BOOKLET CODE: A

NDA _4_ math_(1-120) Hindi and French but not English. 23 students
Q.1 What is the angle between the lines whose di- learn only Hindi and 17 students learn only En-
rection cosine are proportional to (2,3,4) and (1,- glish. The total number of stduendent learning
2,1) respectively? French is 46 and the total number of student
(a) 90° (b) 60° leaning only French is 11.
(c) 45° (d) 30° 6. How many students learn precisely two lan-
2. What is the value of k for which the following guages?
function f(x) is continuous for all x? (a) 35 (b) 40
(c) 30 (d) 13
 x 3  3 x  2 7. How many students learn at least two lan-
 , for x  1 guages?
f  x     x  1
2
(a) 15 (b) 30

k , for x  1 (c) 45 (d) 55
8. What is the total stregth of the class?
for x
(a) 124 (b) 100
(a) 3 (b) 2
(c) 96 (d) 66
(c) 1 (d) -1
9. How many students learn English and French?
3. If p, q and r are rational numbers, then the roots
(a) 30 (b) 43
of the equation
(c) 45 (d) 66
x 2  2 px  p 2  q 2  2qr  r 2  0 are 10. How many students learn at least one languages?
(a) Complex (b) Pure imaginary (a) 45 (d) 51
(c) Irrational (d) Rational (c) 96 (d) None of these

4. If A  1, 2,5, 6 and B  1, 2,3 , then what 11. What is middle term in the expansion of
is  A × B    B × A  is equal to  x
8

1   ?
(a) 1,1 ,(2,1),  6,1 ,  3, 2  2

(b) 1,1 ,(1, 2),  2,1 ,  2, 2  (a)

35 x 4
(b)
17 x5
8 8
(c) 1,1 ,(2, 2)
17 x 4
(d) 1,1 ,(1, 2),  2,5  ,  2,6  (c)
8
(d) None of these

5. What is the differential equation of all parabolas 12. What isthe sum of roots of the equations

 2  3  x   7  4 3  x   2  3   0 ?
whose axed are parallel to Y-axis? 2
2
3
d y d x
(a) 0 (b) 0 (a) 2  3 (b) 2  3
dx3 dy 2
(c) 7  4 3 (d) 4
d 3x d3y
(c) 1 (d) c 13. What is the total number of combinations of n
dy 3 dx 3 different things taken 1,2,3,.....,n at time?
Direction (Q.6-10)-Read the following passage (a) 2n+1 (b) 22n-1
an give answer. (c) 2n-1
(d) 2n-1
The students of a class are offered three lan- 14. One of the roots of the quadratic equation
guages (Hindi, English and French). 15 students
ax 2  bx  c  0 , a  0 is positve and the or-
learn all the three languages whereas 28 stu-
der root is negative. the conditon for this to hap-
dents do no tlearn anuy language. The number
pen is ___
of students learning Hindi and Englsih but no
Fech is twice the number of students learning (a) a  0, b  0, c  0
Hindi and French but not English, The number (b) a  0, b  0, c  0
of student is learning English and French but
Hindi is thrice the number of students learning (c) a  0, b  0, c  0

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 BOOKLET CODE: A

(d) a  0, c  0 (a) f  x  is not continuous at x = 0

15. If the solution of the differential equation
(b) f  x  is differentiable at x = 0
dy ax  3
 represents a cicrle, then what is
dx 2 y  f (c) f  x  is continuous but not differentiable at
the value of a? x=0
(a) 2 (b) 1 (d) None of these
(c) -2 (d) -1 23. What is the condition that one root of the equa-
16. If A, B and C are in AP and b : c  3 : 2 , tion ax 2  bx  c  0 , a  0 should be double
then what is the value of sin C? the other?
1 (a) 2 a 2  9bc
(a) 1 (b) (b) 2b 2  9ac
3
1 (c) 2c 2  9ab
(c) 3 (d) (d) None of these
2 24. Consider the following with regard to a relation
17. The points with position vectors R on set of real numbers defined by xRy if an
10i  3 j ,12i  5 j , ai  11 j only if 3x + 4y =5
are collinear, if the value of a is I. 0R 1
(a) -8 (b) 4 1
(c) 4 (d) 12 II. 1R
2
18. What is the sin of angle between the vectors
i  2 j  3k and i  2 j  3k 2 3
III. R
3 4
 1 1 
19. If sin  sin  cos 1 x   1 then what is x Which of the above are correct?
 5  (a) I and II (b) I and II
equal to? (c) II and III only (d) I, II and III
(a) 0 (b) 1 1
25. The function f  x   k sin x  sin 3x has
4 1 3
(c) (d)
5 5 
20. What is log maximum value at x  . What is the value of
3

