BOOKLET CODE: A

NDA _5_ math_(1-120) Q.9 Form the top of building of height h metren teh
Q.1 What is equation of line passing through (0, 1) angle of depression of an object onthe ground
and making an angle iwth the y-axis eulto the is. What is the distance (in metre) of the obnject
from the foot of the building?
inclination to the line x  y  4 with x-axis?
(a) h cot  (b) h tan 
(a) y  x  1 (b) x  y  1
(c) h cos  (d) h sin 
(c) 2x  y  2 (d) None of these
Q.10 If tan 1 2, tan 1 3 are two angles of a triangle,
 then water is the thrid angle?
Q.2 What is the value of tan ?
12 (a) tan 1 2 (b) tan 1 4 (c)  / 4 (d)  / 3

(a) 2  3 (b) 2  3 Q.11 What is the maximum value of sin 3 cos 2 +

cos 3 sin 2 ?
(c) 2 3 (d) 3 2 (a) 1 (b) 2 (c) 4 (d) 10
Q.3 If 18 , then waht is the value of 4 sin Q.12 What is the value of sinA cosA tan A + cosA
2  2sin  ? sinA cotA?
(a) sinA (b) cosA (c) tanA (d) 1
(a) 1 (b) 1 (c) 0 (d) 2
Q.4 Two poles are 10m and 20m high. The line join- 2 1 5
ing their tops makes an angle of 15° with the Q.13 What is the value of sec2 tan sec tan  ?
 11 
horizontal. What is the distance between the
(a) 121/96 (b) 217/921
poles?
(c) 146/121 (d) 267/121
(a) 10 
3 1 m 
(b) 5 4  2 3 m Q.14 Which one of the following is positive in the third
quardrant?
(c) 20  3  1 m (d) 10  3  1 m (a) sin  (b) cos  (c) tan  (d) sec 
Q.15 What is the value of sin(1920°)?
Q.5 The angle of elevation of a tower at a level
ground is 30°. The angle of elevation becomes 1 1 3 1
(a) (b) (c) (d)
 when moved 10n toward the tower. if the 2 2 2 3
height of tower is 5 3 m, then what is the value Q.16 What is the sum of the sequares of the roots of
of  ? the equation x 2  2x  143  0
(a) 170 (b) 180 (c) 190 (d) 290
(a) 45 (b) 60
(c) 75 (d) None of these Q.17 Let U U  x  N :1  x  10 be the univesal
Q.6 In a ABC , if the angle A,B and C are the in set m N being the set of natural numbers. If
AP, then which one of the following is correct? A A  1, 2, 3, 4, and B  2, 3, 6,10 then
(a) c  a  b (b) c 2  a 2  b 2  ab that is the complanaer of (A - B?
(c) a  b  c  bc (d) b  a  c  ac (b) 1, 4
2 2 2 2 2 2
(a) {4,10}
4
Q.7
1 1
If sin 1  sin sin
1
 sin 1 x , then what is (c) 2,3,5, 6, 7,8,9,10
5
the value of x? (d) 5,6, 7,8,9,10
(a) 3/5 (b) 4/5 (c) 1 (d) 0 Q.18 The solution of the simultaneous linear equations
1 by which one of the following lnear equations?
Q.8 If cos ec   cot   , where   0 , then (a) x  y  5 (b) 2x  y  9
3
what is the value of cos  ? (c) 2x  3y  10 (d) 2x  3y  6
Q.19 Let A = {x:x us a square of a mnatural numebr
3 1 1 and x is less than 100} and B is a set of even
(a) 0 (b) (c) (d)
2 2 2 natural numbers. What is the cardinary of

