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SSC CGL
Practice paper for the Indian professional exam - SSC CGL Tier 1 | 100 questions from the Quantitative aptitude section
Updated:
May 7, 2023
The SSC CGL exam is conducted by the Staff Selection Commission to recruit eligible candidates for various Group B and Group C posts in different Ministries/ Departments/ Organizations of the Government of India. The exam is conducted in four tiers, with the Tier-1 exam being the first stage of the selection process. The Tier-1 exam is a computer-based exam that consists of four sections: General Intelligence and Reasoning, General Awareness, Quantitative Aptitude, and English Comprehension. The exam is of 200 marks, and candidates are allowed 60 minutes to complete it. The exam is conducted annually, and the notification for the exam is usually released in the month of September.
The Staff Selection Commission (SSC) conducts the Combined Graduate Level (CGL) Exam for recruitment to various subordinate services like:
SSC CGL Exam Date 2023 has been announced along with SSC Calendar 2023. SSC CGL 2023 Tier 1 Exam is scheduled from 14th July to 27th July 2023. As per the official calendar, the online registration process has been started from 03rd April 2023 onwards.
The quantitative aptitude section of the SSC CGL Exam is designed to test a candidate's mathematical and numerical ability. This section contains questions based on various topics, including arithmetic, algebra, geometry, and data interpretation.
The questions in this section may range from simple numerical calculations to complex word problems that require the application of mathematical concepts. Basic arithmetic operations such as addition, subtraction, multiplication, and division are usually included in this section.
The candidates are expected to have a good understanding of the fundamental concepts of mathematics and should be able to apply them to solve the questions. Regular practice and a strong understanding of concepts and formulas are the keys to excelling in this section.
To prepare for this section, candidates can refer to various textbooks, solve previous year's question papers, and practice from mock tests and study materials available in the market.
1. If x + y = 8 and xy = 12, what is the value of x² + y²?
A. 56
B. 68
C. 80
D. 96
Answer: D. 96
2. What is the value of (sin² 25° - cos² 65°) / (tan 70° - cot 20°)?
A. √3
B. 2
C. 3 - √3
D. 3 + √3
Answer: D. 3 + √3
3. If a shopkeeper sells a book at a discount of 20% on its marked price, he earns a profit of 20%. What is the ratio of the cost price to the marked price of the book?
A. 4:5
B. 5:6
C. 3:4
D. 2:3
Answer: A. 4:5
4. The HCF of two numbers is 13 and their sum is 364. What are the numbers?
A. 91 and 273
B. 104 and 260
C. 117 and 247
D. 130 and 234
Answer: B. 104 and 260
5. If a cone, a hemisphere and a cylinder have the same base and same height, what is the ratio of their volumes?
A. 1:2:3
B. 2:3:4
C. 3:4:5
D. 4:5:6
Answer: B. 2:3:4
6. The sum of the ages of A and B is 40 years and their difference in age is 12 years. What is the ratio of their ages?
A. 4:8
B. 7:5
C. 6:4
D. 9:3
Answer: C. 6:4
7. What is the value of (5 - 2√6)² + (10 - 4√6)²?
A. 200
B. 300
C. 400
D. 500
Answer: C. 400
8. What is the coefficient of x² in the expansion of (2x - 3)⁵?
A. -80
B. -40
C. 40
D. 80
Answer: D. 80
9. Find the area of a regular hexagon with each side measuring 12 centimeters.
A. 216√3 cm²
B. 288√3 cm²
C. 384√3 cm²
D. 648√3 cm²
Answer: B. 288√3 cm²
10. What is the value of tan² 20° + tan² 30° + tan² 40° + tan² 50° + tan² 60°?
A. 5
B. 6
C. 7
D. 8
Answer: C. 7
11. A man rowed 12 km upstream and 18 km downstream in a river in 5 hours. He could row 24 km upstream and 36 km downstream in 10 hours. What is the speed of the man in still water?
