MATHS — PRACTICE SET 26

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: 25                                                                                        MAXIMUM TIME: 25 minutes

1. If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11?

A) 4x + 6y
B) x + y + 4
C) 9x + 4y
D) 4x – 9y

2. A worker was engaged for a certain number of days. But he remained absent for some days and was paid Rs 1387. Had he worked all the days, he would have earned Rs 1752. How many days did he work for?

A) 19
B) 21
C) 24
D) 29

3. Find the smallest number when is divide by 8, 5 and 11 leaves remainders 5, 2 and 6 respectively.

A) 237
B) 242
C) 245
D) 337

4. If x = b + c – 2a; y = c + a – 2b; z = a + b – 2c, then find the value of x² + y² – z² + 2xy

A) 0
B) a + b + c
C) a – b + c
D) a + b – c

5. 

A) -125
B) 1
C) 125
D) 140

6. Two types of oil A and B are mixed in the ratio 3:2. 1/4th of the mixture is wasted. To the remaining mixture additional amount of oil A is mixed so that the ratio becomes 5:3. If the quantity of the new mixture be 1200 litre, find the quantity of original mixture and also additional amount of A mixed later.

A) 1500,     50
B) 2000,     50
C) 2000,     75
D) 1500,     75

7. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

A) Rs 45
B) Rs 50
C) Rs 55
D) Rs 60

8. A man invested 1/3 of his capital at 7% per annum, 1/4 at 8% per annum and the remainder at 10% per annum. If his annul income is Rs 561, the capital is?

A) 6600
B) 6500
C) 7000
D) 7500

9. A person bought 2 bicycles for Rs 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get Rs 5 more. the difference of cost price of the two bicycles was?

A) Rs 50
B) Rs 40
C) Rs 35
D) Rs 75

10. Rahul borrows Rs 1,00,000 from a bank at 10% p.a. simple interest and clears the debt in five years. If the installments paid at the end of the first, second, third and fourth years to clear the debt are Rs 10,000, Rs 20,000, Rs 30,000 and Rs 40,000 respectively, what amount should be paid at the end of the fifth year to clear the debt?

A) Rs 20,000
B) Rs 24,500
C) Rs 30,000
D) Rs 35,900

11. The difference between the simple interest received from two different sources on Rs 1500 for 3 years in Rs 13.50. The difference between their rates of interest is?

A) 0.1%
B) 0.2%
C) 0.3%
D) 0.4%

12. A is 60% more than B, and B is 20% less than C; then what is the ratio between A : B : C.

A) 20 : 32 : 25
B) 30 : 32 : 45
C) 32 : 20 : 25
D) 25 : 32 : 20

13. A man leaves point ‘P’ and reaches the point ‘Q’ in 5 hrs. Another man leaves the point ‘Q’ 2 hrs later and reaches the point ‘P’ in 7 hrs. Find the time in which the first man meets the second man?

A) 3 hours 30 minutes
B) 3 hours 45 minutes
C) 4 hours
D) 4 hours 15 minutes

14. Two trains, one from station A to station B, and the other from B to A start simultaneously. After meeting, the trains reach their destination after 9 hours and 16 hours respectively. The ratio of their speeds is?

A) 2:3
B) 4:3
C) 6:7
D) 9:16

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. If the area of ΔABD is 20.9 cm², what is the total surface area of the pyramid?

A) 48.9 cm²
B) 54.9 cm²
C) 58.9 cm²
D) 74.9 cm²

16. A right circular cylinder is formed by rolling a rectangular sheet of metal of length 24 cm and breadth 22 cm along its length. The volume of the cylinder is?

A) 924 cc
B) 462 cc
C) 1008 cc
D) 528 cc

17. The angles of an acute angle triangle are all distinct integers. If the smallest angle has the largest possible value, find the sum of two other angles.

A) 60°
B) 61°
C) 121°
D) 125°

18. How many sides does a regular polygon have whose interior and exterior angle are in the ratio of 2:1.

A) 3
B) 5
C) 6
D) 12

19. O is centre of a circle. Two cords AC and BD intersect at P. If ∠AOB =15 and ∠APB=30, find tan² ∠APB + Cot² ∠COD

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

20. In a right triangle ABC with ∠A equal = 90°, find ∠B and ∠C so that sin(B) = cos(B).

A) ∠B = 30°, ∠C = 60°
B) ∠B = 40°, ∠C = 50°
C) ∠B = 45°, ∠C = 45°
D) ∠B = 60°, ∠C = 30°

21. If sec θ + tan θ = p, then sin θ is?

A) ¹⁄_(p²+1)
B) ¹⁄_(p²-1)
C) ^(p²+1)⁄_(p²-1)
D) ^(p²-1)⁄_(p²+1)

22. Find the angle of elevation of the sun when the shadow of a pole of 18 m height is $6\sqrt{3}$m long.

A) 30°
B) 60°
C) 45°
D) 50°

QUESTIONS 23 to 25. The following pie-chart shows excess of expenditure by a family on various items over its savings, which amounts to Rs 8,000 in a month. Study the chart and answer the questions based on this pie-chart. 

23. What is the total expenditure of the family for the month?

A) Rs 40,000
B) Rs 48,000
C) Rs 45,000
D) Rs 50,000

24. How much more amount is spent on food than on housing?

A) Rs 1,000
B) Rs 3,000
C) Rs 2,000
D) Rs 2,500

25. The ratio of expenditure on food to the savings is?

A) 3 : 2
B) 2 : 1
C) 4 : 3
D) 3 : 4

MATHS —- PRACTICE SET 26 —- SOLVED 

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