Microsoft Word - Practice Test-02 - 4 Year Program.doc

1

Vidyamandir Classes Admission test for IITJEE

Test Name Practise Test - 01

Time

Total marks

3 Hour

200

Read the following Instructions very carefully before you proceed. Section - I and Section - II.




The paper contains total of 40 Objective Type Questions divided into two sections:




Section - I contain 20 questions and Section - II contain 20 questions. Each question has 4 choices (A), (B), (C) and (D), out of which only one choice is correct.




For each question in Section - I, you will be given 4 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (–1) marks (NEGATIVE MARKING) will be given.




For each question in Section - II, you will be given 6 marks if you have darkened only the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (–2) marks (NEGATIVE MARKING) will be given.

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Vidyamandir Classes Admission test for IITJEE

2

SECTION - I 1.

2.

Five - eighth of 576 is how much more than four - ninth of 486 ? (A) 126 (B) 135 (C) 168 The simplified value of the given expression

(A)

4 ( 4 x − 3)

(B)

( 3x − 8 )

(D)

144

(D)

( 2 x + 8)

9 x 2 − 64 is : 1 x −1− x 1− 4+ x

(C)

4 (3x + 8)

3.

An article is sold at a loss of 20% . Had it been sold for ` 663 more, it would have fetched a profit of 12.5% . Find the cost price the article. (A) ` 1760 (B) ` 1960 (C) ` 2040 (D) ` 2520

4.

The ratio of the present ages of A and B is 2 : 5. After n years, the ratio of their ages will be 1 : 2 . If the sum of their present ages is 42 years, then find the value of n. (A) 6 (B) 8 (C) 12 (D) 15

5.

In a rectangle, length is twice the breadth. If the length of a rectangle is increased by 20% and its breadth is increased by 10% . The percentage increase in its perimeter will be : (A) 12% (B) 13.33% (C) 10% (D) 16.67%

6.

Arjun spent ` 12 to purchase some pens and pencils. The cost of a pen and a pencil are in the ratio 3 : 2 . The total cost of a pen and a pencil is ` 3. If the total number of pens and pencils he purchased is 7, find the number of pens he purchased. (A) 3 (B) 4 (C) 6 (D) 5

7.

 a1 2 x −2 a x   The simplified value of the given expression  5 1 2 −2 × 3 −1  x a x a   

(A)

3

a8

(B)

3

a −8

(C)

3

x 2 a −5

−4

is :

(D)

3

x −2 a 5

8.

Find the number of coins, 5 cm in diameter and 0.14 cm in thickness, that are needed to be melted to form a solid cylinder of height 315 cm and radius 5 cm (A) 900 (B) 90000 (C) 9000 (D) None of these

9.

A circle has an area of 2464 sq. cm. Find its circumference (in cm). (Assume π =

(A) 10.

176

(B)

198

(C)

154

(D)

22 7

)

132

I have got some chocolates to be distributed. When they are put in packets of 2, 3, 4 or 5 each, I am left with one. If they are put in packets of seven, I am left with none. What is the minimum number of chocolates that I have ? (A) 301 (B) 201 (C) 411 (D) None of these

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Vidyamandir Classes Admission test for IITJEE

11.

From the same staring point, Arun and Bharat traveled in opposite directions. Each of them traveled 7 km, took a right turn and traveled 9 km further. What is the distance between Arun and Bharat ? 130 km

(A)

(B)

2 120 km

520 km

(C)

(D)

None of these

12.

Find the least natural number which must be subtracted from 980 in order to obtain a perfect square. (A) 17 (B) 15 (C) 19 (D) 21

13.

Suresh starts from his office and walks 20m towards east. Then he turns right and walks 20m and then walks 15m towards west to reach the bus stand. In which direction is the bus stand with respect to his office ? (A) North-east (B) North-west (C) South-east (D) South - west

14.

( x % of y ) + ( y% of x ) (A)

15.

17.

2 1m

( ) 

2 If 3m ÷ 3m 

(A) 16.

x% of xy

3

is equal to :

(B)

2% of xy

(C)

20% of xy

(D)

2% of 100 xy

−6

(D)

−3

(D)

765559

= 81 . What is the value of m ?

(B)

6

(C)

If MASTER is coded as 411259, then POWDER will be coded as: (A) 765459 (B) 765493 (C) 765449 Give that : A > B = A divided by B, A < B = A multiplied by B, A @ B = average of A and B,

A × B = sum of A and B, Thus the value of expression [{(6 > 2) × (2 @ 6)} < (9 @ 11)] @ [(10 × 2) < {(1 × 2) > (1 × 1)}] will be : (A) 26 (B) 28 (C) 44 (D)

18.

6  5 1 5 The value of  of 1  ÷  2 ÷ 3  is : 13   7 4 7

(A)

20

(B)

169

19.

1

(C)

5

(D)

4

1

119 180

1 1   + 2 + 2 +  simplifies to : 2+ 2 2 −2 

(A) 20.

42

2− 2

(B)

2

(C)

2+ 2

(D)

2 2

By what least number 675 be multiplied to obtained a number which is a perfect cube ? (A) 5 (B) 6 (C) 7 (D) 8

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4

SECTION – II 21.