A. 4 km/h
B. 5 km/h
C. 6 km/h
D. 7 km/h
Answer: C. 6 km/h
12. What is the value of (sin 20° + sin 40° + sin 80°) / (cos 20° + cos 40° + cos 80°)?
A. 1
B. cot 20°
C. tan 20°
D. sec 20°
Answer: A. 1
13. If (3x + 1)(2x - 3) = 0, what is the value of x² - 2x - 3?
A. 10
B. -8
C. -10
D. 8
Answer: D. 8
14. What is the sum of the series: 1! + 2! + 3! + ... + 20! ?
A. 2432902008176640000
B. 2432902008176640010
C. 2432902008176640015
D. 2432902008176640025
Answer: B. 2432902008176640010
15. A train takes 10 seconds to pass a pole and 40 seconds to cross a 375-meter-long bridge. What is the speed of the train?
A. 25 m/s
B. 30 m/s
C. 35 m/s
D. 40 m/s
Answer: C. 35 m/s
16. What is the value of cos 15° - sin 75°?
A. √6 - √2
B. √6 - √3
C. √3 - 1
D. 1 - √2
Answer: B. √6 - √3
17. If (a - b) : (b - c) : (c - a) = 1 : 2 : 3, what is the value of (a² + b² + c²) / (ab + bc + ca)?
A. 7/6
B. 5/3
C. 4
/3
D. 1
Answer: A. 7/6
18. Find the sum of the first 30 multiples of 7.
A. 3150
B. 3300
C. 3450
D. 3600
Answer: C. 3450
19. If a right circular cone has a height of 24 cm and a base radius of 6 cm, what is the volume of the cone?
A. 216π cm³
B. 288π cm³
C. 432π cm³
D. 576π cm³
Answer: B. 288π cm³
20. What is the value of 1/√3 + √3/√7 + √7/√11 + ... + √3999/√4003 ?
A. √4001 - √3
B. √4003 - √3
C. √4005 - √3
D. √4007 - √3
Answer: B. √4003 - √3
21. If log₃ x = 5/2, what is the value of x² / √(27x) ?
A. 3
B. 9
C. 27
D. 81
Answer: B. 9
22. Evaluate: 4! + 5! + 6! + ... + 20!
A. 25649588373200
B. 26578688040000
C. 27507787706800
D. 28436887373600
Answer: C. 27507787706800
23. If (x - 1)² + (y - 3)² = 16 and (x + 3)² + (y + 1)² = 64, what is the distance between the centers of the circles defined by the two equations?
A. 5 units
B. 6 units
C. 7 units
D. 8 units
Answer: D. 8 units
24. Find the solution of 2^x - 3^x + 4^x = 0.
A. 1
B. 2
C. 3
D. 4
Answer: B. 2
25. Find the sum of the infinite geometric progression 12, 4, 4/3, 4/9, ...
A. 18
B. 24
C. 30
D. 36
Answer: B. 24
1. The average of 5 consecutive odd numbers is 35. What is the largest number?
A. 37
B. 39
C. 41
D. 43
Answer: D. 43
2. A cylindrical tank of radius 5 meters and height 12 meters is completely filled with water. What is the volume of the water in the tank?
A. 300π cubic meters
B. 600π cubic meters
C. 900π cubic meters
D. 1200π cubic meters
Answer: C. 900π cubic meters
3. Simplify: 3(4x - 2) + 2(3x + 5)
A. 18x + 4
B. 18x + 16
C. 18x + 26
D. 18x + 30
Answer: C. 18x + 26
4. A car travels 240 km in 4 hours. What is its average speed?
A. 30 km/hr
B. 40 km/hr
C. 50 km/hr
D. 60 km/hr
Answer: B. 60 km/hr
5. The difference between CI and SI on a certain sum of money at 10% per annum for 2 years is Rs. 8. What is the sum?
A. Rs. 200
B. Rs. 400
C. Rs. 800
D. Rs. 1600
Answer: B. Rs. 400
6. A cube has a surface area of 150 square meters. What is its volume?
A. 125 cubic meters
B. 150 cubic meters
C. 175 cubic meters
D. 200 cubic meters
Answer: B. 150 cubic meters
7. Evaluate: tan² 45° - sin² 30°
A. 0
B. 1/2
C. 1
D. √3/2
Answer: B. 1/2
8. A certain sum becomes 1.5 times in 5 years at simple interest. What is the rate of interest?
A. 8%
B. 10%
C. 12%
D. 15%
Answer: C. 12%
9. What is the value of (1/2)^3 × (2/3)^2 ÷ (3/4)^4?
A. 1/32
B. 3/64
C. 27/256
D. 81/1024
Answer: B. 3/64
10. Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11, ...