  1 k?
log a  a 2  1  log equal
a  a2  1 1
(a) 3 (b)
to? 3
(a) 1 (b) 2 1
(c) 2 (d)
1 2
(c) 2 (d)
2 26. What is the value of the determinant
21. 5 books ar to be chosen form a lot of 10 books.
If m is the numebr of sways of choice when x 1 x  2 x  4
one specified book is always included and n is x3 x5 x8
?
the number of ways of choice when a speficied x  3 x  10 x  14
book is always excluded, then which one of the
following is correct? (a) x  2 (v) x 2  2
(a) m  n (b) m  n (c) 21 (d) -2
(c) m  n  1 (d) m  n  2 27. Consider the following statements in respect of
22. Which one of the following is correct in
the function f  x   x  1, x   1,1
3

respectof the function only if f  x   x  x

2

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f  x  /2
f  cos x  dx
I. is increasing in  1,1 (a) 0 (b)  0

II. f  x  has no root in  1,1 .  /2

(c) 2  f  cos x  dx (d) 1
0
Which of the statements given above is/are cor-
rect? 34. Find the value of k inwhich the sytem of equa-
(a) Only I tions kx  2 y  5 and 3 x  y  1 has no
(b) Only II soluition?
(c) Both I and II (a) 0 (b) 3
(d) Neither I nor II (c) 6 (d) 15
28. The largest value of 2 x 3  3 x 2  12 x  5 for 35. In how many ways 6 girls can be seatedintwo
chairs?
2  x  2 occurs when- (a) 10 (b) 15
(a) x  2 (b) x  1 (c) 24 (d) 30
(c) x  2 (d) x  0
9  27 
dx 36. What is the value of log10    log10  
x
8  32 
29. What is 
0 1  2 sin 2 x
equal to
3
  log10   ?
(a)  (b) 4
3
(a) 3 (b) 2
 2 (c) 1 (d) 0
(c) (d)
3 3 1 1
37. Which term of a series ,  ,1..... is 128 ?
4 2
x 4 5 (a) 9th (b) 10th
7 x 7 (c) 11th (d) 12th
30. If 5 and 7 are the roots of the equation
5 8 x 38. If x  y  4 , then how many non-zero positive
integer ordered pair (x, y)?
= 0, then wha is the third root?
(a) 4 (b) 5
(a) -12 (b) 9
(c) 6 (d) 8
(c) 13 (d) 14
39. In a binary number syster, assume that a = 00111
31. In a GP of positve terms, any term is equal to
and b = 01110, then in a decimal system b/a,
one-third of the sum of next terms. What is the
which is equal to-
common ratio of the GP?
(a) 1 (b) 2
3 1 3 1 (c) 4 (d) 5
(a) (b)
2 2 1 1 1 1
40. If    , then a,b,c is equal to-
ba bc a c
3 1
(c) (d) 13 (a) AP (b) GP
3 (c) HP (d) None of these
32. If 1  tan 1  tan   2 , then what is 1

1
41. What is modulus of ?
1  3i 1  3i
    equal to?
(a) 30° (b) 45° 3 9
(a) (b)
(c) 60° (d) 90° 5 25
33. If f  x  is an even function, then what is 3 5
(c) (d)
 25 3
 f  cos x  dx equal to/
0
42. Let M be the set of men and R is a relation 'is
son of' defined on M. Then R is-
(a) an equivalence relation

