26. SSC CGL 2023 

Exam Date 24/07/2023 

Exam Time 11:45 AM - 12:45 PM 

Section : Quantitative Aptitude 

Q.1 If $\left( x+\frac{1}{x} \right)=2\sqrt{2}$, what is the value of $\left( {{x}^{6}}+\frac{1}{{{x}^{6}}} \right)$? 

1. 180 

2. 216 

3. 198 

4. 234 

Q.2 If $\tan x=-\frac{12}{5}$, where x lies in the second quadrant, what the value of sin x — cot x? 

1. $\frac{156}{209}$ 

2. $\frac{169}{156}$ 

3. $\frac{144}{169}$ 

4. $\frac{209}{156}$ 

Q.3 Which of the following options gives an expression equivalent to sin(A + B)? 

1. sinAcosB + cosAsinB 

2. cosAcosB – sinAsinB 

3. sinAcosB – cosAsinB 

4. cosAcosB + sinAsinB 

Q.4 Find the least number divisible by 2, 3, 5, 6, 9 and 18, which is a perfect square. 

1. 144 

2. 400 

3. 3600 

4. 900 

Q.5 A pipe can fill a tank in 30 hours. Due to a leakage at the bottom, it is filled in 50 hours. How much time will the leakage take to empty the completely filled tank? 

1. 85 hours 

2. 70 hours 

3. 60 hours 

4. 75 hours 

Q.6 Three numbers are in the ratio $\frac{4}{5}:\frac{5}{6}:\frac{9}{10}$. The difference between the smallest and the greatest numbers is 12. Find the number which is NEITHER the smallest NOR the greatest.

1. 104 

2. 96 

3. 108 

4. 100 

Q.7 The simple interest on ₹800 for 6 years at 5.5% per annum is equal to the simple interest on ₹600 at 4% per annum for a certain period of time. The period of time is: 

1. 12 years 

2. 9 years 

3. 10 years 

4. 11 years 

Q.8 Two men walk from a place at speeds of 9 km/h and 12 km/h, respectively. The 1st man takes 20 minutes more than the second one to cover the journey. Find the distance of the journey. 

1. 13 km 

2. 12 km 

3. 15 km 

4. 10 km 

Q.9 Simplify the following expression. 

(4x + 1)2 - (4x + 3)(4x - 1) 

1. (4x + 1) 

2. (4x - 3) 

3. 4x 

4. 4 

Q.10 Study the given table and answer the question that follows. 

The table shows the number of students studying in six different classes of six different schools. 

What is the respective ratio of students studying in class IX of schools Q and R together to those studying in class VI of schools S and T together? 

1. 143 : 150 

2. 181 : 127 

3. 150 : 143 

4. 127 : 181 

Q.11 A dishonest shopkeeper sells millet at ₹20 per kg which he has bought at ₹16 per kg and he is giving 800 gm instead of 1000 gm. Find his actual profit percentage. 

1. 58.36% 

2. 54.25% 

3. 52.12% 

4. 56.25% 

Q.12 The length of the common chord of two circles of radii 15 cm and 13 cm, whose centres are 14 cm apart, is: 

1. 12 cm 

2. 24 cm 

3. 15 cm 

4. 14 cm 

Q.13 The following table shows the marks distribution among the students in a class. 

How many students scored less than 20 marks? 

1. 2 

2. 5 

3. 7 

4. 6 

Q.14 A can do a certain piece of work in 1.5 times the number of days in which B and C together can do it. If A and B together can do the said piece of work in 30 days and C alone can do it in 120 days, then how many days will B take to do this piece of work alone? 

1. 50 

2. 75 

3. 60 

4. 45 

Q.15 The marked price of a mobile phone is ₹15,000 and the shopkeeper sold it for ₹13,500. What is the rate of discount offered by the shopkeeper? 

1. 12% 

2. 11% 

3. 9% 

4. 10% 

Q.16 In a circular race of 4225 m, X and Y start from the same point and at the same time at speeds of 54 km/h and 63 km/h. When will they meet again for the first time on the rack when they are running in the opposite direction? 

1. 150 seconds 

2. 120 seconds 

3. 140 seconds 

4. 130 seconds 

Q.17 In a class of 60 students, 20 are girls. The average weight of the boys in the class is 40 kg, while that of all the girls is 35 kg. What is the average weight (in kg) of the entire class (correct to two decimal places)? 

1. 36.67 

2. 33.33 

3. 40.67 

4. 38.33 

Q.18 If Cosec θ + Cot θ = m, find the value of $\frac{{{m}^{2}}-1}{{{m}^{2}}+1}$ . 

1. 1 

2. 0 

3. −Sinθ 

4. Cos θ 

Q.19 P and Q together can complete a piece of work in 6 days. If P can alone complete the work in 18 days, then the number of days required for Q to finish the work is: 

1. 9 days 

2. 8 days 

3. 10 days 

4. 11 days 

Q.20 The value of x3 + y2 when x = 1, y = 2 is: 

1. 5 

2. 4 

3. 1 

4. 2 

Q.21 The value of tan5° tan25° tan45° tan65°  tan85° is equal to _________. 

1. 4 

2. 3 

3. 1 

4. 2 

Q.22 The length, breadth, and height of a room are 10 m, 8 m and 6 m respectively. Find thecost of white washing the walls of the room and the ceiling at the rate of ₹7.50 per m2 . 

1. ₹2,220 

2. ₹2,000 

3. ₹2,150 

4. ₹1,850 

Q.23 In an election between two candidates, 10% of the voters in the voter list did not cast their vote, whereas 10% of the votes cast were found to be invalid. The winning candidate got 56% of the valid votes and won the election by a margin of 1,458 votes. What is the total number of voters enrolled in the voter list? 

1. 14,000 

2. 16,000 

3. 13,000 

4. 15,000

Q.24 Aarti can type 85 pages in 10 hours. Aarti and Bina together can type 500 pages in 40 hours. How much time will Bina take to type 40 pages? 

1. 14 hours 

2. 15 hours 

3. 12 hours 

4. 10 hours 

Q.25 In ΔABC, D is the mid-point of BC and G is the centroid. If GD = 10 cm, then the length of AD is _________. 

1. 20 cm 

2. 15 cm 

3. 30 cm 

4. 10 cm