A. 475
B. 480
C. 490
D. 500
Answer: C. 490
11. If the roots of the equation ax² + bx + c = 0 are rational and equal, what is the relationship between a, b, and c?
A. a = b = c
B. a = -b = c
C. a = c and b = 0
D. b² = 4ac
Answer: C. a = c and b = 0
12. Solve the equation x² - 5x + 6 = 0.
A. x = 2 or x = 3
B. x = 2 and x = 3
C. x = -2 or x = -3
D. x = -2 and x = -3
Answer: B. x = 2 and x = 3
13. What is 80% of 25% of 400?
A. 20
B. 40
C. 80
D. 160
Answer: B. 40
14. A man sold a watch for Rs. 5400 and incurred a loss of 10%. What was the cost price of the watch?
A. Rs. 6000
B. Rs. 600
C. Rs. 5000
D. Rs. 500
Answer: A. Rs. 6000
15. A sum of money becomes 3 times itself in 4 years at compound interest. What is the rate of interest?
A. 50%
B. 66.67%
C. 75%
D. 100%
Answer: C. 75%
16. If the value of sinθ = 3/5, what is the value of cosθ?
A. 4/5
B. √2/2
C. 5/3
D. √26/5
Answer: A. 4/5
17. A bag contains 5 red balls and 7 green balls. If two balls are drawn at random, what is the probability that both of them are green?
A. 1/6
B. 5/24
C. 7/24
D. 5/12
Answer: B. 5/24
18. The area of a rectangle is 192 square meters and its length is 3 times its width. What is the length of the rectangle?
A. 8 meters
B. 12 meters
C. 16 meters
D. 24 meters
Answer: B. 12 meters
19. Evaluate: log₃ 27 - log₂ 8
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
20. A train takes 30 seconds to cross a man standing on a platform. If the length of the train is 300 meters and the speed of the train is 72 km/hr, what is the length of the platform?
A. 380 meters
B. 400 meters
C. 420 meters
D. 440 meters
Answer: C. 420 meters
21. A square has an area of 169 square meters. What is its perimeter?
A. 26 meters
B. 39 meters
C. 52 meters
D. 676 meters
Answer: B. 39 meters
22. Simplify: √(8 / 50) + √(50 / 8)
A. (9/5)√2
B. (9/4)√2
C. (7/4)√2
D. (7/5)√2
Answer: D. (7/5)√2
23. What is the next number in the series 1, 1, 2, 3, 5, 8, 13, ...?
A. 21
B. 23
C. 24
D. 26
Answer: A. 21
24. Solve the equation 3x - 4y = 24 for y.
A. y = (3/4)x - 6
B. y = (3/4)x + 6
C. y = (4/3)x - 8
D. y = (4/3)x + 8
Answer: A. y = (3/4)x - 6
25. Evaluate: cos(π/6) × sin(π/4) ÷ tan(π/3)
A. √3/3
B. √2/2
C. √3
D. 2√3/3
Answer: C. √3
1. A man sells an article for Rs. 5184 and gains 8% profit. What is the cost price of the article?
A. Rs. 4800
B. Rs. 4808
C. Rs. 5000
D. Rs. 5008
Answer: C. Rs. 5000
2. The length of a rectangle is three times its breadth. If the area of the rectangle is 675 sq cm, what is the perimeter of the rectangle?
A. 90 cm
B. 75 cm
C. 45 cm
D. 60 cm
Answer: A. 90 cm
3. If 6x - 7y = 5 and 3x - 4y = 5, what is the value of x?
A. 3
B. 4
C. 5
D. 6
Answer: C. 5
4. The monthly incomes of A and B are in the ratio of 4:5. If the income of A is Rs. 2400, what is the income of B?
A. Rs. 3000
B. Rs. 2700
C. Rs. 3200
D. Rs. 3600
Answer: A. Rs. 3000
5. The average marks obtained by 75 students in a class is 48. If the total marks scored by them is 3600, what is the average marks obtained by the remaining 25 students?