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 BOOKLET CODE: A
(b) a symmetric relation only 50. What is the sum of the focal distances of a point
(c) a transitive relation only
(d) none of the above x2 y 2
of an ellipse   1?
43. What is the locus of the point which is at a dis- x2 b2
tance 8 units to the left of Y-axis? (a) a (b) b
(a) X = 8 (b) Y = 8 (c) 2a (d) 2b
(c) X = -8 (d) Y = -8 51. What is the degree of the following differential
44. The number 10101111 in binary system is repre- equation?
sented in decimal system by which one of the 2/3
following numbers?  d3y  d3y dy
 3  43 5  0
(a) 157 (b) 175  dx  dx 3
dx
(c) 571 (d) 751
45. There are 4 letters and 4 directed envelopes. (a) 1 (b) 2
These 4 letters are randomly inserted into the 4 (c) 3 (d) 4
envelops. What is the probability that the letters 1 1
are inserted into the corresponding envelops? 52. What is the sum of 3   ....?
3 3 3
(a) 11/12 (b) 23/24
(c) 1/24 (d) None of these 3 3 3
46. The average daily income of workers of a fac- (a) (b)
tory including of the owner is rs.110. However,
2 2
if the income of the owner is excluded, the av- 2 3
erage daily income of the remaining 9 workers (c) (d) 3
is rs.76. What is the daily income of the owner? 2
(a) 300 (b) 316 53. What does the differential equation
(c) 322 (d) 416 dy
47. If A, B and C are non-empty sets such that y xa
dx
A  C= , then what is  A  B   C  B  (where a is a constant) represent?
equal to? (a) A set of circles having centre on the Y-axis
(b) A set of circles having centre on the X-axis
(a) A  C (b) A  B
(c) A set of ellipses
(c) B  C (d)  (d) A pair of straight lines
48. If A = {4n + 2 |n| is a natural number} and B =
{3n|n| is a natural number}, then what is  0  1 0 
54. If A    and B    such that
1 1   2 1
 A  B equal to?
(a) {12n2 + 6n|n is a natural number} A2  B , then what is the value of  ?
(b) {24n + 12|n is a natural number} (a) -1 (b) 1
(c) {60n + 30|n is a natural number} (c) 2 (d) 4
(d) {12n - 6|n is a natural number} 55. What is the value of n, if
49. If the matrix P 15, n  1 : P 16, n  2   3 : 4 ?
  (a) 10 (b) 12
A  (c) 14 (d) 15
  
56. If 3 is the root of the equations x 2  8 x  k  0 ,
is such that A 2  I , then which one of the fol-
then what is the value of k?
lowing is correct?
(a) -15 (b) 9
(a)   0,   1 or   1,   0 (c) 15 (d) 24
(b)   0,   1 or   1,   1 57. Two straight lines x  3 y  2  0 and
(c)   1,   0 or   1,   1 2x  6 y  6  0
(d)   0,   0 (a) Never intersect
(b) interect at a single point

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 BOOKLET CODE: A
(c) intersect at infinte number of points 65. The vector a lies inthe plane of vectors b and c.
(d) intersect at more than one point (but finite Which one of the following is correct?
numberof points) .
(a) a  b  c   0 .
(b) a  b  c   1
58. If  a, 0  ,  0, b  and 1,1 are collinear, what is
(c) a. b  c   1 (d) a. b  c   3
 a  b  ab  equal to/ 66. What is the projection of the vector i  2 j  k
(a) 2 (b) 1
(c) 0 (d) -1 on the vector 4i  4 j  7 k ?

3 1  1 1  5 19
59. A  and B    , then which of (a) (b)
0 4  0 2 2 9
the following is/are correct? 5 11
I. AB is defined. (c) (d)
II. BA is define 4 3
III. Ab = BA 67. Which one of the following options is correct?
Select the correct answer using the codes given (a) sin 2 30,sin 2 45,sin 2 60 are in Gp
below.
(a) Only I (b) Only II (b) sin 2 30, cos 2 45, cos 2 60 are in Gp
(c) Both I and II (d) I, II and III (c) sin 2 30, cot 2 45, cot 2 60 are in Gp
60. Using the digits 1,2,3,4 and 5 only once, how
many numbers greater than 41000 can be (d) tan 2 30, tan 2 45, tan 2 60 are in Gp
formed? 68. If sum of squares of the roots of the equation
(a) 41 (b) 48
(c) 50 (d) 55 x 2  kx  b  0 is 2b, what is k equal to?
61. If an angle  is divide into two parts A and B (a) 1 (b) b
such that A - B = x and tan A ; tan B = 2 : 1, (c) -b (d) 0
then what is sinx equal to 69. If one root of the equation ax 2  bx  c  0 ,
(a) 3sin  (b)  2 sin   / 3 a  0 is reciprocal of the other root, then which
one of the following is correct?
(c)  sin   / 3 (d) 2sin  (a) a  c (b) b  c
62. A man standing on the bank of a river serves (c) a  c (d) b  0
that the angle of elevation of the top of a tree 70. If  is the imaginary cube root of unity, then
just on the opposite bank is 60°. The angle of
 
