# maths question paper by sunilkbri

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```									81-E                                            2

General Instructions :
i)     The question-cum-answer booklet contains two Parts, Part – A & Part – B.
ii)    Part – A consists of 60 questions and Part – B consists of 16 questions.
iii)   Space has been provided in the question-cum-answer booklet itself to answer
the questions.
iv)    Follow the instructions given in Part – A and write the correct choice in full in
the space provided below each question.
v)     For Part – B enough space for each question is provided. You have to answer
the questions in the space provided.
vi)    Space for Rough Work has been printed and provided at the bottom of each page.

PART – A
Four alternatives are suggested to each of the following questions / incomplete
statements. Choose the most appropriate alternative and write the answer in the
space provided below each question.                                 60 × 1 = 60
1.     A = { 1, 2, 4 } and B = { 1, 4, 5 } . The set denoted by A I B is
(A)    { 4, 5 }                        (B)   { 1, 5 }
(C)    { 1, 4 }                        (D)   { 2, 5 }

Ans. :
2.     If     U =   { 1, 2, 3, 4, 5, 6 }
A =   { 1, 2, 3 }
B =   { 2, 4 } , then the diagram that denotes A   I B is

(A)                                            (B)

(C)                                            (D)

Ans. :

( SPACE FOR ROUGH WORK )

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3.   With respect to the Venn diagram given below n ( A ) is

A                      B

8      5      7

(A)    8                                    (B)   5

(C)    7                                    (D)   13.

Ans. :

4.   Among the formulae given below, De Morgan’s law is denoted by
(A)    n(A)+n(B)=n(A U B)+n(A I B)

(B)    n ( A )  l   = n ( U )–n(A)

(C)    A U (B I C)=(A U B) I (A U C)

(D)    ( A I B )  l     = A  l   U B  l .

Ans. :

5.   A and B are two sets. If n ( A ) = 11, n ( B ) = 7 and n ( A I B ) = 3, then n ( A U B
) is

(A)    21                                   (B)   15

(C)    8                                    (D)   10.

Ans. :
6.   In a sequence T n = 2n 2 – 1 the pair of first two terms is

(A)    3, 7                                 (B)   1, 3

(C)    1, 7                                 (D)   1, 15.

Ans. :

( SPACE FOR ROUGH WORK )

VIII I-E-912130                                                                [ Turn over
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7.     Among the following, arithmetic progression is

(A)   1, 4, 6, ……                              (B)   12, 10, 14, ……

(C)   35, 30, 25, ……                           (D)   8, 13, 19, …… .

Ans. :
8.     Which one of the following formulae is related to geometric progression ?
n
(A)   S n =      (a +l)                        (B)   T  n = a + ( n – 1 ) d
2
2ab
(C)   H =                                      (D)   T  n = ar n – 1 .
a + b

Ans. :
9.     The harmonic mean between 1 and 4 is
7                                                8
(A)                             (B)
5                                                5
6                                                7
(C)                             (D)                    .
5                                                4

Ans. :
 1        2 
10.    If A =                   then A + A   l is
 3        4 
 2      5                                     2    4 
(A)                                          (B)            
 5      8                                     6    8 
    0    – 1                                  2    5 
                                                       .
(C)                                          (D)
 – 1      0                                   8    5 

Ans. :
      0         3a 
11.    If A =                      is a skew symmetric matrix, then the value of a is
 a – 8          0 

(A)   – 4                                      (B)   4

(C)   – 2                                      (D)   2.

Ans. :

( SPACE FOR ROUGH WORK )

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12.   The value of       P  2 is

(A)   16                             (B)   28

(C)   56                             (D)   15.

Ans. :

13.   A boy has 4 shirts, 3 pants and 2 caps. The different ways of wearing these items is

(A)   9                              (B)   24

(C)   6                              (D)   5.

Ans. :
14.   The value of |3  + |2  – |0  is
—     —     —

(A)   7                              (B)   8

(C)   5                              (D)   4.

Ans. :

15.   Number of straight lines that can be drawn by using 6 non-collinear points is

(A)   30                             (B)   15

(C)   9                              (D)   6.

Ans. :

16.   There are 4 men and 3 women in a group. Number of ways to form a committee of
2 men and 1 woman is given by

(A)   4P 2 × 3P 1                    (B)   4P 2 × 3C 1

(C)   4C 2 × 3C 1                    (D)   4C 2 × 3P 1 .

