Ace of PACE Sample Paper

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / CHURCHGATE / NERUL / POWAI

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.

2.

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

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

3.

4.

5.

1 12

(B)

5 12

(C)

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

1 x

1

If x

x 2

2

1 x 2

1 6

(D)

(C) 33

(D) 37

(C) 2

The quadratic equation whose roots are (A) x –

7

(D) 8

(D) None of these

7 and

2

(B) x – 7 = 0

0

25 6

, then x is equal to (B) 1

2

(D) 104

1 is equal to y

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

(A) 0 6.

(C) 105

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

8.

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

9.

In this figure, AB || CD,

EFD is equal to

A

C

60o

D 30o

B

E

F o

(A) 20

(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

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

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%

14.

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

15.

In the given figure x + y is equal to

o x 55

O

(A) 45o

y

(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

17.

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

18.

19.

1 sin 2 sec 2 When simplified the trigonometric expression 1 cos 2 cos ec 2 (A) sin (B) tan (C) cot

reduces to (D) tan 2

The square root of 8 4 3 is (A) 2

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

21.

The product of two consecutive odd numbers is 195, the smaller of them is (A) 15 (B) 5 (C) 13 (D) 3

22.

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%

23.

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

24.

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

25.

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

26.

The sides of a triangle are in ratio 4 : 6 : 7, then the triangle is (A) acute angled (B) obtuse angled (C) right angled

27.

28.

(D) impossible

The angles of a pentagon in degrees xo, (x + 20o), (x + 40o), (x + 60o) and (x + 80o). The smallest angle of the pentagon is (A) 88o (B) 78o (C) 68o (D) 58o In the adjoining figure K is equal to (A) 109o (B) 1120 (D) 79o

C 30o E

(C) 75o

K 45o 34o

D

B

A

29.

A 25 metre long ladder is placed against a high vertical tower such that the foot of the ladder is 7 metres from the foot of the tower. If the top of the ladder slides 4 metres downwards then the foot of the ladder will slide by (A) 2 metres (B) 4 metres (C) 8 meters (D) 16 meters

30.

In a circle of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. The distance of the chord BC from the centre O is A 6 5-x B

(A) 3.6 cm 31.

C

x O

5

(B) 1.4 cm

(C) 1 cm

(D) 4.6 cm

ABCD is cyclic quadrilateral AB is the diameter of the circle through A, B, C, D. If BAC = 35o, then ADC is equal to C

D

A

(A) 125o

35o O

B

(B) 135o

(C) 145o

(D) 155o

32.

Ram mother’s present age is six times Ram’s present age. Ram’s age five years from now will be one third of his mother’s present age. What are their present ages? (a) Ram : 6, Mother: 29 (b) Ram : 5, Mother: 30 (c) Ram : 30, Mother: 5 (d) Ram : 8, Mother: 32

33.

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4. At the rate Rs100 per metre it will cost the village panchayat Rs75000 to fence the plot. What are the dimensions of the plot? (a) length = 375, breadth = 150 (b) length = 275, breadth = 100 (c) length = 175, breadth = 120 (d) length = 120, breadth = 150

34.

Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby.The rest 9 are drinking water from the pond. Find the number of deer in the herd. (a) 75 (b) 76 (c) 71 (d) 72

35.

If N is divided by 9 then the remainder is 5, what will be the remainder if N is divided by 3 (A) 2 (B) 1 (C) 0 (D) None of these

36.

Number of diagonals of a pentagon are? (A) 8 (B) 5

(C) 10

(D) None of these

37.

If all 7's are replaced by the digit 6 , then the number of 6's in series 1,2,3,4.....99, 100 will be (A) 31 (B) 32 (C) 33 (D) none of these

38.

The ratio of areas of incircle and circumcircle of an equilateral triangle will be (A) 1/3 (B) ¼ (C) 2/3 (D) None of these

39.

The ratio of areas of incircle and circumcircle of an iscoceles right angled triangle is (A) ½ (B) ¼ (C) 1/3 (D) none of these

40.

A school has 378 girl students and 675 boy students. The school is divided into strictly boys or strictly girls sections. All sections in school have the same number of students. Given this information, what are the numbers of sections in the school? (A) 25 (B) 39 (C) 36 (D) 34

41.

The last digit of the number obtained by multiplying the numbers 81 × 82 × 83 × 84 × 85 × 86 × 87 × 88 × 89 will be: (A) 0 (B) 9 (C) 7 (D) 2

42.

The average marks of a group of 20 students on a test is reduced by 4 when the topper who scored 90 marks is replaced by a new student. How many marks did the new student have? (A) 8 (B) 20 (C) 15 (D) 10

43.

If 5 kg of salt costing Rs. 5 / kg and 3 kg of salt costing Rs. 4 / kg are mixed , find the average cost of the mixture per kilogram (A) Rs. 4.5 (B) Rs. 4.625 (C) Rs. 4.75 (D) Rs. 4.125

44.

If x1/3 + y1/3 + z1/3 = 0, then (A) x + y + z = 3 xyz (B) x + y + z = 0

45.

(A) x 46. 47.

3 , find the value of x2 +

If x = 2 +

1 x

2

2

(B) x

49.

50.

(D) x3 + y3 + z3 = 0

1 x2

2

2

The value of x , when 3 4 x 7 – 5 = 0 is (A) 3 (B) 11

(C) 14

(D) all the above

(C) 33

(D) 12

Which of the following might not be an integer? (A) Square of an integer (B) Product of two integers (C) Sum of two integers

48.

1 x

(C) ( x + y + z)3 = 27 xyz

(D) Ratio of two integers

(10 y) = 2 and 2x y = y , then find x and y : If (A) 30 , 6 (B) 15 , 6 (C) 15 , 17

(D) 16 , 17

The reciprocal of sec x + tan x is going to be (A) sec x – tan x (B) cos x (C) sin x

(D) None of these

Ratio of sides of rectangle is 2. Its area is 4 cm2 , then the perimeter of rectangle is : (A) 4 2 (B) 6 2 (C) 8 2 (D) 10 2