27
elevationis 30° from a point at a point at a dis- what is 2    2 2 equal to?
tance ym from the bank. What is the height of
the tree? (a) 327 ω (b) 327 ω
(a) ym (b) 2ym (c) 327 (d) 327
3y y 71. What is the acute angle between the planes
(c) m (d) m
2 2 x  y  2 z  3 and 2 x  y  z  11 ?
63. If P, Q and R at three non-collinear points, then (a)  / 5 (b)  / 4
what is PQ  PR equal to? (c)  / 6 (d)  / 3
(a) Null set (b) { P } 72. What is the area bounded by the curves y = ex ,
(c) {P,Q,R} (d) {Q,R} y = e-x and the straight line x = 1?
64. A,B,C,D and E are coplanar points and three of
them lie in a straight line. What is the maximum  1  1
number of triangles that can be drawn with these (a)  e   sq unit (b)  e   sq unit
 e  e
points as their vertices?
(a) 5 (b) 9  1   1 
(c) 10 (d) 12 (c)  e   2  sq unit (d)  e   2  sq unit
 e   e 

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73. What are the points of intersection of th curve 80. What is the mean of the above frequency distri-
bution?
4 x  9 y  1 with its conjugate axis?
2 2
(a) 25 (b) 26
(a) 1/ 2,0  and  1 / 2,0  (c) 27 (d) 28

(b)  0, 2  and  0, 2  2  x 1 1 
81. If the matrix A 
 1 3  x 0  is singu-
(c)  0,3 and  0, 3  
  1  3  x 
(d) No such point exists
74. What is the locus of a point which moves equi- lar, then what is the solution set S?
distant from the coordinate axes?
(a) S  0, 2,3 (b) S  1, 2,3
(a) x  y  0 (b) x  2 y  0
(c) 2 x  y  0 (d) None of these (c) S  1, 2, 3 (d) S  2,3

82. What is the range of f  x   cos 2 x  sin 2 x ?

x 1 
75. What is  e  x   dx equal to?
 2 x (a)  2, 4 (b)  1,1
(a) xe x  C (b) e x x  C
(c)   2, 2  (d)   2, 2 
(c) 2e
x
 xC (d) 2 xe x  C 83. What is the solution of the differential equation
76. Let p,q,r and s respectively the magnitudes of dy 1 y2
the vectors  0?
dx 1  x2
3i  2 j , 2i  2 j  k , 4i  j  k , 2i  2 j  3k .
Which one of the following is correct? (a) sin 1 y  sin 1 x  C
(a) r  s  q  p (b) s  r  p  q (b) sin 1 y  sin 1 x  C
(c) r  s  p  q (d) s  r  q  p
(c) 2sin 1 y  sin 1 x  C
77. In a ΔABC , if c = 2, A = 120°, a a  6 , then
what is C equal to- (d) 2sin 1 y  sin 1 x  C
(a) 30 (b) 45  
(c) 60° (d) 75 84. If z  1   cos  i sin , then what is z
5 5
78. equal to -
 
Consider the following statements in respect of (a) 2 cos (b) 2sin
5 5
the above frequency distribution.
I. The median is contained in the modal class.  
(c) 2sin (d) 2 cos
II. The distribution is bel-shaped. 10 10
Which of the above statements is/are correct? 85. If xi  yj  zk is a unit vectro and
(a) Only I (b) Only II
(c) Both I and II (d) Neither I nor II x : y : z  3 : 2 : 3 , then what is the value of
Direction (Q.79-80) the following table gives teh z?
continuous frequency distribution of a continu-
ous variable X. 3
(a) (b) 3
Class Interval 0-10 10-20 20-30 30-40 40-50 16
Frequency 5 10 20 5 10 3
79. What is the median of the above frequency dis- (c) (d) 2
4
tribution?
Directions (Q.86-89) Read the following in for-
(a) 23 (b) 24
mation carefullyand give the answer.
(c) 25 (d) 26

