MATH SET 03

1.If cos@ cosec23⁰=1, then the value of @ is

a)23⁰ b)37⁰ c)63⁰ d)67⁰

2.One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is:

a)37% b)12-1/7% c)46% d)24-2/7%

3.  x, y ,z are three sums of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then we have

a)  z² =xy b)xyz =1 c)x²=yz d)y²=zx

4.  If the area of a circle of radius x is 5π, find the area of a circle of radius 3x.

(A) 10π(B) 15π(C) 20π(D) 30π(E) 45π

5. If the length and width of a rectangle are each doubled, the area is increased by

(A) 50% (B) 100% (C) 200% (D) 300% (E) 400%

6. The area of one circle is 9 times as great as the area of another. If the radius of the smaller circle is 3, find the radius of the larger circle.

(A) 9 (B) 12 (C) 18 (D) 24 (E) 27

7. The volumes of two similar solids are 250 and 128. If a dimension of the larger solid is 25, find the corresponding side of the smaller solid.

(A) 12.8 (B) 15 (C) 20 (D) 40 (E) cannot be determined

8.The area of a trapezoid whose bases are 10 and 12 and whose altitude is 3 is

(A) 66 (B) 11 (C) 33 (D) 25 (E) 16 ½

9. The circumference of a circle whose area is 16π is

(A) 8π (B) 4π (C) 16π (D) 8 (E) 16

10. . Find the perimeter of a square whose diagonal is 8.

(A) 32 (B) 16 (C) 32 2 (D) 16 2 (E) 32 3

11. The length of the line segment joining the point A(4, –3) to B(7, –7) is

(A) 221 (B) 185 (C) 7 (D) 6 12 (E) 5

12. Find the number of degrees in each angle of a regular pentagon.

(A) 72 (B) 108 (C) 60 (D) 180 (E) 120

13. If the angles of a triangle are in the ratio 5 : 6 : 7, the triangle is

(A) acute (B) isosceles (C) obtuse (D) right (E) equilateral

14.Last year my age was a perfect square number. Next year it will be a cubic number. What is my present age?

a)25 yrs b)27 yrs c)26 yrs d)24 yrs.

15. The average of three numbers 70, @7 and 5@ is 57. If @ represents the same digit, then it must be

a)3 b)6 c)4 d)7

16. The base of a triangle is 2 cm more than twice its altitude. If the area is 12 sq. cm, its altitude will be

a)6 cm b) 5 cm c)4 cm d) 3 cm

17. If a + b =5, a² + b² =13, the value of a-b (where a>b) is

a)2 b)-1 c)1 d)-2

18. The value of (sec@ - cos@) (cosec@ -sin@)(tan@ +cot@) is

a)2 b)0 c)1 d)3/2

19. G is the centroid of triangle ABC. If AG = BC, then <BGC is

a)60⁰ b)120⁰ c)90⁰ d)30⁰

^{20. tan70 tan230 tan600 tan670 tan830 is equal to}

^{a)1/root3 b)1 c)0 d) root3}

21.A bookseller makes 8% profit after selling the book at 10% discount. The ratio of the cost price to the marked price is

a)4:5 b)5:4 c)5:6 d)6:5

22.A certain sum of money is distributed to A and B in the ratio 2:5. If A received Rs.100, then the money received by B is

a)Rs.200 b)Rs.150 c)Rs. 250 d) Rs. 300

23.Three years ago, the average age of a family of 8 members was 30 yrs. If one child is also included in the family, the present average age of the family remained the same. Then the present age of the child is

a)3 yrs b)4 yrs. C)6 yrs. D)1 yrs.

24.The value of 1372 x 1458 is

a)116 b)126 c)106 d)136