MATHS — PRACTICE SET 18 — 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. The ratio between the difference of denominator and numerator and the sum of denominator and numerator of a fraction is 2 : 9. What is the fraction?

A) 2/9
B) 5/6
C) 8/9
D) 7/11

2. Find the unit’s digit in 276²ⁿ – 161³ⁿ, if ‘n’ is a natural number.
A) 1
B) 3
C) 5
D) 6

3. (19²³)²⁵ divided by 16. Find remainder.

A) 3
B) 11
C) 15
D) 79

4. If x² + y² + z² = 2(x – y -z) – 3; then value of 2x – 3y + 4z is (assume x, y, z all are the real numbers)

A) 0
B) 1
C) 7
D) 3

5. If x = 2 + 2^1/3 + 2^2/3, then find x³ – 6x² + 6x

A) 0
B) 1
C) 2
D) 8

6. Samir’s age is one fourth of his father’s age and two third of his sister Reema’s age. What is the ratio of the age of Samir, Reema and their father respectively.

A) 10 years
B) 7 years
C) 13 years
D) 8 years

7. Jitesh started a business by investing Rs 50,000. After six months, Rahul joined her with a capital of Rs 80,000. After 3 years, they earned a profit of Rs 24,500. What was Jitesh’s share in the profit?

A) Rs 9,423
B) Rs 10,250
C) Rs 12,500
D) Rs 10,500

8. At a discount of 10% of the entire purchase Ram could have bought 1 more kg of sugar by paying only 5% of the original amount more. How many kilograms of sugar has Ram bought?

A) 7 kg
B) 5 kg
C) 6.5 kg
D) 6 kg

9. A shopkeeper sells a transistor at 15% above its cost price. If he had bought it at 5% more than what he paid for it and sold it for Rs 6 more, he would have gained 10%. The cost price of the transistor is?

A) Rs 1200
B) Rs 1175
C) Rs 1350
D) Rs 1300

10. A computer is available for Rs. 39000 cash or Rs. 17000 as cash down payment followed by five monthly installments of Rs. 4800 each. What is the rate of interest per annum under the installment plan?

A) 35.71%
B) 37.71%
C) 36.71%
D) 38.71%

11. The difference between the simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs 124.05. What is the principal?

A) Rs 4500
B) Rs 5800
C) Rs 8000
D) Rs 12000

12. A and B can do a work in 12 days, B and C can do the same work in 15 days, C and A can do the same work in 20 days. The time taken by A, B and C to do the same work is?

A) 12 days
B) 11 days
C) 8 days
D) 10 days

13. A man starts A to B at 12 pm and another man starts B to A at 2 pm. They meet each other at 4:05 pm and both of them reach their destination at the same time, what is that time?

A) 6 pm
B) 7 pm
C) 6:45 pm
D) 6:15 pm

14.

The diagram shows a square-based pyramid with base lengths 10 cm and height 12 cm
What is the surface area of the pyramid?

A) 260 cm²
B) 340 cm²
C) 360 cm²
D) 400 cm²

15. If each side of a rectangle is increased by 50%, then its area will be increased by?

A) 50%
B) 100%
C) 125%
D) 250%

16. ABCD is a rhombus having area √3 unit². BD is joined and O is the point of intersection of the bisectors of ∠ADB and ∠ABD. From O a perpendicular is drawn to BD. Its length is 4cm. Then BC =? Given ∠DCB = 60°.

A) 8√3
B) 3√3
C) 8
D) 48√3

17. The lateral side of an isosceles triangle is 15 cm and the altitude is 8 cm. What is the radius of the circumscribed circle?

A) 16 cm
B) 225/16 cm
C) 325/16 cm
D) 17 cm

18. N is the perpendicular from a point P of a circle with radius 7 cm on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is?

A) 26/7
B) 72/7
C) 47/7
D) 86/7

19. In ΔABC, ∠A is a right angle and AD is perpendicular to BC. If AD = 4 cm, BC = 12 cm, then the value of (cotB + cotC) is?

A) 4
B) 3/2
C) 6
D) 3

20. The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is?

A) 2.3 m
B) 4.6 m
C) 7.8 m
D) 9.2 m

MATHS — PRACTICE SET 18 (IN PDF) — TEST WITH SOLUTION