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 BOOKLET CODE: A
A B C is a triangle right angles at B. The 94. Consider the following statements with regard
hypotneus (AC) is four times the perpendicular to correlation coefficent r between variables x
(BD) drawn to ir from the opposite vertex and and y.
AD < DC. I. r  1 or  1 means there is a linear relation
86. What is one of the acute angle of the triangle?
between x and y.
(a) 15° (b) 30°
(c) 45° (d) None of these II. 1  r  1 and r 2 is a measure of the linear
87. What is ABD ? relationship between the variables.
(a) 15° (b) 30° Which of the statements given above is/are cor-
(c) 45° (d) None of these rect?
88. What is AD : DC equal to? (a) Only I (b) Only II
(c) Both I and II (d) Neither I nor II

(a) 7  2 3 :1  
(b) 7  2 3 :1 95. If the values of a set are measured in cm, what
will be the unit of variance?
(c) 1: 2 (d) None of these (a) cm (b) cm2
89. What is tan  A  C  equal to? (c) cm 3
(d) No unit
(a) 0 (b) 1 96. A box contains 6 distinct dolls. From this box, 3
(c) 2 (d) None of these dolls are randomly selected one by one with re-
90. What is the radius of the sphere placement.
What is the probability of selecting 3 distinct
x  y  z x yz 0?
2 2 2
dolls?
(a) 5/54 (b) 12/25
3 1 (c) 1/20 (d) 5/9
(a) (b)
4 2 97. for the equation ax 2  by 2  2hxy  2 gx  2 fy
3 1  c  0 where a  0 , to represent a circle, the
(c) (d) condition will be-
2 3
91. An experiment consists of flipping a coin and (a) a  b and c  0 (b) f  g and h  0
then flipping it a second time if head occurs. if a (c) a  b and h  0 (d) f  g and c  0
tail occurs ont he first flip, then a six-faced die 98. If A and B are events such that
is tossed onec. Assuming taht the ocutcomne
are equally likely, what is the probability of get- P  A  B   0.5 ,  
P B  2.8 and
ting one head and one tail?
(a) 1/4 (b) 1/36 P  A / B   0.4 , then what is P  A  B  equal
(c) 1/6 (d) 1/8 to?
92. If in general, the value of sin A is known, but the (a) 0.08 (b) 0.02
value of A is not knwon, then how many values (c) 0.8 (d) 0.2
of tan (A/2) can be calculated? 99. Consider the following relations among the
(a) 1 (b) 2 angles  ,  and  made by a vector with the
(c) 4 (d) 4 coordinates axes
93. Consider the following
I. cos2α + cos2 + cos2 = -1
 2   II. sin 2  sin 2   sin 2   1
I. cosec1   3
 3 Which of th above is/are correct?
 2   (a) Only I (b) Only II
II. sec 1   (c) Both I and II (d) Neither I nor II
 3 6 100. Which one of the following points lies on the
Which of the above is/are correct? plane 2 x  3 y  6 z  21 ?
(a) Only I (b) Only II
(c) Both I and II (d) Neither I nor II (a)  3, 2, 2  (b)  3, 7,1

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 BOOKLET CODE: A
(a) 0 (b) P(A) + P (B)
(c) 1, 2,3 (d) 1,1, 1
(c) P(A)P(B) (d) P(A)P(B/A)
 109. If x  sin   cos  and y  sin  .cos  , then
101. If 
0
4
tan n xdx,
what is the value of x 4  4 x 2  4 y 2  4 y  1 ?
then what is I n  I n  2 equal to? (a) 0 (b) 1
(c) 2 (d) None of these
(a) 1 / n (b) 1 /  n  1

