SSC CGL Undated PYQs

Question 1

If Sin θ = 20/29 , then what is the value of Sec Sin θ ?

Accepted Answer

Given Sin θ = Perpendicular/Hypotenuse = 20/29. Base = √(29² - 20²) = √441 = 21. Therefore, Sec θ = Hypotenuse/Base = 29/21.

Question 2

If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?

Accepted Answer

Volume is proportional to r²h. A 25% increase in radius makes r² become 25/16. To keep volume constant, height must become 16/25, which is a reduction of 9/25 or 36%.

Question 3

What is the slope of the line perpendicular to the line passing through the points (3 , -2) and (4 , 2)?

Accepted Answer

The slope of the line through (3, -2) and (4, 2) is (2 - (-2))/(4 - 3) = 4. The perpendicular line's slope is the negative reciprocal, -1/4.

Question 4

In the following question, select the missing number from the given series. 19, 11, 13, 16, 15, 17, 13, 19, 21, ?

Accepted Answer

The sequence consists of three interleaved series. The first series (1st, 4th, 7th terms) is 19, 16, 13, decreasing by 3. The next term is 13 - 3 = 10.

Question 5

In the following question, out of the four alternatives, select the alternative which will improve the bracketed part of the sentence. In case no improvement is needed, select "no improvement". I would love to come to your party! Thank you for (invites) me.

Accepted Answer

The preposition 'for' must be followed by a gerund (verb + -ing) when it acts as the object of the preposition. Thus, 'inviting' is the correct form.

Question 6

Improve the bracketed part of the sentence. He jumped off the train while it (had been running).

Accepted Answer

The action of jumping happened while the train was in continuous motion. Past continuous tense ('was running') correctly describes an ongoing action in the past.

Question 7

Doldrums pressure belts lies in between which of the following latitudes?

Accepted Answer

The Doldrums, or equatorial low-pressure belt, lies between 5° North and 5° South latitudes. It is characterized by calm, light winds due to intense heating at the equator.

Question 8

Who among the following devised the technique IVF (In vitro Fertilization)?

Accepted Answer

Robert Edwards, a British physiologist, pioneered the IVF technique alongside Patrick Steptoe. This breakthrough in reproductive medicine led to the birth of the first test-tube baby in 1978.

Question 9

Which among the following is not an example of emulsion?

Accepted Answer

An emulsion is a colloid of two or more immiscible liquids. Curd is a gel (liquid dispersed in a solid), not an emulsion like milk, butter, or whipped cream.

Question 10

Which film won the award for Best Film at the 61st Filmfare Award held in 2016?

Accepted Answer

Sanjay Leela Bhansali's 'Bajirao Mastani' won the Best Film award at the 61st Filmfare Awards in 2016. It dominated the ceremony, winning several other major categories including Best Director.

Question 11

If a - b = -1 and ab = 6, then what is the value of a3 - b3?

Accepted Answer

Use the identity a³ - b³ = (a - b)³ + 3ab(a - b). Substituting the given values, we get (-1)³ + 3(6)(-1) = -1 - 18 = -19.

Question 12

If 35 % 31 = 12, 92 % 30 = 14 then what is the value of 15 % 24 = ?

Accepted Answer

The logic is to add the individual digits of both numbers. For 15 % 24: (1+5) + (2+4) = 6 + 6 = 12.

Question 13

Who among the following is the executive head of state in India? ?

Accepted Answer

Article 53 of the Constitution states that the executive power of the Union is vested in the President. Thus, the President is the executive head of the Indian state.

Question 14

"Forests" is listed in the __________ list given in the Seventh Schedule in the Constitution of India.

Accepted Answer

Originally in the State List, "Forests" was moved to the Concurrent List by the 42nd Amendment Act, 1976, allowing both central and state governments to legislate on it.

Question 15

Which amongst the following is not in the list of Maharatna?

Accepted Answer

At the time this question was asked, Hindustan Petroleum Corporation Limited (HPCL) was a Navratna, not a Maharatna. It was later granted Maharatna status in 2019.

Question 16

The weights of 4 boxes are 80, 60, 90 and 70 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?

Accepted Answer

The sum of all four boxes is 300 kg. The combinations of three boxes give 210, 220, 230, and 240 kg. Thus, 290 kg cannot be formed.

Question 17

If D and E are points on the sides AB and AC respectively of a triangle ABC such that DE||BC. If AD = x cm, DB = (x – 3) cm, AE = (x + 3) cm and EC = (x – 2) cm, then what is the value (in cm) of x?

Accepted Answer

By the Basic Proportionality Theorem, AD/DB = AE/EC. Substituting the values gives x/(x-3) = (x+3)/(x-2). Cross-multiplying yields x^2 - 2x = x^2 - 9, which simplifies to 2x = 9, so x = 4.5.

Question 18

How many diagonals are there in octagon?

Accepted Answer

The number of diagonals in an n-sided polygon is calculated using the formula n(n-3)/2. For an octagon, n=8. Therefore, 8(8-3)/2 = (8 × 5)/2 = 20 diagonals.

Question 19

Select the related number from the given alternatives. 99 : 101 :: 100 : ?

Accepted Answer

The pattern involves adding 2 to the first number to get the second number. Since 99 + 2 = 101, similarly, 100 + 2 = 102.

Question 20

If a + b = 4 and ab = -5, then what is the value of a3 + b3?

Accepted Answer

Use the formula a³ + b³ = (a + b)³ - 3ab(a + b). Substitute the values: (4)³ - 3(-5)(4) = 64 + 60 = 124.