Ans. :

( SPACE FOR ROUGH WORK )

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n                   n
17.    If        C  r = 10 and       P  r = 20, then the value of r is

(A)       200                                (B)   30

(C)       10                                 (D)   2.

Ans. :
18.    In a statistical data, sum of the squares of deviations of 10 scores is 130. The
variance is

(A)       1300                               (B)   140

(C)       13                                 (D)   130.

Ans. :
19.    The variance of a statistical data is 16. The standard deviation is

(A)       4                                  (B)   4·5

(C)       32                                 (D)   250.

Ans. :
20.    The coefficients of variations of Anand and Shankar in 5 class tests are 7·5 and 12·3
respectively. The true statement of comparison among the following is

(A)       Shankar has higher consistency

(B)       Shankar has lower consistency

(C)       both have equal consistency

(D)       Anand has lower consistency.

Ans. :
21.    The L.C.M. of 18x 3 y 4 z 9 and 15x 4 y 7 z 5 is
(A)       90x 4 y 7 z 5                      (B)   90x 3 y 4 z 5

(C)       90x 4 y 7 z 9                      (D)   90x 4 y 4 z 9 .

Ans. :
( SPACE FOR ROUGH WORK )

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22.   If a, b, c are variables, then         ∑      a  2 + b is
a‚ b‚ c

(A)       a 2 + b + b  2 + c + c 2 + a         (B)   a  2 – b + b  2 – c + c 2 – a

(C)       a 2 + b – c + b  2 + c – a           (D)   a 2 + b  2 + c 2 .

Ans. :

23.    ∑   x ( y – z )        is expanded and simplified to obtain
x‚ y‚ z

(A)       xy – xz                              (B)   0

(C)       xz – xy                              (D)   y(z–x)

Ans. :

24.   If a + b + c = 0, then the value of ( a + b ) ( b + c ) ( c + a ) is

(A)       abc                                  (B)   0

(C)       ± abc                                (D)   – abc.

Ans. :

25.   The factors of a 2 – b  2 are

(A)       (a–b)(a–b)                           (B)   (a+b)(a+b)

(C)       ( a – b ) 2                          (D)   ( a + b ) ( a – b ).

Ans. :

( SPACE FOR ROUGH WORK )

VIII I-E-912130                                                                            [ Turn over
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26.    The sum of      9a      and         25a   is

(A)       34a                                  (B)       8a

(C)   8 a                                      (D)   2 a .

Ans. :
8
27.    If the denominator of                is rationalised and simplified, its form is
2

(A)   4 2                                      (B)   4

(C)   8 2                                      (D)   8.

Ans. :

28.    When       10 – 2 is multiplied by its rationalised factor we get

(A)   6                                        (B)   8

(C)   96                                       (D)   98.

Ans. :
29.    The set of like radicals among the following is

3             3
(A)        10 , 4       7                      (B)   6 2 , 10 2

(C)    54 8 , 5         4
3                  (D)   4 3 ,4 2 .

Ans. :
30.    The quadratic equation among the following is

(A)   a 3 + 3 = 2a                             (B)   x + 5 = 10
2
(C)   x+4(x +1)=0                              (D)   y =        .
y

Ans. :

( SPACE FOR ROUGH WORK )

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31.   The discriminant of the quadratic equation ax 2 + bx + c = 0 is
b
(A)   –                             (B)   b  2 – 4ac
a

c                                   – b ±  b  2 – 4ac
(C)                                 (D)                     .
a                                          2a

Ans. :
32.   If the roots of the quadratic equation x 2 + 4x + c = 0 are equal, then the value of c
is

(A)   3                             (B)   4

(C)   5                             (D)   12.

Ans. :
33.   The sum and product of the roots of the quadratic equation             4x 2   + 1 = 0 are
respectively

(A)   1 and 4                       (B)   0 and 1
1                                1
(C)   0 and –                       (D)   0 and    .
4                                4

Ans. :
34.   The hypotenuse of a right-angled triangle is 13 cm. If one side of the remaining is
5 cm greater than the other, they can be related with each other as

(A)   x + ( x + 5 ) = 13            (B)   x 2 + (  x 2 + 5 ) = 13 2

(C)   x 2 + ( x + 5 ) 2 = 13 2      (D)   x 2 + ( 5 – x ) 2 = 13 2 .

