36. SSC CGL 2023 

Exam Date 26/07/2023 

Exam Time 5:15 PM - 6:15 PM 

Section : Quantitative Aptitude 

Q.1 Expand and simplify the algebraic expression: 

(x-5)2 + (x+3)2 + 4x 

1. 2(x2 - 17) 

2. 2(x2 + 17) 

3. (x2 + 17) 

4. 2(x2 - 5x + 17) 

Q.2 Triangle ABC is circumscribed around circle D. Segments AQ, BR and SC measure 13, 10.5 and 6 cm, respectively. The perimeter of triangle ABC is:  

1. 15 cm 

2. 59 cm 

3. 29.5 cm 

4. 108 cm 

Q.3 What is $\tan \frac{\theta }{2}$$\tan \frac{\theta }{2}$? 

1. $\frac{\cos \theta }{1-\cos \theta }$ 

2. $\frac{\cos \theta }{1-\sin \theta }$ 

3. $\frac{\sin \theta }{1+\cos \theta }$ 

4. $\frac{\sin \theta }{1-\cos \theta }$ 

Q.4 Study the graph carefully. 

The decrease in imports in 1976 was what percent of the imports in 1975?  

1. 48.07% 

2. 49% 

3. 50% 

4. 48% 

Q.5 If (a + b + c) = 14, and (a3 + b3 + c3 – 3abc) = 98, find the value of (ab + bc + ca). 

1. 65 

2. 63 

3. 64 

4. 60 

Q.6 Ram bought a cell phone and paid 30% less than its original price. He sold it at 50% profit on the price he had paid. The percentage of profit earned by Ram on the original price was: 

1. 25% 

2. 5% 

3. 50% 

4. 15% 

Q.7 In an examination of 7 papers of 100 marks each, there were 3 mathematics papers, 2 English papers and 2 Hindi papers. D gets average marks of 45, 55 and 60 in mathematics, English and Hindi, respectively. What are the average marks per paper? 

1. 54.1 

2. 52.1 

3. 56.5 

4. 55.6 

Q.8 The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 3 

2. What is the product of the two given numbers? 

1. 160 

2. 240 

3. 200 

4. 320 

Q.9 The force (in pound-force) needed to keep a car from skidding on a curve varies directly with the weight of the car (in pounds) and the square of its speed (in miles per hour [mph]) and inversely with the radius (in feet) of the curve. Suppose 6125 pound force is required to keep a 2750 pound car, travelling at a speed of 35 mph, from skidding on a curve of radius 550 feet. How much pound-force is then required to keep a 3600 pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet? 

1. 12240 

2. 11960 

3. 12000 

4. 12150 

Q.10 A sum of money at simple interest amounts to ₹1,200 in 3 years and to ₹1,350 in 4 years. The sum is: 

1. ₹850 

2. ₹450 

3. ₹650 

4. ₹750 

Q.11 A watch is purchased for ₹3,200 and sold for ₹2,700. Calculate the percentage loss up to two places of decimal. 

1. 15.62% 

2. 16.50% 

3. 15.18% 

4. 16.12% 

Q.12 In 1 km linear race, P beats Q by 120 metres or 30 sec. What is the time taken by P to cover the race? 

1. 235 sec 

2. 240 sec 

3. 220 sec 

4. 250 sec

Q.13 In the figure, PT is a tangent. If TP=12 cm, PB = x + 7 cm and PA = x cm, then find the value of x. 

1. 7 

2. 5 

3. 9 

4. 6 

Q.14 A circular running path is 1452 m in circumference. Two men start from the same point and walk in opposite direction at the speed of 7.5 km/h and 9 km/h, respectively. When will they meet for the first time? 

1. 5.71 min 

2. 5.17 min 

3. 5.28 min 

4. 5.82 min 

Q.15 Simplify the following expression.  

120 ÷ 15 of 4 + [ 11 × 4 ÷ 4 of { 4 × 2 - ( 8 - 11 ) } ] 

1. $\frac{61}{120}$ 

2. 3 

3. –3 

4. $\frac{120}{61}$ 

Q.16 Find the value of the given expression 14 ÷ 7 × 1 + 3 – [18 – {15 – (7 – 7 – 2)}] 

1. 6 

2. 4 

3. 3 

4. 5 

Q.17 If A= 22.5°, What is the value of (10$\sqrt{2}$ sin 2A – 7 $\sqrt{2}$ cos2A + 9tan2A)? 

1. 6 

2. 15 

3. 10 

4. 12 

Q.18 Ramesh alone can complete a work in 24 days. Ramesh and Somesh can complete it in 8 days. How long will Somesh alone take to complete the work? 

1. 10 days 

2. 14 days 

3. 15 days 

4. 12 days 

Q.19 Find the value of x in the given figure where TP ( tangent on point 'I') = 15 cm. PB = 2x + 3 cm. PA = 9 cm. 

1. 18 cm 

2. 21 cm 

3. 11 cm 

4. 15 cm 

Q.20 Study the given table and answer the question that follows. 

The table shows the marks distribution among the students in a class. 

How many students scored more than 40 marks? 

1. 3 

2. 5 

3. 2 

4. 4 

Q.21 If the volume of a cube is 4096 cm3, then what is the length of the side of the cube? 

1. 14 cm 

2. 16 cm 

3. 12 cm 

4. 18 cm 

Q.22 15 men complete a work in 10 days. 15 women complete the same work in 12 days. If all these men and women work together, then the number of days required to complete that work is: 

1. $6\frac{11}{4}$ 

2. $4\frac{3}{11}$ 

3. 7$7\frac{2}{11}$ 

4. $5\frac{5}{11}$ 

Q.23 What smallest positive number should be subtracted from 2 and 3 so that 4 is the 3rd proportion to them? 

1. 3 

2. 4 

3. 2 

4. 1 

Q.24 sin 600° cos 750° + sin 150° cos 240° = ? 

1. –1 

2. 1 

3. $\frac{1}{2}$ 

4. $\frac{2}{3}$ 

Q.25 Three successive discounts of 10% are available on the sale of a washing machine with a marked price of ₹55,000. Find the final selling price (in ₹) of the washing machine. 

1. 40000 

2. 40095 

3. 44000 

4. 42095