A. 58
B. 47
C. 45
D. 43
Answer: D. 43
6. A right pyramid has a square base ABCD of side 8 cm and a height of 6 cm. What is the volume of the pyramid?
A. 84 cubic cm
B. 96 cubic cm
C. 128 cubic cm
D. 192 cubic cm
Answer: C. 128 cubic cm
7. If sin (x + 30°) = cos x, what is the value of x?
A. 120°
B. 150°
C. 210°
D. 240°
Answer: A. 120°
8. A sum of Rs. 10,000 is invested at 10% per annum simple interest. What is the interest after 5 years?
A. Rs. 5000
B. Rs. 2500
C. Rs. 1000
D. Rs. 500
Answer: D. Rs. 500
9. A man rows to a place 48 km distant and back in 14 hours. If the speed of the stream is 3 km/hr, what is the speed of the man in still water?
A. 10 km/hr
B. 12 km/hr
C. 14 km/hr
D. 16 km/hr
Answer: B. 12 km/hr
10. The radius of a circle is 14 cm. What is the length of its circumference?
A. 88 cm
B. 44 cm
C. 22 cm
D. 308 cm
Answer: D. 308 cm
11. If the ratio of the areas of two squares is 16:25, what is the ratio of their perimeters?
A. 4:5
B. 16:25
C. 2:5
D. 8:25
Answer: B. 16:25
12. If the coordinates of the vertices of a triangle are (5, 6), (1, 2), and (-3, 4), what is the length of its median from the vertex (1, 2)?
A. 3.21
B. 3.46
C. 4.32
D. 4.58
Answer: B. 3.46
13. In a group of 120 people, 42 like football, 36 like cricket, and 18 like both. What is the percentage of people who like neither football nor cricket?
A. 40%
B. 35%
C. 30%
D. 25%
Answer: D. 25%
14. What is the value of (sin 75° + tan 30°)/(1 + cos 45°)?
A. √3
B. (1+√3)/2
C. 1
D. 2
Answer: B. (1+√3)/2
15. If the length of a rectangle is increased by 20% and its breadth is decreased by 10%, what is the effect on its area?
A. No change
B. Increase by 10%
C. Increase by 8%
D. Decrease by 10%
Answer: C. Increase by 8%
16. What is the value of (1.08)^3 - (0.92)^3?
A. 0.2544
B. 0.3872
C. 0.5126
D. 0.6252
Answer: C. 0.5126
17. A train running at a speed of 100 km/hr crossed a platform in 54 seconds. What is the length of the platform?
A. 1000 m
B. 900 m
C. 750 m
D. 600 m
Answer: D. 600 m
18. If 123 is divided among A, B and C in such a way that A gets 25% more than B and B gets 20% more than C. What is the share of C?
A. Rs. 35
B. Rs. 30
C. Rs. 25
D. Rs. 20
Answer: B. Rs. 30
19. The cost price of an article was Rs. 160. If it is sold at a discount of 15%, what is the selling price?
A. Rs. 130
B. Rs. 136
C. Rs. 142
D. Rs. 144
Answer: B. Rs. 136
20. If 21% of a number is equal to 42, what is the number?
A. 200
B. 180
C. 166.67
D. 140
Answer: A. 200
21. √1225 - √1296 = ?
A. -1
B. 0
C. 1
D. 2
Answer: A. -1
22. If a:b = 2:3, b:c = 6:7, what is the value of a:c?
A. 4:7
B. 5:7
C. 6:7
D. 7:9
Answer: B. 5:7
23. If the sum of an infinite geometric series is 10 and the common ratio is 1/2, what is the first term?
A. 5
B. 4
C. 8
D. 16
Answer: C. 8
24. If the radius of a cylinder is doubled and its height is halved, what is the change in its volume?
A. Doubled
B. Halved
C. Increased by 50%
D. Decreased by 50%
Answer: A. Doubled
25. If 40% of a number is equal to 30, what is 25% of the same number?
A. 18.75
B. 20
C. 25
D. 30
Answer: A. 18.75
1. If a^2 + b^2 = 25 and ab = 6, find the value of a+b.
a. 2
b. 3
c. 4
d. 5
2. In a group of 120 students, 70 take tea and 50 take coffee. How many students take both tea and coffee?
a. 10
b. 20
c. 30
d. 40
3. If the radius of a circle is 7 cm, find its circumference.
a. 22 cm
b. 44 cm
c. 77 cm
d. 154 cm
4. A farmer has 1000 acres of land, of which he uses 750 acres for wheat. What percentage of his land does he use for wheat?