Ans. :
1
35.   If the roots of a quadratic equation are 0 and –     , the equation is
2
1
(A)   2x 2 + x = 0                  (B)   x 2 +        =0
2

(C)   2x 2 + 1 = 0                  (D)   2x 2 – x = 0.

Ans. :

( SPACE FOR ROUGH WORK )

VIII I-E-912130                                                                      [ Turn over
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36.    If the roots of the quadratic equation mx 2 + 6x + 1 = 0 have to be equal, then the
value of m is

(A)   6                                 (B)      1

(C)   9                                 (D)      5

Ans. :
37.    If a  2 = b  2 + c 2 , then c is given by

(A)   ±   b  2 + a  2                   (B)      ±    a 2 + b  2

(C)   ±   a – b                         (D)      ±    a 2 – b  2 .

Ans. :
38.    If A = 4πr 2 , r is given by

A                                A
(A)   ±                                 (B)
4π                               4π

Aπ
(C)   4Aπ                               (D)              .
4

Ans. :
39.    Twice the square of a number added to three times the number is equal to 65. This
statement in the form of equation is

(A)   3x 2 + 2x = 65                    (B)      2x 2 + 3x = 65

(C)   2x 2 + 3x 2 = 65                  (D)      3x 2 + 2x 2 = 65.

Ans. :
40.    In a quadratic equation if the value of b 2 – 4ac = – 7, the nature of the roots of the
quadratic equation is

(A)   real and equal                    (B)      real and distinct

(C)   imaginary                         (D)      negative numbers.

Ans. :

( SPACE FOR ROUGH WORK )

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41.   Parabola is the name of the graph of

(A)   linear equation                  (B)     simultaneous equation

(C)   quadratic polynomial equation (D)        polynomial equation.

Ans. :
42.   The correct statement among the following is

(A)   8 ≡ – 7 ( mod 3 )                (B)     7 ≡ – 2 ( mod 4 )

(C)   10 ≡ 6 ( mod 3 )                 (D)     18 ≡ 10 ( mod 5 ).

Ans. :
43.   If 3x ≡ 2 ( mod 4 ), then value of x is
(A)   1                                (B)     2
(C)   3                                (D)     4.

Ans. :
44.   In the given figure, the line segment which subtends right angle in the semicircle is

(A)   AB                               (B)     CO
(C)   DE                               (D)     FG.

Ans. :
45.   For two concentric circles,
(A)   direct common tangents can be drawn
(B)   transverse common tangents can be drawn
(C)   common tangents cannot be drawn
(D)   both direct and transverse common tangents can be drawn.

Ans. :

( SPACE FOR ROUGH WORK )

VIII I-E-912130                                                                  [ Turn over
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46.    In the figure, DE      BC, AD : AB = 1 : 2, BC = 6 cm, then DE is

(A)   1 cm                               (B)   2 cm
(C)   3 cm                               (D)   4 cm.

Ans. :
AB               BC              AC
47.    In ∆ ABC and ∆ DEF if                =                =         ,   then the correct pair of
DE               EF              DF
corresponding equal angles is
(A)   ∠ A and ∠ E                        (B)   ∠ C and ∠ F
(C)   ∠ B and ∠ D                        (D)   ∠ A and ∠ F.

Ans. :
48.    The two corresponding sides of similar triangles are 3 cm and 4 cm. The area of
larger triangle is 48 sq.cm. The area of smaller triangle is

(A)   80 sq.cm                           (B)   64 sq.cm

(C)   36 sq.cm                           (D)   27 sq.cm.

Ans. :
49.    A straight pole of height 2 ft casts a shadow of 6 ft long at a definite time. The height
of another pole which casts a shadow of 12 ft at the same time is
(A)   3 ft                               (B)   4 ft
(C)   8 ft                               (D)   20 ft.

Ans. :
50.    Two circles of radii 4 cm and 2 cm have their centres 7 cm apart. These circles
(A)   touch each other externally        (B)   touch each other internally
(C)   do not touch each other            (D)   intersect each other.

Ans. :
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51.   Two circles touch each other internally. The distance between their centres is
1·5 cm. If the radius of one circle is 3·5 cm, then the radius of the other circle is

(A)   5 cm                                 (B)   4 cm

(C)   3 cm                                 (D)   2 cm.

Ans. :
52.   In the given figure, O is the centre of the circle. AC and BC are the tangents. If
∠ BOC = 65° then ∠ ACO is

(A)   25°                                  (B)   35°

(C)   65°                                  (D)   115°.

