MATHS — PRACTICE SET 12 — SOLVED 

These Practice Sets for Maths are specially designed keeping in view of the pattern that we see in the various competitive exams, especially the Combined Graduate Level Examination (CGLE), SI Delhi Police and CPO Exam, and Grade-II DAAS (except Geometry and Trigonometry)  of the Staff selection Commission (SSC) and the DSSSB. I hope they’ll help you immensely.

QUESTIONS: 20                                                                              MAXIMUM TIME: 20 minutes

1. 84 Maths books, 90 physics books, and 120 chemistry books of equal thickness have to be stacked topic-wise. How many books will be there in each stack so that each stack will have the same height too?

A) 6
B) 12
C) 21
D) 18

2. A woman sells to the first customer half her stock of apples and half an apple, to the second customer half an apple and half of her remaining stock and so also to a third customer and to a fourth customer. She finds that she has now 15 apples left. How many apples had she at first?

A) 150
B) 180
C) 200
D) 250

3. In (2⁴¹ – 1)/9 what will be the remainder?

A) 1
B) 2
C) 3
D) 4

4. If a/b = b/c = c/d; then √[(a – b + c) (b – c + d)] /[√(ab) – √(bc) + √(cd)]

A) -2
B) 0
C) 1
D) 2

5. a⁴ + a²b² + b⁴ = 8,
and a² + ab + b² = 4; then ab = ?

A) 0
B) 1
C) 2
D) 3

6. A shopkeeper sells milk with 5% water. In this 2 liters of milk how much milk should be mixed so that water become 4%?

A) 0.4 liter
B) 0.5 liter
C) 1 liter
D) 1.5 liter

7. Average age of five men is 26; one 35-year old man joins them. What is the new average?

A) 27.5
B) 27.75
C) 31.25
D) 31.83

8. A, b & c are three friends with their incomes in ratio 7 : 9 : 12 and expenditure in 8 : 9 : 15 . If savings of A is 1/4 of his income then find the ratio of their savings?

A) 56 : 99 : 69
B) 53 : 89 : 69
C) 56 : 89 : 72
D) 64 : 89 : 72

9. After an increase in sugar price by 40%, a family reduced its consumption of sugar to the extent that there should be an increase on sugar expenses only by 10%. If the earlier consumption of sugar was 28 kg, what will be their new consumption?

A) 20 kg
B) 18 kg
C) 22 kg
D) 25 kg

10. A man purchases a certain number of mangoes at 3 per rupee and the same number of mangoes at 4 per rupee. He mixes them together and sells them at 3 per rupee. What is his gain or loss percent?

A) 100/7
B) 50/7
C) 75/11
D) 80/11

11. A bank gives compound interest on deposits at the rate of 5% for the first year, 6% for the second year and 10% for the third year; find the effective rate of interest for one year. Also find the initial deposit If the sum after three years is Rs 12243.

A) 11000
B) 13000
C) 15000
D) 10000

12. One pipe can fill a tank three times as fast as another pipe. If the two pipes together can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in?

A) 81 minutes
B) 108 minutes
C) 144 minutes
D) 192 minutes

13. If a person leaving his home for the bus stop at 4 km/h, notices that the bus has gone 7 minutes before already. And if he leaves his home at 6 km/h, he reaches the bus stop early by 8 minutes. Find the distance between his house and the bus stop.

A) 1 km
B) 1.5 km
C) 2 km
D) 3 km

14. The radius of a cylinder is 10 cm and height is 4 cm. The number of centimeters that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is?

A) 25
B) 16
C) 5
D) 4

15. The height of a circular cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases is?

A) 2/3
B) 3/2
C) 2
D) 1/2

16. The value of k for which the graph of (k – 1)x + y – 2 = 0 and (2 – k)x – 3y + 1 = 0 are parallel is?

A) 1/2
B) -1/2
C) 2
D) -2

17. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

A) 17.05
B) 27.85
C) 22.45
D) 26.25

18. AB is the diameter of a circle with centre O and P is a point on it. If ∠POA=120, then the value of ∠PBO=?

A) 60
B) 70
C) 55
D) 80

19. A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is 60°. When he retires 80 m from the corner, along the same straight line, he finds the angle to be 30°. The length of the field in meters is?

A) 40
B) 20√2
C) 20
D) 40√2

20. If tanA ÷ cotA = 2, then the value of tan⁷A + cot⁷A is?
A) 2
B) 64
C) 16
D) 128

MATHS — PRACTICE SET 12 (IN PDF) — TEST WITH SOLUTION