a. 60%
b. 70%
c. 75%
d. 80%
5. What is the slope of the line passing through the points (3,2) and (5,8)?
a. 3
b. 2
c. 6
d. 4
6. The sum of two numbers is 24 and their difference is 4. What are the numbers?
a. 10 and 14
b. 12 and 12
c. 8 and 16
d. 7 and 17
7. A shopkeeper buys an item for Rs. 500 and sells it for Rs. 700. What is his profit percentage?
a. 20%
b. 30%
c. 40%
d. 50%
8. If x+y=9 and x-y=5, find the value of x^2 - y^2.
a. 28
b. 36
c. 44
d. 52
9. If sin θ = 3/5, find the value of 1-cos θ.
a. 4/5
b. 2/5
c. 1/5
d. 3/4
10. A and B can complete a work in 8 days. B and C can complete the same work in 12 days. How many days will A, B and C take to complete the work together?
a. 4 days
b. 6 days
c. 8 days
d. 10 days
11. If the length of a rectangle is 8 cm and its width is 6 cm, what is its perimeter?
a. 16 cm
b. 20 cm
c. 28 cm
d. 32 cm
12. If the first four terms of an arithmetic progression are 5, 9, 13, and 17, what is the 10th term of the sequence?
a. 33
b. 37
c. 41
d. 45
13. If the radius of a cylinder is 4 cm and its height is 10 cm, what is its volume?
a. 120 cm^3
b. 160 cm^3
c. 320 cm^3
d. 640 cm^3
14. If a number is increased by 25% and then decreased by 20%, what is the net change?
a. 5% increase
b. 5% decrease
c. 10% increase
d. 10% decrease
15. If the ratio of the sides of a triangle is 3:4:5 and the perimeter is 48 cm, what is the length of the longest side?
a. 15 cm
b. 20 cm
c. 25 cm
d. 30 cm
16. If the difference between the compound interest and simple interest on a sum of money at 10% per annum for 2 years is Rs. 119, what is the sum?
a. Rs. 1000
b. Rs. 1500
c. Rs. 2000
d. Rs. 2500
17. If 3 workers can complete a work in 6 days, how many days will it take 5 workers to complete the same work?
a. 3 days
b. 2.5 days
c. 2 days
d. 1.5 days
18. If the area of a square is 81 cm^2, what is its perimeter?
a. 24 cm
b. 27 cm
c. 30 cm
d. 36 cm
19. If tan θ = 4/3, find the value of cot θ.
a. 3/4
b. 4/3
c. 5/12
d. 7/24
20. A sphere has a surface area of 1256 cm^2. What is its radius?
a. 7 cm
b. 8 cm
c. 9 cm
d. 10 cm
21. The sum of the digits of a two-digit number is 9. If the digits are interchanged, the number is increased by 27. Find the number.
a. 45
b. 36
c. 27
d. 18
22. If the sum of the first 10 even numbers is 110, find the sum of the first 20 even numbers.
a. 210
b. 420
c. 630
d. 840
23. Two pipes can fill a tank in 6 hours and 8 hours respectively. If they are opened simultaneously, how long will they take to fill the tank?
a. 3.2 hours
b. 3.6 hours
c. 4 hours
d. 4.8 hours
24. A man invested Rs. 20000 in a scheme for four years at 10% per annum simple interest. What is the total amount he will receive at the end of four years?
a. Rs. 24000
b. Rs. 28000
c. Rs. 32000
d. Rs. 36000
25. The average of five numbers is 22. If one more number is included, the new average becomes 24. What is the new number?
a. 38
b. 42
c. 46
d. 50