SSC CGL Undated PYQs

Question 1

What is the simplified value of tan (θ/2) + cot (θ/2)?

Accepted Answer

Convert to sine and cosine: sin(θ/2)/cos(θ/2) + cos(θ/2)/sin(θ/2) = 1/(sin(θ/2)cos(θ/2)). Multiply numerator and denominator by 2 to get 2/sin(θ), which equals 2 cosec θ.

Question 2

If the profits are added to the company's reserves and the reserves stood at Rs 150 lakhs at the end of 2015, what were the reserves (in Rs. lakhs) in the beginning of 2012?

Accepted Answer

Subtract the total profits from 2012 to 2015 (which sum to 40 lakhs) from the final reserves (150 lakhs) to find the initial reserves: 150 - 40 = 110 lakhs.

Question 3

In the following question, select the related word from the given alternatives. Ampere : Electric current : : Fathom : ?

Accepted Answer

Ampere is the standard unit used to measure electric current. Similarly, a fathom is a unit of length used specifically to measure the depth of water.

Question 4

The internal bisectors of ∠Q and ∠R of triangle PQR meet at O. If ∠P = 70°, then what is the measure of ∠QOR (in degrees)?

Accepted Answer

For internal angle bisectors meeting at O, the angle formed is ∠QOR = 90° + ∠P/2. Substituting ∠P = 70°, we get 90° + 35° = 125°.

Question 5

What is the area (in sq cm) of a circle whose circumference is 26.4 cm?

Accepted Answer

Given circumference 2πr = 26.4, we find radius r = (26.4 × 7) / 44 = 4.2 cm. The area is πr² = (22/7) × 4.2² = 55.44 sq cm.

Question 6

If Cosec θ = 17/8, then Cot θ = ?

Accepted Answer

Cosec θ = Hypotenuse/Opposite = 17/8. Using the Pythagorean triplet (8, 15, 17), the adjacent side is 15. Therefore, Cot θ = Adjacent/Opposite = 15/8.

Question 7

There are five girls - R, S, T, P and Q sitting in a row facing north. T is sitting exactly in the middle of the row. Q is sitting to the immediate right and immediate left of P and T respectively. S is not sitting at the extreme end. Who is sitting third to the left of R?

Accepted Answer

The seating arrangement from left to right is P, Q, T, S, R. T is in the middle, Q is between P and T. S is not at the end. Third to the left of R is Q.

Question 8

If a + b = 8 and ab = 15, then what is the value of a3 + b3?

Accepted Answer

Find the values of a and b. Since a + b = 8 and ab = 15, the numbers are 5 and 3. Then a³ + b³ = 5³ + 3³ = 125 + 27 = 152.

Question 9

In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question? 54 x 9 - 3 ÷ 4 = ?

Accepted Answer

Replace the symbols according to the given rules: 54 ÷ 9 + 3 - 4. Using BODMAS, first divide (54 ÷ 9 = 6), then add (6 + 3 = 9), and subtract (9 - 4 = 5).

Question 10

A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together?

Accepted Answer

Total work = LCM(72, 24, 36) = 72 units. Efficiencies: A=1, B=3, C=2. Total efficiency = 1+3+2 = 6 units/day. Time taken together = 72 / 6 = 12 days.

Question 11

If the tickets for Screen 1, Screen 2 and Screen 3 are Rs 350, Rs 300 and Rs 250 respectively, then which screen has the maximum total revenue for three shows?

Accepted Answer

Revenue is calculated by multiplying the ticket price by the number of tickets sold. Based on the provided data, Screen 3 generates the highest total revenue across the three shows.

Question 12

A sum fetched a total simple interest of Rs 1200 at the rate of 7.5%/yr in 4 years. What is the sum (in Rs)?

Accepted Answer

Using the Simple Interest formula: SI = (P × R × T) / 100. Here, 1200 = (P × 7.5 × 4) / 100. 1200 = P × 30 / 100, which gives P = 4000.

Question 13

A boat goes a certain distance at 40 km/hr and comes back the same distance at 24 km/hr. What is the average speed (in km/hr) for the total journey?

Accepted Answer

For equal distances, the average speed is calculated using 2xy/(x+y). Here, it is (2 × 40 × 24) / (40 + 24) = 1920 / 64 = 30 km/hr.

Question 14

The process of depositing a layer of zinc on iron is called ___________ .

Accepted Answer

Galvanisation is a protective process where a layer of zinc is applied to iron or steel to prevent it from rusting. The zinc acts as a sacrificial barrier.

Question 15

At what time the percentage change in number of parked cars is the maximum?

Accepted Answer

Calculate the percentage change for each given time interval using the formula: ((New - Old) / Old) × 100. The interval from 8 am to 9 am yields the highest percentage value.

Question 16

If 29$14 = 6, 37$25 = 3 then what is the value of 84$62 = ?

Accepted Answer

The pattern is the sum of the digits of the first number minus the sum of the digits of the second number. For 84$62: (8+4) - (6+2) = 12 - 8 = 4.

Question 17

If 9x3=3; 15x3=5; 60x5=12; then what is the value of 27x3 = ?

Accepted Answer

The 'x' symbol represents division in this pattern. 9/3=3, 15/3=5, and 60/5=12. Therefore, 27 divided by 3 equals 9.

Question 18

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2 + 15x + 1)?

Accepted Answer

Given 3x + 1/(5x) = 7, multiplying by 5x gives 15x² + 1 = 35x. Substitute this into the denominator: 5x / (35x + 15x) = 5x / 50x = 1/10.

Question 19

Excluding stoppages, the speed of a bus is 72 kmph and including stoppages, it is 60 kmph. For how many minutes does the bus stop per hour?

Accepted Answer

Stoppage time per hour is calculated as (Difference in speed / Speed without stoppage) × 60. Here, it is ((72 - 60) / 72) × 60 = (12 / 72) × 60 = 10 minutes.

Question 20

There are how many vocal cords in the human voice box?

Accepted Answer

The human voice box, or larynx, contains exactly two vocal cords. They are twin infoldings of mucous membrane that vibrate to produce sound.