Mr. A, Miss B, Mr. C and Miss D are sitting around the table and discussing their trades. I. Mr. A sits opposite to cook II. Miss B sits right to the barber III. The washerman is on the left of the tailor IV. Miss. D sits opposite to Mr. C What are the trades of A and B ? (A) Tailor and Barber (B) Tailor and Cook (C) Barber and Cook (D) Washerman and Cook

22.

A goat is tied to a corner of a rectangular shed of dimensions 14m × 7m with a 21m long rope. It can graze outside the shed as far as it can move while tied to the rope. Find the area it can graze. (A) 240 sq. m (B) 1560.5 sq. m (C) 1543.5 sq. m (D) 1232 sq. m

23.

On a rainy day, water pooled on a rectangular terrace of length 20m and breadth 16m is collected in an empty cylindrical vessel of radius 3.5 m. What will be the height of the water level in the vessel, if the terrace recorded a rainfall of 1.5 cm ? (A) 3.16 cm (B) 8.63 cm (C) 12.47 cm (D) 6.23 cm

24.

N workmen could have built a dam in 50 days. 80 of them did not turn up. Find N, if the work took 70 days for completion. (A) 340 (B) 320 (C) 350 (D) 280

25.

Anil wants to divide ` 20 into a number of bags so that one can ask for any amount between ` 1 and ` 20, he can give the proper amount by giving certain number of these bags without taking out the amount from them. What is the minimum number of bags he will require, if each bag has whole number of rupees? (A) 5 (B) 6 (C) 7 (D) 20

26.

If a0 = 1 ; an = 2an − 1 if n is odd, an = an − 1 if n is even, then value of

(A) 27.

28.

16

(B)

32

64

(C)

a19 is a9

(D)

8

If a + b + c + d = 0 then ( a + d ) + ( b + d ) + ( c + d ) is equal to : 2

2

2

(A)

a 2 + b2 + c 2 + d 2

(B)

a 2 + b2 + c 2 + 3d 2

(C)

a 2 + 2b2 + 3c 2 + 4d 2

(D)

None of these

If

a 1 b c 1 d e 1 abc = , = 2, = , = 3 and = then what is the value of ? f 4 def b 3 c d 2 e

(A)

3 8

(B)

27 8

(C)

3 4

(D)

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27 4

5

Vidyamandir Classes Admission test for IITJEE

29.

3 z  x   y  z 2   2 z   If x = 6, y = 7 , z = 8 , find the value of  y −  2 z −   − − 3 1 + + x  z   z  x 3xy     

(A) 30.

0

(B)

1

x  is : 2 

−1

(D)

2

15

(D)

10

(C)

If x = 31 3 + 3−1 3 , then the value of 3 x 3 − 9 x will be :

(A)

12

(B)

9

(C)

Paragraph for Q.31 - 33 Study the following information carefully and answer the given questions : ‘P’, ‘Q’, ‘R’, ‘S’, ‘T’, ‘X’, ‘Y’ and ‘Z’ are sitting around a circular table facing the center, I. ‘S’ sits exactly between ‘Z’ and ‘T’ II. ‘Z’ sits second to the left of ‘T’ and second to the right of ‘Q’. III. ‘Y’ sits third to the left of ‘X’. IV. ‘P’ is not an immediate neighbour of ‘Q’.

31. 32.

33.

‘P’ : ‘Z’ then ‘Q’ : ? (A) ‘S’

‘Z’

(C)

‘P’

(D)

‘R’

Who is immediate right of ‘S’ ? (A) ‘R’ (B) ‘Z’

(C)

‘Y’

(D)

‘T’

Who sits third to the left of ‘Z’ ? (A) ‘R’ (B) ‘P’

(C)

‘Y’

(D)

‘T’

(B)

34.

In counting m coloured balls, some blue and some white, it was found that 49 of the first 50 counted were blue. Thereafter 7 out of every 8 counted were blue. If, in all 90% or more of the balls counted were blue, the maximum value of m is : (A) 180 (B) 200 (C) 210 (D) 220

35.

Find the missing value in the grid.

36.

(A)

56

(B)

89

(C)

49

(D)

100

216

35

123

721 ?

36

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12 2 cm, then the area of the triangle is :

(A) 37.

64

81

24 2 cm 2

(B)

24 3 cm 2

(C)

48 3 cm 2

(D)

64 3 cm 2

The curved surface area of a right circular cylinder of base radius r is obtained by multiplying its volume by :

(A)

2r

(B)

2 r

(C)

2r 2

(D)

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2 r2

Vidyamandir Classes Admission test for IITJEE

6 38.

If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area of its curved surface is :

(A)

39.

550 cm 2

(B)

(

(C)

704 cm 2

(D)

1254 cm 2

(C)

240

(D)

256

(C)

43

(D)

44

)

The square root of 2722 − 1282 is :

(A) 40.

154 cm 2

144

200

(B)

If x ∗ y = x + y + xy , the value of 6 * 24 is :

(A)

41

42

(B)

ANSWERS Section - I 1

2

3

4

5

6

7

8

9

10

D

C

C

A

D

C

B

C

A

A

11

12

13

14

15

16

17

18

19

20

C

C

C

B

B

A

C

C

B

A

Section - II 21

22

23

24

25

26

27

28

29

30

B

D

C

D

A

B

A

A

B

D

31

32

33

34

35

36

37

38

39

40

C

D

A

C

D

D

B

B

C

B

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