# MATHS — PRACTICE SET 19 — SOLVED

#### MATHS — PRACTICE SET 19 — 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 product of two numbers is 2028 and their HCF is 13. The number of such pairs is?**

A) 1

B) 2

C) 3

D) 4

**2. A man fill a basket with eggs in such a way that every minute he adds same number of eggs already present in the basket. This way the basket gets completely filled in 60 min. After how many minutes the basket was 1/4th full?**

A) 15 minutes

B) 20 minutes

C) 30 minutes

D) 58 minutes

**3. When a number is divided by 7 the remainder is 4 and when the number is divided by 6, the remainder is 3. What will be the number?**

A) 32

B) 46

C) 39

D) 53

**4. (27 + √756) ^{1/3} + (27 – √756)^{1/3} = ?**

A) 0

B) 1

C) 3

D) 7

**5. If xy + yz + zx = 0; then 1/(x² – yz) + 1/(y² – zx) + 1/(z² – xy) is equal to**

A) 1

B) 0

C) 3

D) x+y+z

**6. Zinc and copper are in the ratio 5 : 3 in 400 gm of an alloy. How much of copper (in grams) should be added to make the ratio 5 : 4?**

A) 66

B) 72

C) 200

D) 50

**7. The average of 8 numbers is 20. The average of first two numbers is 31/2 and that of the next three is 64/3. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eighth number is?**

A) 25

B) 27

C) 35

D) 17

**8. The total salary of A, B and C is Rs 666. If they spend 80%, 85%, 75% of their salaries respectively, their savings are 7 : 6 : 9. Then salary of C is?**

A) Rs 300

B) Rs 250

C) Rs 216

D) Rs 245

**9. In an election 68 votes are invalid. the winning candidate secures 52% and wins by 98 votes. The total number of votes polled are?**

A) 6000

B) 4500

C) 3534

D) 2518

**10. A shopkeeper gives 2 items free for every 3 items purchased. In effect what discount is being offered ?**

A) 30%

B) 35%

C) 40%

D) 45%

**11. A man deposited Rs 400 for 2 years, Rs 550 for 4 years and Rs 1200 for 6 years. He received Rs 1020 as the total simple interest. The rate of interest per annum is?**

A) 7%

B) 7.5%

C) 7.25%

D) 10%

**12. A does a work in 6 days, B in 8 days, and C in 10 days. A worked alone for 2 days before leaving and then B and C worked together for 2 days and after that B left. The remaining work was finished by C alone. How long did it take to finish the work?**

A) 37/6 days

B) 37/5 days

C) 6 days

D) 8 days

**13. A motorboat whose speed is 15 km/h in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is?**

A) 2 km/h

B) 3 km/h

C) 4 km/h

D) 5 km/h

**14. For which values of p and q, will the following pair of linear equations have infinitely many solutions?
4x + 5 y = 2
(2p + 7q)x + (p + 8q)y = 2q – p + 1.**

A) 1, 2

B) 2, -1

C) -1, 2

D) 3, -1

**15. Length of each equal side of an isosceles triangle is 10 cm and the included angle between those two sides is 45°. Find the area of the triangle.**

A) 25√2 cm²

B) 35√2 cm²

C) 5√2 cm²

D) 15√2 cm²

**16. In the figure given below, XYZ is a right angle triangle in which ∠Y is 45° and ∠X is 90°. ABCD is a square inscribed in it whose area is 64 cm². What is the area of the ΔXYZ?**

A) 12 cm²

B) 140 cm²

C) 144 cm²

D) 64 cm²

FIGURE

**17. The perimeter of a rhombus is 40 cm and the measure of an angle is 60°, then the area is?**

A) 50√3 cm²

B) 100√3 cm²

C) 100√3/2 cm²

D) 55 √3 cm²

**18. **

A) 4 cm

B) 3 cm

C) 2.5 cm

D) 5 cm

**19. If 2sinX + 15cos²X = 7, then the value of cotX = ?**

A) 3/4 or -√5/2

B) 3/4 or -2/√5

C) 4/3 or -√5/2

D) 4/3 or -2/√5

**20. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is?**

A) 21.6 m

B) 23.2 m

C) 24.72 m

D) 22.54 m