(c) n /  n  1 (d) 1 /  n  2 
110. What is lim
x 
 a 2 x 2  ax  1  a 2 x 2  1 
102. what is the equation of the line joining the origin equal to?
with the point of intersection of the lines 1
4 x  3 y  12 and only 13 x  4 y  12 ? (a) (b) 1
2
(a) x  y  1 (b) x  y  1 (c) 2 (d) 0
(c) 3 x  4 y (d) x  y sin x
103. If the sum of the squares of the distancee of the 111. What is  x
dx equal to?

point  x, y  from the points  a, 0  and  a, 0 

cos x
is b 2 , then which one of the following is cor- (a) C (b) 2 cos x  C
2
rect?
(a) x 2  a 2  b 2  y 2  cos x
(c) C (d) 2cos x  C
2
(b) x  a  2b  y
2 2 2 2
112. Which of the following is the unit vector per-
(c) x  a  b  y
2 2 2 2
pendicular to the vector 4i  2 j and 3i  2 j ?
(d) x 2  b 2  b 2  y 2 i j i j
(a) (b)
If f  x   2 then what is f '  x  equal to 2 2
x
104.
i jk
(a) 2 x  In 2  (b) x  x  1 2
2 x 2
(c) k (d)
2
(c) 2  In 2  (d) 2 x  log10 2 
x 1 2
113. Consider the following statements in respect of
105. In an examination there are 3 multiple choice the vectors
questions and each question has 4 choices. If a u1  1, 2,3 , u2   2, 3,1 , u3  1,3, 2  and
student randomly selects answer for all the 3
questions, what is the probability that the stu- u4   4, 6, 2 
dent will not answer all the 3 questions correctly?
(a) 1/64 (b) 63/64 I. u1 is parallel to u4 .
(c) 1/12 (d) 11/12 II. u2 is parallel to u4 .
106. What is the geometric mean of the data
2,4,8,16,32? III. u2 is parallel to u3 .
(a) 2 (b) 4 Which of the statements given above is/are cor-
(c) 8 (d) 16 rect?
107. What is the cumulative frequency curve of sta- (a) Only I (b) Only II
tistical data commonly called? (c) Only III (d) Both I and II
(a) Cartogram (b) Histogram
114. The line mx  ny  1 passes through the points
(c) Ogive (d) Pictogram
108. If A and B are two mutually exclusive events, 1, 2  and  2,1 . What is the value of m?
then what is P  AB  equal to? (a) 1 (b) 3

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 BOOKLET CODE: A

1 1
(c) (d)
2 3
115. What is the solution set for the equation
x 4  26 x 2  25  0 ?
(a) 5, 1,1, 5 (b) 5, 1

(c) 5,1 (d) 5,0,1,5

 sin  cos x  dx equal to

1
116. What is

x x2 
x2
(a)  K (b)  K
2 2 2 2
x x 2 
x2
(c)   K (d)  K
2 2 2 2
117. If  and  are the roots of the equation
4 x 2  3 x  7  0 , then what is the value of
 2
  2  ?
(a) 47 / 49 (b) 49 / 47
(c) 47 / 49 (d) 49 / 47
118. What is the equation of the line passing through
(2, -3) and parallel to Y-axis?
(a) Y = -3 (b) Y = 2
(c) X = 2 (d) X = -3
119. What is the set of points (x, y) satisfying the
equations x 2  y 2  4 and x  y  32 ?

(a)  2, 0  ,  2, 0  ,  0, 2

(b)  0, 2  ,  0, 2 

(c)  0, 2  ,  2,0 

(d)  2,0  ,  2, 0  ,  0, 2  ,  0, 2 

120. Consider the following statements:
I. The inverse of a square matrix, if it exists, is
unique.
II. If A and B are singular matrices of order n,
then AB is also a singualr matrix of order n.
Which of the statements given above is/are cor-
rect?
(a) Only I (b) Only II
(c) Both I and II (d) Neither I nor II

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 BOOKLET CODE: A

OURS ACADEMY:Near Bus Stand, Rishi Nagar, Hisar. M.9467134541,9812130823

 BOOKLET CODE: A

OURS ACADEMY:Near Bus Stand, Rishi Nagar, Hisar. M.9467134541,9812130823

 BOOKLET CODE: A

OURS ACADEMY:Near Bus Stand, Rishi Nagar, Hisar. M.9467134541,9812130823