Time : 2 hrs

ACE OF PACE SAMPLE TEST PAPER

Max.Marks: 150

Marking Scheme: Each question carries +3 for correct answer. There is no negative marking in the paper.

1.

If 562 – 512 = 5p, then p is equal is (A) 107 (B) 106

(C) 105

(D) 104

2.

If x and y are positive with x – y = 2 and xy = 24 then (A)

1 x

1 is equal to y

(D)

1 12

(B)

5 12

(C)

1 6

25 6

3.

If x = 2, y = 3, then xx + yy is equal to (A) 30 (B) 31

(C) 33

(D) 37

4.

If x = 2, y = 1 and z = -3, then x3 + y3 + z3 – 3xyz is equal to (A) 0 (B) 2 (C) 6 If x (A) 0

(D) 8

5.

1 x 2

2

1 x 2

, then x is equal to (B) 1 (C) 2 (D) None of these

6.

The quadratic equation whose roots are (A) x –

2

7 and

7

0

(B) x – 7 = 0

2

7 is (C) x + 7

2

0

(D) x2 + 7 = 0

7.

A man sold two horses for Rs. 400 each. He gained 5 % on one and lost 5 % on the other, which of the following statements is true? 1 1 (A) Gains % (B) Loses % 4 4 (C) Neither gains nor loses (D) Incomplete information A corporation declares an annual dividend of 6% Ravi owns 325 shares (par value Rs. 75). The dividend received by Ravi is. (A) Rs. 1463.75 (B) 1462.75 (C) 1462.50 (D) Rs. 1461.70 In this figure, AB || CD, A

8.

9.

EFD is equal to

C D 30o

60o B F

E

(A) 20

o

(B) 25o

(C) 30o

(D) 35o

10.

The two numbers are such that their product is equal to their sum but the numbers are different. The numbers are (A) 12, 14 (B) 11, 11 (C) 2, 2 (D) 1.1, 11 The sides AB, BC, CA of a right angled triangle are 17, 15, 8 respectively; the value of tan A. sec B is equal to 8 17 15 17 (A) (B) (C) (D) 17 8 17 15

11.

12.

tan is not defined when (A) 0o (B)

is equal to /4

(C)

/6

(D)

/2

13.

If the diameter of the circle is increased by 200 percent its area is increased by (A) 100% (B) 200% (C) 300% (D) 800% If the area of an equilateral triangle is 64 3 cm2, then the side of the triangle is (A) 12 cm (B) 14 cm (C) 16 cm (D) 18 cm In the given figure x + y is equal to

14.

15.

o x 55

O

y

(A) 45o

(B) 55o

(C) 110o

(D) 125o

16.

A boy goes to school with the speed of 3 km/h and returns with the speed of 2 km/h. If he takes 5 hours in all, then the distance (in kilometres) between the village and school is (A) 6 (B) 7 (C) 8 (D) 9 The length, breadth and height of a rectangular parallelopiped are in the ratio 5 : 4 : 3 and its surface area is 13536 cm2. Its length, breadth and height are respectively (A) 60 cm, 48 cm, 36 cm (B) 60 cm, 45 cm, 36 cm (C) 60 cm, 48 cm, 30 cm (D) 55 cm, 45 cm, 35 cm

17.

18.

1 sin 2 sec 2 When simplified the trigonometric expression 1 cos 2 cos ec 2 (A) sin (B) tan (C) cot The square root of 8 4 3 is (A) 2

reduces to (D) tan 2

19.

3

(B) 2 3 1

(C)

6

2

(D)

6

3

20.

A land mark on the bank of a river is observed from two points A and B on the opposite banks of the river. The lines of sight make equal angles of 45o with the bank of the river. If AB = 1 km, then the width of the river (in kilometre) is 3 1 3 (A) (B) 2 (C) (D) 2 2 2 2 The product of two consecutive odd numbers is 195, the smaller of them is (A) 15 (B) 5 (C) 13 (D) 3 A trader lists his articles 20% above C.P. and allows a discount of 10% on cash payment. His gain percent is (A) 10% (B) 8% (C) 6% (D) 5% Ashok invests Rs. 3,000 for a year and Sunil joins him with Rs. 2,000 after 4 months. After the year they receive a return of Rs. 2,600. Sunil’s share is (A) Rs. 800 (B) Rs. 1200 (C) Rs. 750 (D) Rs. 900 What is the total number of candidates at an examination if 31% fail and the number of those who fail is 248? (A) 650 (B) 750 (C) 800 (D) None of these If three numbers are in the ratio 3 : 2 : 5 and they are such that the sum of their squares is equal to 1862, the middle one is (A) 12 (B) 10 (C) 14 (D) None of these The...