# MATHS — PRACTICE SET 24 — SOLVED

#### MATHS — PRACTICE SET 24 — 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. What is the unit digit in (7 ^{95} – 3^{58})?**

A) 0

B) 4

C) 6

D) 7

**2. If the sum of two numbers is 55 and the HCF and LCM of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to?**

A) ^{55}⁄_{601}

B) ^{601}⁄_{55}

C) ^{11}⁄_{120}

D) ^{120}⁄_{11}

**3. Find the number when it is divided by 9, 11, 13 leaves remainders 1, 2, 3 respectively.**

A) 640

B) 620

C) 649

D) 658

4.

A) 0

B) 1

C) 5

D) 2

5.

**6. A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1?**

A) 1/3

B) 1/4

C) 2/5

D) 2/3

**7. The average of the work done by (x – 2) men in (x + 2) days and work done by (x + 3) men in (x – 2) days is 15 : 16. Find the value of ‘x’.**

A) 26

B) 13

C) 10

D) 12

**8. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?**

A) 3 : 5 : 2

B) 3 : 5 : 5

C) 6 : 10 : 5

D) 3 : 5 : 10

**9. If a milkman sells milk at cost price but mixes water in it, he gains 25% on cost price. Then what will be the percentage of water in the mixture?**

A) 25%

B) 30%

C) 20%

D) 27%

**10. A seller uses 920 gm in place of 1 kg to sell his goods. When he sells his articles at 15% gain on CP, the actual percentage of profit is?**

A) 25%

B) 30%

C) 20%

D) 15%

**11. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?**

A) 6.06%

B) 6.07%

C) 6.08%

D) 6.09%

**12. Reena borrowed Rs 6450 at 5% simple interest repayable in 4 equal installments. What will be the annual installment payable by him ?**

A) 1710

B) 1800

C) 1910

D) 1860

**13. A does 2/3 part of a work in 4 day. B does 3/5 part of that work in 6 day. If they work together then in how many day work has to be done?**

A) 3 days

B) 2 days

C) 15/4 days

D) 23/8 days

**14. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is?**

A) 3 : 1

B) 1 : 3

C) 2 : 4

D) 4 : 2

**15. A pyramid is with a triangular base ABC, where AB = 5 cm, BC = 4 cm and CA = 3 cm. The point D is vertically above the point C. What is the volume of the pyramid?**

A) 16 cm³

B) 20 cm³

C) 24 cm³

D) 32 cm³

**16. The length of a rectangle is increased by 40%. By what percentage the width of the rectangle have to be decreased to maintain the same area?**

A) 28.5%

B) 28%

C) 27.75%

D) 35%

**17. In ΔABC, P is a point on AB such that ∠ACP = ∠ABC. If AC = 9 cm, CP = 12 cm and BC = 15 cm, find AP.**

A) 11.2 cm

B) 10.2 cm

C) 8.0 cm

D) 7.2 cm

**18. In a circle, AB is diameter, CD is chord of length equal to radius of the circle. AC and BD when produced intersect at point E. Find ∠AEB?**

A) 60°

B) 65°

C) 70°

D) 55°

**19. In ΔABC, ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD is drawn || to AB, then ∠ACD is?**

A) 40°

B) 60°

C) 80°

D) 20°

**20. A vertical pole fixed to the ground is divided in the ratio 1:9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 15 m away from the base of the pole, what is the height of the pole?**

A) 60√5 m

B) 15√5 m

C) 15√3 m

D) 60√3 m