SSC CGL Undated PYQs

Question 1

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

Accepted Answer

Use the formula a³+b³+c³-3abc = (a+b+c)[(a+b+c)² - 3(ab+bc+ca)]. Substitute the given values: 9 × [9² - 3(18)] = 9 × [81 - 54] = 9 × 27 = 243.

Question 2

Noor Jahan was the wife of which Mughal emperor? 9/7/2017 Staff Selection Commision

Accepted Answer

Noor Jahan, originally named Mehr-un-Nissa, was the twentieth and most beloved wife of the Mughal Emperor Jahangir. She wielded immense political power and influence during his reign.

Question 3

What is the value of sin (–π/3) + cos(–π/6)?

Accepted Answer

Using trigonometric identities, sin(-θ) = -sin(θ) and cos(-θ) = cos(θ). Thus, sin(-π/3) = -√3/2 and cos(-π/6) = √3/2. Their sum is -√3/2 + √3/2 = 0.

Question 4

What is the minimum age required to become vice-president of India?

Accepted Answer

According to Article 66 of the Indian Constitution, a candidate must be a citizen of India and have completed 35 years of age to be eligible for the Vice-President's office.

Question 5

Sum of twice a fraction and 3 times its reciprocal is 29/3. What is the fraction?

Accepted Answer

Let the fraction be x. The equation is 2x + 3/x = 29/3. Checking option 4 (9/2): 2(9/2) + 3(2/9) = 9 + 2/3 = 29/3. It satisfies the condition.

Question 6

A commodity market has a _________ structure, if there is one seller of the commodity, the commodity has no substitute, and entry into the industry by another firm is prevented.

Accepted Answer

A monopoly exists when a single seller controls the entire market for a unique product with no close substitutes, and high barriers prevent new competitors from entering.

Question 7

The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?

Accepted Answer

Using the distance formula: (k - 2)² + (-5 - 7)² = 13². This gives (k - 2)² + 144 = 169, so (k - 2)² = 25. Thus, k - 2 = 5, meaning k = 7.

Question 8

At which of the following stadium Sachin Tendulkar scored his 100th international century?

Accepted Answer

Sachin Tendulkar scored his historic 100th international century against Bangladesh in March 2012 at the Sher-e-Bangla National Stadium in Mirpur, Dhaka.

Question 9

India's first official census operation was undertaken in which year?

Accepted Answer

The first complete and official census of India was conducted in 1881 under Lord Ripon. A partial, non-synchronous census had occurred earlier in 1872 under Lord Mayo.

Question 10

Which of the following won the Best Feature Film Award at the 64th National Film Awards held in the year 2017?

Accepted Answer

The Marathi film 'Kaasav', directed by Sumitra Bhave and Sunil Sukthankar, won the Best Feature Film at the 64th National Film Awards in 2017 for its environmental theme.

Question 11

The average product curve are inverse ____ shaped. 9/7/2017 Staff Selection Commision

Accepted Answer

The average product (AP) curve initially rises, reaches a maximum, and then falls due to the law of variable proportions, making it an inverse U-shaped curve.

Question 12

__________ says that if we keep increasing the employment of an input, with other inputs fixed, eventually a point will be reached after which the resulting addition to output (i.e., marginal product of that input) will start falling.

Accepted Answer

The Law of diminishing marginal product states that adding more of one factor of production, while holding others constant, will eventually yield lower per-unit returns.

Question 13

The ratio of number of cans of orange, pineapple and mixed fruit juices kept in a store is 8 : 9 : 15. If the store sells 25%, 33.33% and 20% of orange, pineapple and mixed fruit juices cans respectively, then what is the ratio of number of cans of these juices in the remaining stock? ?

Accepted Answer

Calculate remaining quantities: Orange is 75% of 8 = 6. Pineapple is 66.67% (2/3) of 9 = 6. Mixed fruit is 80% of 15 = 12. The new ratio is 6:6:12, which simplifies to 1:1:2.

Question 14

Sultan Mahmud was a ruler of_____.

Accepted Answer

Sultan Mahmud, also known as Mahmud of Ghazni, was the ruler of the Ghaznavid Empire. He ruled from the city of Ghazni in present-day Afghanistan and is famous for his invasions of India.

Question 15

A fraction is greater than its reciprocal by 9/20. What is the fraction?

Accepted Answer

Let the fraction be x. Given x - 1/x = 9/20. Checking options, if x = 5/4, then 5/4 - 4/5 = (25-16)/20 = 9/20. Thus, 5/4 is correct.

Question 16

Two trains are moving in the opposite direction at speed of 30 km/hr and 45 km/hr respectively, whose lengths are 450 m and 550 m respectively. What is the time taken (in seconds) by slower train to cross the faster train?

Accepted Answer

Relative speed in opposite directions is 30 + 45 = 75 km/hr, which is 125/6 m/s. Total distance is 450 + 550 = 1000 m. Time = 1000 / (125/6) = 48 seconds.

Question 17

Select the related letters from the given alternatives. WUV : TRS :: QOP : ? WUV : TRS :: QOP : ?

Accepted Answer

Each letter in the first term is shifted backward by 3 positions to get the second term (W-3=T, U-3=R, V-3=S). Applying this to QOP gives NLM.

Question 18

ax + 3y = 6 has slope -2/3. What is the value of a?

Accepted Answer

The equation ax + 3y = 6 can be rewritten as y = (-a/3)x + 2. The slope is -a/3. Equating -a/3 = -2/3 gives a = 2.

Question 19

If 'P 3 Q' means 'P is daughter of Q', 'P 5 Q' means 'P is father of Q', 'P 7 Q' means 'P is mother of Q' and 'P 9 Q' means 'P is sister of Q', then how is J related to K in J 3 L 9 N 3 O 5 K?

Accepted Answer

J is L's daughter. L is N's sister, and N is O's daughter, making L, N, and K siblings (O is their father). Thus, J is K's sister's daughter, i.e., niece.

Question 20

In the following question, select the odd letters from the given alternatives.

Accepted Answer

In all options except LNQ, the letters follow a +2, +2 pattern (e.g., F+2=H, H+2=J). LNQ follows a +2, +3 pattern, making it the odd one out.