# MATHS —- PRACTICE SET 25 —- SOLVED

## MATHS —- PRACTICE SET 25 —- SOLVED

**QUESTIONS: 25 MAXIMUM TIME: 25 minutes**

**1. The sum of the digits of a two digit number is 10. If 18 be subtracted from it, the digits in the resulting number will be equal. What is the number?**

A) 82

B) 91

C) 73

D) 64

**2. Find the sum of the series **

**1 +**

^{4}**⁄**

_{7}**+**

^{9}**⁄**

_{7²}+

^{16}**⁄**

_{7³}+ ………infiniteA) ^{49}⁄_{27}

B) ^{36}⁄_{49}

C) ^{49}⁄_{36}

D) ^{27}⁄_{49}

**3. If the number 23583ab is completely divisible by 80, then the value of a – b is**

A) 2

B) 3

C) 4

D) 0

4.

A) 4

B) 3

C) 1

D) 2

**5. If x + ^{1}⁄_{x} = 5; then calculate ^{2x}⁄_{(3x² – 5x +3)}**

A) 1/2

B) 5

C) 1/5

D) 2/5

**6. 4a = 5b, 7b = 9c, then f****ind a : b : c = ?**

A) 45 : 36 : 28

B) 30 : 36 : 25

C) 36 : 45 : 28

D) 36 : 30 : 25

**7. A began a business with Rs 85,000. He was joined afterwards by B with Rs 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?**

A) 4 months

B) 5 months

C) 6 months

D) 8 months

**8. In the New York stock exchange there are 45% female employees and thus the number of male employees is exceeded by 72. Hence the total number of employees in the New York stock exchange is?**

A) 700

B) 720

C) 650

D) 800

**9. A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade for Rs 31350. Find at what price he must sell the first grade bicycle so that if he sells the second grade bicycles at 3 quarters of this price, he may make a profit of 40 percent on his outlay.**

A) Rs 1791.60

B) Rs 1600

C) Rs 1600.80

D) Rs 1700

**10. The interest of one rupee in one month is 1 paise. What is the rate of interest?**

A) 10%

B) 12%

C) 10.75%

D) 11%

**11. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is?**

A) Rs 1550

B) Rs 1650

C) Rs 1750

D) Rs 2000

**12. A and B can complete a work individually in 60 and 40 days. Both start working simultaneously, but 4 days before the work is scheduled to get over B leaves. Find the total number of days taken for the work to be completed.**

A) 26 days

B) 26.4 days

C) 26. 8 days

D) 30 days

**13. Two cars start simultaneously from place A and B 100 km apart, towards each other. A bird sitting on one car starts at the same time towards the other car, and as soon as it reaches the second car, it flies back to the first car and it continues in this manner flying backwards and forwards from one car to the other until the cars meet. Both cars travel at a speed of 50 km/h and the bird flies at 100 km/h. Total distance covered by the bird will be?**

A) 100 km

B) 200 km

C) 50 km

D) 80 km

**14. Length of the diagonal of a square is 8 cm. A circle has been drawn circumscribing the square. The area of the portion between circle and square is?**

A) ^{102}⁄_{7}

B) ^{128}⁄_{7}

C) ^{162}⁄_{7}

D) ^{182}⁄_{7}

**15. There is a rectangular field with dimensions 31 m × 10 m. We have to dig a rectangular hole in the field with dimensions 4 m × 2.5 m and 1.5 m deep and the volume of that hole is to be spread on the round equally, tell how much the level of the ground will raise.**

A) 0.5 m

B) 0.05 m

C) 0.75 m

D) 1.5 m

**16. Inside a square ABCD, ΔBEC is an equilateral triangle. If CE and BD intersect at O, then ∠BOC = ?**

A) 60

B) 75

C) 90

D) 120

**17. The ratio of the areas of two isosceles triangles having equal vertical angles is 1 : 4. The ratio of their heights will be?**

A) 1 : 2

B) 3 : 4

C) 2 : 3

D) 6 : 7

**18.**

A) 80°

B) 85°

C) 70°

D) 75°

**19. The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle.**

A) 10, 10√2

B) 10, 200

C) 15, 10√2

D) 10, 12

**20. If tan θ = 2, then the value of ^{8sin θ + 5cos θ}⁄_{sin³ θ + 2cos³ θ + 3cos θ} is?**

A) ^{21}⁄_{5}

B) ^{8}⁄_{5}

C) ^{7}⁄_{5}

D) ^{16}⁄_{5}

**21. From the foot and the top of a building of height 230 m, a person observes the top of a tower with angles of elevation of b and a respectively. What is the distance between the top of these buildings if tan a = 5/12 and tan b = 4/5? **

A) 400 m

B) 250 m

C) 600 m

D) 650 m

**22. A train travelling got accidental 50 km after the journey and therefore proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late. Had the accident occurred 24 km further, it would have reached the destination only 15 minutes late. Normal speed of the train?**

A) 19.2 km/h

B) 19 km/h

C) 20 km/h

D) 24 km/h

QUESTIONS 23 to 25. The following pie-chart shows the number of students admitted in different faculties of a college. Study the chart and answer.

**23. If 1000 students admitted in science, what is the ratio of students in science and arts?**

A) 7 : 5

B) 7 : 6

C) 5 : 6

D) 6 : 5

**24. If 1000 students admitted in science, what is the total number of students?**

A) 1800

B) 3600

C) 360

D) 180

**25. How many students are more in commerce than in law if 1000 students are in science?**

A) 2000

B) 500

C) 20

D) 200