.2) = 0.22. Then {3.22 - 0.22} = 3. Next, [6 + 7 - 3] = 10. Finally, 21 - 10 = 11.

Question 5

A shopkeeper, on the eve of Diwali, allowed a series of discounts on television sets. Find the selling price of a television set, if the marked price of television is ₹1,200 and successive discounts are 15% and 10%.

Accepted Answer

First discount: 15% of ₹1200 = ₹180. Price after first discount = ₹1200 - ₹180 = ₹1020. Second discount: 10% of ₹1020 = ₹102. Selling price = ₹1020 - ₹102 = ₹918.

Question 6

The value of the expression (1.552+ 0.552+ 1.55 x 0.55) is equal to:

Accepted Answer

The expression is (a² + b² + ab). Multiplying this by (a - b) gives (a³ - b³). Here a=1.55 and b=0.55, so the answer is 1.55³ - 0.55³.

Question 7

A certain sum of money becomes seven times itself when invested at a certain rate of simple interest, in 14 years. How much time (in years, rounded off to 2 decimal places) will it take to become 18 times itself at the same rate?

Accepted Answer

If a sum becomes N times in T years, then (N-1) is proportional to T. So, (7-1)/14 = (18-1)/T. Solving for T gives T = (17*14)/6 = 39.67 years.

Question 8

The following table shows the marks (out of 100) obtained by five students in five different subjects.Student/SubjectMathsPhysicsChemistryEnglishPhysical EducationTarun6580758590Rohit6976808894Mohit7384779095Shobhit7685768678Sumit9088788268Who obtained 79% marks in all the subjects taken together?

Accepted Answer

Each subject is out of 100, so total marks are 500. 79% of 500 is 395. Calculate the sum of marks for each student and find who scored 395. Tarun scored 65+80+75+85+90 = 395.

Question 9

The average temperature of a city for the first sixteen days of January is 22ºC, and the average temperature for the last sixteen days of the same month is 26ºC. If the average temperature for the entire month is 24ºC, what is the temperature on the sixteenth day?

Accepted Answer

Total temperature for first 16 days = 16 * 22 = 352. Total for last 16 days = 16 * 26 = 416. Total for 31 days = 31 * 24 = 744. Sixteenth day temp = (352 + 416) - 744 = 768 - 744 = 24ºC.

Question 10

Select the most appropriate meaning of the given idiom.On the ball

Accepted Answer

The idiom 'on the ball' means being alert, knowledgeable, and quick to react to situations. Option 3 accurately reflects this meaning.

Question 11

Select the most appropriate ANTONYM of the underlined word.Their sporting achievements at the highest level are beingutterlyignored.

Accepted Answer

The word 'utterly' means completely or totally. Its antonym would be something indicating a small degree, which is 'minimally'.

Question 12

Select the option that can be used as a one-word substitute for the underlined group of words in the following sentence.Despite recent superficial moves toward political reconciliation, Libya remains in the grip of a bloodstained corrupt militaryexclusive circle of people with a common purpose.

Accepted Answer

The phrase 'exclusive circle of people with a common purpose' perfectly describes a 'clique'. This word refers to a small, exclusive group of people.

Question 13

The following sentence has been divided into parts. One of them may contain an error. Select the part that contains the error from the given options. If you don’t find any error, mark ‘No error’ as your answer.Neither my brother nor my brothers-in-law / attended the meeting / as his health is not more good.

Accepted Answer

The phrase 'not more good' is grammatically incorrect. The correct comparative form for 'good' is 'better'. Therefore, it should be 'not good' or 'not better'.

Question 14

Select the option that can be used as a one-word-substitute for the given group of words.A false idea or belief

Accepted Answer

A 'fallacy' is a mistaken belief, especially one based on unsound argument. This perfectly matches the definition of a false idea or belief.

Question 15

Select the option that expresses the given sentence in passive voice.Ishika saw the tiger in the forest.

Accepted Answer

To change to passive voice, the object ('the tiger') becomes the subject, 'saw' changes to 'was seen', and the original subject ('Ishika') becomes the agent with 'by'.

Question 16

Select the most appropriate synonym of the given word.Abundant

Accepted Answer

The word 'Abundant' means existing in large quantities; plentiful. 'Ample' also means enough or more than enough; plentiful. Thus, 'Ample' is the most appropriate synonym.

Question 17

Identify the most appropriate antonym of the given word.Timid

Accepted Answer

Timid means showing a lack of courage or confidence. Daring means adventurous or bold. Thus, Daring is the most appropriate antonym.

Question 18

Select the most appropriate synonym of the given word.Stationary

Accepted Answer

The word 'stationary' means not moving. 'Still' also means not moving or at rest, making it the correct synonym.

Question 19

Select the option that can be used as a one-word substitute for the given group of words.An instrument for viewing distant objects in space.

Accepted Answer

A telescope is specifically designed to observe distant objects, especially in space. The other options serve different viewing or recording purposes.

Question 20

Identify the most appropriate ANTONYM of the given word.Secure

Accepted Answer

The word 'Secure' means to protect or make safe. The most appropriate antonym is 'Attack', which means to harm or assault.