SSC CGL Undated PYQs

Question 1

The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (1/2)∠BAC, then what is the value (in degrees) of ∠BAC?

Accepted Answer

Using the exterior angle theorem, ∠ACD = ∠ABC + ∠BAC. Let ∠BAC = 2x, so ∠ABC = x. Thus, 3x = 114°, giving x = 38°. Therefore, ∠BAC = 2x = 76°.

Question 2

After two successive discounts of 20% and 35%, an article is sold for Rs 50700. What is the marked price (in Rs) of the article?

Accepted Answer

Let Marked Price be MP. Selling Price = MP × (1 - 0.20) × (1 - 0.35) = MP × 0.80 × 0.65 = 0.52 MP. So, 0.52 MP = 50700, which gives MP = 97500.

Question 3

Who invented the hot air balloon?

Accepted Answer

The hot air balloon was invented by the Montgolfier brothers, Joseph-Michel and Jacques-Étienne, in 1783 in France. It was the first successful human-carrying flight technology.

Question 4

A and B have to type a book together containing 120 pages. A takes 9 hrs to type 36 pages and B takes 5 hrs to type 40 pages. A typed first 60 pages alone and the last 60 pages were typed by A and B together. How much time (in hours) will be taken to type the complete book?

Accepted Answer

A's rate is 4 pages/hr and B's is 8 pages/hr. A takes 15 hours for the first 60 pages. Together, they type 12 pages/hr, taking 5 hours for the rest. Total time = 15 + 5 = 20 hours.

Question 5

What is the simplified value of [(sec3x – tan3x)/(sec x – tan x)] – 2 tan2x – sec x tan x?

Accepted Answer

Use the a³-b³ formula to get sec²x + sec x tan x + tan²x. Subtracting 2tan²x and sec x tan x leaves sec²x - tan²x, which equals 1.

Question 6

If a retailer offers a discount of 20% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

Accepted Answer

Let CP = 100. Since SP = CP, SP = 100. A 20% discount means SP is 80% of MP. So, 0.8 × MP = 100, giving MP = 125. Markup is 25%.

Question 7

If the price of pen decreases by 20%, then a man can buy 10 more pens for Rs 100. What is the new price (in Rs) of each pen?

Accepted Answer

A 20% decrease on Rs 100 saves Rs 20. This saved amount is used to buy the 10 extra pens. Therefore, the new price per pen is 20 / 10 = Rs 2.

Question 8

Arrange the given words in the sequence in which they occur in the dictionary. 1. Globe 2. Group 3. Glitch 4. Gap 5. Glade 1. Globe 2. Group 3. Glitch 4. Gap 5. Glade

Accepted Answer

Compare letters alphabetically. 'Gap' comes first. Among 'Gl' words, 'Glade' (a), 'Glitch' (i), and 'Globe' (o) follow in order. 'Group' (r) is last. Sequence: 4, 5, 3, 1, 2.

Question 9

X and Y both start from a same point. X walks 17 m West, then turns to his right and walks 13 m. At the same time, Y walks 9 m North, then turns East and walks 7 m, then turns to his left and walks 4 m. Where is Y now with respect to the position of X?

Accepted Answer

X's final position is 17m West and 13m North. Y's final position is 7m East and 13m North (9+4). Since both are 13m North, Y is 17 + 7 = 24m East of X.

Question 10

Ratio of present ages of Pankaj and Punit is 5 : 6 and the sum of their ages is 33 years. What will be the difference (in years) of their ages?

Accepted Answer

The sum of the ratio parts is 5 + 6 = 11. Since 11 parts equal 33 years, 1 part equals 3 years. The difference in their ratio is 6 - 5 = 1 part, which is 3 years.

Question 11

If a3 + b3 = 152 and a + b = 8, then what is the value of ab?

Accepted Answer

Use the formula a³ + b³ = (a+b)((a+b)² - 3ab). Substituting the values gives 152 = 8(64 - 3ab). Simplifying this yields 19 = 64 - 3ab, so 3ab = 45, meaning ab = 15.

Question 12

Name the Commission that came to India in 1928 to reform India's constitutional system.

Accepted Answer

The Simon Commission, officially the Indian Statutory Commission, arrived in India in 1928 to study constitutional reform. It was widely boycotted because it had no Indian members.

Question 13

Δ XYZ is right angled at Y. If m∠Z = 60°, then what is the value of (1/√2) Sec X?

Accepted Answer

Since ∠Y = 90° and ∠Z = 60°, ∠X must be 30°. Sec 30° is 2/√3. Multiplying by 1/√2 gives 2/√6.

Question 14

Under which of the following jurisdiction can any individual, whose fundamental right has been violated, can directly move the Supreme Court for remedy?

Accepted Answer

Article 32 of the Constitution grants the Supreme Court Writ Jurisdiction. It allows individuals to directly approach the SC to issue writs for the enforcement of their Fundamental Rights.

Question 15

Select the related number from the given alternatives. 99 : 101 :: 90 : ?

Accepted Answer

The pattern is based on a base of 100 (10^2). 10^2 - 1 = 99 and 10^2 + 1 = 101. Similarly, 10^2 - 10 = 90, so the next number is 10^2 + 10 = 110.

Question 16

Presence of large amounts of nutrients in waters also causes excessive growth of _________ algae.

Accepted Answer

Excess nutrients in water bodies lead to the rapid multiplication of free-floating, microscopic planktonic algae, which eventually causes algal blooms and depletes dissolved oxygen.

Question 17

Which of the following are constituents of Indian Parliament? (i) The President (ii) The Council of States (Rajya Sabha) (iii) The House of the People (Lok Sabha) ?

Accepted Answer

Article 79 of the Indian Constitution states that the Parliament consists of the President and two Houses: the Council of States (Rajya Sabha) and the House of the People (Lok Sabha).

Question 18

If (2)# * 4 = 2 and (4)# * 4 = 16, then what is the value of A in (6)# * A = 18? ?

Accepted Answer

The pattern is x³ ÷ y = z. For the first, 2³ ÷ 4 = 2. For the second, 4³ ÷ 4 = 16. Thus, 6³ ÷ A = 18, which gives 216 ÷ A = 18, so A = 12.

Question 19

The Tomara Rajputs, were defeated in the middle of the twelfth century by the Chauhans of _________.

Accepted Answer

The Tomara Rajputs, who established Delhi, were defeated by the Chauhans (Chahamanas) of Ajmer in the mid-12th century, leading to Chauhan control over Delhi.

Question 20

In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 cm2. What is the area (in cm2) of triangle FGE?

Accepted Answer

The medians intersect at the centroid G. The area of the triangle formed by joining two midpoints and the centroid is 1/12 of the total area. Thus, 156 / 12 = 13 cm².