# MATHS — PRACTICE SET 20 — SOLVED

#### MATHS — PRACTICE SET 20 — 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 unit’s digit in 71 ^{7 }× 63^{6 }× 65^{3}?**

A) 1

B) 2

C) 4

D) 5

**2. When a number is divided by 24, the reminder is 16. The reminder when the same number is divided by 12 is?**

A) 1

B) 2

C) 3

D) 4

**3. If ^{1}⁄_{x+1} + ^{2}⁄_{y+2 }+ ^{1009}⁄_{z+1009} = 1**

**the value of ^{x}⁄_{x+1 }+ ^{y}⁄_{y+2 }+ ^{z}⁄_{z+1009} = ?**

A) 0

B) 2

C) 3

D) 4

**4. If (x – a) : (x – b) : (x – c) = 11 : 9 : 5; where x = (a+b+c)/2 then what is a : b : c**

A) 5 : 6 : 9

B) 7 : 8 : 10

C) 8 : 9 : 12

D) 2 : 3 : 5

**5. Arun, Kamal and Vinay invested Rs 8000, Rs 4000 and Rs 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs 4005, then what will be the share of Kamal?**

A) Rs 890

B) Rs 1335

C) Rs 1602

D) Rs 1780

**6. The ratio of numbers of boys and girls is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, then the % of students who do not get scholarship is?**

A) 50%

B) 56%

C) 76%

D) 80%

**7. A dishonest milkman professes to sell his milk at cost price but he mixes water with it and thereby gains 25%. Percentage of water in the mixture is ?**

A) 25%

B) 22%

C) 20%

D) 18%

**8. 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%

**9. Worker A is 50% as efficient as B. C does half of the work done by A & B together. If C alone does the work in 40 days, then A, B, C together can do the work in how many days?**

A) 40 days

B) 20 days

C) 40/3 days

D) 40/7 days

**10. Two trains start simultaneously from two stations Howrah and Delhi, respectively towards each other on the same track. The distance between the two stations is 560 km and the speeds of trains are 30 km/h and 40 km/h. Simultaneously with the trains, a sparrow sitting on the top of one of the train starts towards the other and reverses its direction on reaching the other train and so on. If the speed of sparrow is 80 km/h then the distance that the sparrow flies before being crushed between the train is.**

A) 500 km

B) 555 km

C) 600 km

D) 640 km

**11. A friction clutch is in the form of a frustum of a cone, the diameters of the ends being 32 cm and 20 cm and length 8 cm. Find its bearing surface and volume.**

A) 817.14 cm², 4324.57 cm³

B) 917.14 cm², 4342.57 cm³

C) 800.24 cm², 4224.75 cm³

D) 850.24 cm², 4304.75 cm³

**12. If a metallic cone of radius 30 cm and height 45 cm is melted and recast into metallic spheres of radius 5 cm; find the number of spheres.**

A) 81

B) 41

C) 80

D) 40

**13. asec@ + btan@ + c = 0 and psec@ + qtan@ + r = 0;**

**then (br – qc)² – (pc – ar)² = ?**

A) 1

B) 4

C) 0

D) 3

**14. In ΔABC, AB = 3, AC = 4. The bisector of ∠A divides the side BC at D, then find BD : DC.**

A) 1 : 2

B) 4 : 3

C) 3 : 4

D) 3 : 7

**15. An isosceles ΔABC is right angled at B. D is a point inside the ΔABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, find sin 75.**

**16. PQ is a chord of length 8 cm of a circle with center O and of radius 5 cm. The tangents at P and Q intersect at a point T. The length of TP is? **

A) 15/4 cm

B) 20/3 cm

C) 21/4 cm

D) 10/3 cm

QUESTIONS 17 to 20. The following graph shows the demand and production of cotton by 5 companies A, B, C, D and E. Study the graph and answer the questions.

**17. The production of the company D is how many times that of the production of the company A?**

A) 1.8

B) 1.5

C) 0.5

D) 0.4

**18. The demand for company B is what percent of the demand for company C?**

A) 1.5

B) 2.5

C) 25

D) 30

**19. What is the ratio of companies having more demand than production to those having more production than demand?**

A) 2 : 3

B) 4 : 1

C) 3 : 2

D) 1 : 4

**20. What is the difference (in tonnes) between average demand and average production of the five companies taken together?**

A) 320

B) 420

C) 2100

D) 20