Ans. :
53.   In the given figure, O is the centre of the circle. XY is a tangent. If ∠ PQY = 55°,
∠ OPQ is

P

O
55°

X                                              Y
Q

(A)   125°                                 (B)   120°

(C)   110°                                 (D)   35°.

Ans. :

( SPACE FOR ROUGH WORK )

VIII I-E-912130                                                                    [ Turn over
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54.    A = 2πr ( r + h ). This formula can be used to find

(A)   lateral surface area of a cylinder

(B)   total surface area of a cylinder

(C)   volume of a cylinder

(D)   surface area of a sphere.

Ans. :
55.    Volume of a hemisphere can be calculated by using the formula
1                                        4
(A)   V =      πr 2 h                    (B)    V =     πr 3
3                                        3
2                                        3
(C)   V =      πr 3                      (D)    V =     πr 3 .
3                                        4

Ans. :
56.    The solid described by revolution of a semicircle about a fixed diameter is

(A)   cone                               (B)    cylinder

(C)   hemisphere                         (D)    sphere.

Ans. :
57.    The volume of a cone is 90 cm 3 . The volume of a cylinder whose height and radius
is same as that of the cone is

(A)   30 cm 3                            (B)    45 cm 3

(C)   90 cm 3                            (D)    270 cm 3 .

Ans. :
58.    The volume of a cylinder is 1540 cm 3 . Its height is 10 cm. The area of its base is

(A)   15400 sq.cm                        (B)    154 sq.cm

(C)   1540 sq.cm                         (D)    1550 sq.cm.

Ans. :

( SPACE FOR ROUGH WORK )

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59.   A polyhedral graph is given in the figure. The polyhedral solid obtained by this is

(A)   Icosahedron                    (B)   Dodecahedron

(C)   Hexahedron                     (D)   Tetrahedron.

Ans. :

60.   Which of the following is a traversable network ?

(A)                                  (B)

(C)                                  (D)

Ans. :

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VIII I-E-912130                                                                   [ Turn over
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PART – B

61.    There are 10 boxes on a table. Ramu places 4 marbles in first box, 7 marbles in the
second box, 10 marbles in the third box and so on. Find the total number of marbles
placed in all the boxes.                                                         2

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 0   1 
62.   If A =         , find A  2 .                                2
 2   3 

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63.    The marks scored by Rani in 5 class tests are 56, 60, 59, 68, 57. Find the standard
deviation for these scores.                                                      2

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64.   If a + b + c = 0, prove that a  3 + b  3 + c 3 ≡ 3 abc.            2

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65.    Rationalise the denominator and simplify :

5 –  3
2
5 +  3

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66.   In the given figure, O is the centre of the circle. AB = 2 cm, AC = 3 cm, CE = 6 cm.
Find DE.                                                                          2

E
A

C   . .O
B
D

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VIII I-E-912130                                                               [ Turn over
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67.    Three circles of radii 3·5 cm, 4·5 cm and 5 cm touch each other externally as shown
in the figure. Find the sides of ∆ ABC and perimeter of ∆ ABC given that A, B and C
are the centres of the circles.                                                  2

3·5 cm        4·5 cm
A   .                    .B

5 cm
.
C

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68.   Construct the matrix for the given network.                  2

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69.    Solve 4x 2 – 3x – 2 = 0 using formula.              2

( SPACE FOR ROUGH WORK )

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70.   Draw a circle of radius 3 cm. Draw a chord AB of length 5 cm in it. Construct a
tangent to the circle at A.                                                  2

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VIII I-E-912130                                                           [ Turn over
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71.    Draw the plan of a level ground using the information given below.

( Scale : 1 cm = 10 m )                                              2
Metres
To C
100
D 30          70
E 30          50          20 B
30
From A

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72.   Find the LCM of x 3 + 2x 2 + 2x + 1 and x 3 – x  2 – x – 2.            4

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VIII I-E-912130                                                     [ Turn over
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73.    State and prove Pythagoras theorem.                4

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2                        1
74.   In an H.P., the 10th term is        and third term is     . Find the eleventh term.     4
13                       3

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VIII I-E-912130                                                                    [ Turn over
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75.    Draw two direct common tangents to the circles of radii 4 cm and 2 cm having their
centres 8 cm apart.                                                             4

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76.   Draw the graph of y = 2x 2 .                                 2

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