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AB? 
1
1
What does the series 1  3  3  .....
2
(a) 4 (b) 5 Q.30
(c) 9 (d) None of these 3
represent ?
1 2  1 0  (a) AP (b) GP
Q.20 If A    and B    ? then what
 2 3 1 0  (c) HP (d) None of these
Q.31 The angle of elevation of the tip of a flag staff
is determinant of AB?
from a point 10m due South of its base is 60°.
(a) 0 (b) 1 (c) 10 (d) 20
What is the height fotghe flastaffcorrect to the
a ab ac nearest metre?
(a) 15m (b) 16m (c) 17 m (d) 18 m
ab b 2
bc
Q.21 What is the value of sin  cos 
ac bc  c2 Q.32 What is the value of  ?
cos ec sec 
(a) 4abc (b) 4a2bc (a) 1 (b) 1/2 (c) 1/3 (d) 2
(c) 4a b c
2 2
(d) -4a2b2c2 Q.33 If tan   sec   4 , then what is the value of
Q.22 What is the distance bnetween the lines 3x + 4y
= 0 and 6x + 8y = 18? sin  ?
(a) 0 (b) 3 units (c) 9 units (d) 18 units (a) 8/17 (b) 8/15 (c) 15/17 (d) 23/25
Q.23 The number 292 in decimal system is expressed 1 4 12 
in binary system by Q.34 What is the value of cos cos  cos 1 
(a) 100001010 (b) 100010001  5 13 
(c) 100100100 (d) 101010000 (a) 63/65 (b) 33/65 (c) 22/65 (d) 11/65
Q.24 What is the arithmetic mean of first 16 natural Q.35 What is the angle subtended by1m pole at a
numbers with weights beings the number itself? distance 1km on the ground in sexgeismal mea-
(a) 17/2 (b) 33/2 (c) 11 (d) 187/2 sure?
Q.25 What is the mode for the data 20, 20, 21, 21, 21, 9 9
21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, (a) deg ree (b) deg ree
50 50
23, 24, 24, 25/
(a) 7 (b) 21 (c) 22 (d) 25 (c) 3.4 min (d) 3.5 min
Q.26 A and B are two matrices such that AB = A and Q.36 .
If cotA cot A cot B  2 , then what is the value
BA = B, then what is the value of B2? .
of cos (A + B)  A  B  sec  A  B  ?
(a) B (b) A (c) I (d) -I
Q.27 The geometric mean and harmonic mean of two (a) 1/3 (b) 2/3 (c) 1 (d) -1
non-negative observations are 10 and 8, respec- Q.37 Consider the following statements
tively. then what is the arithmetic mean of the 1. Every zero matrix is a square matrix.
observations? 2. a matrix has a numerical value.
(a) 4 (b) 9 (c) 12.5 (d) 5 3. A unit matrix is a diagonal matrix.
Q.28 Consider the following statements Q.38 If the sequence {Sn} is a geometic progression
1. A continuous random variable can take all and s2s11 = sp,s8, then what is the value of p?
value in an interval. (a) 1 (b) 3
2. A random variabkle which takes a fintie (c) 5
numebr of values is necessarily discrete. (d) Cannot be determined
3. Contruction of a frequency distribution is Q.39 In the expansion of (1 + x)n, What is the sun of
based on data which are discrete. even binomial coefficeints?
Which of the above statement are correct? (a) 2n (b) 2n-1
(a) Both 1 and 2 (b) Both 2 and 3 (c) 2 n+1
(d) None of these
(c) Both 1 and 3 (d) All of these Q.40 The value of the term independ of x in the
Q,29 What is the nth tem of the sequence 9
 2 1
1,5,9,13,17,...? expanion of  x  
(a) 2n -1 (b) 2n+1  x
(c) 4n-3 (d) None of these (a) 9 (b) 18 (c) 48 (d) 84

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Q.41 What is the number of ways that 4 boys and 3 how many passed in both semesters?
girls can be seated so that boys and girls alter- (a) 30 (b) 40 (c) 70 (d) 140
nate? Q.51 If a matrix A has in verses B and C, then whcih
(a) 12 (b) 72 (c) 120 (d) 144 one of the following is correct?
Q.42 If the difference between the roots of (a) B may not be equal to C
(b) B should be equal to C
ax 2  bx  c  0 is 1, then which one of the
(c) B and C should be unit matrices
following is correct?
(d) None of these
(a) b  a  a  4c  (b) a  b  b  4c 
2 2
Q.52 Three dice are thrown. What is the probability
that the same number will appear on each of
(c) a  c  a  4c  (d) b  a  b  4c 
2 2
them?
Q.43 If one of the roots of the equation (a) 1/6 (b) 1/18 (c) 1/24 (d) 1/36
Directions (Q.Nos.53-54) The equation
x 2  ax  b  0 is 1, then what is the value of formed by multiplying each root of
(1 - b)?
(a) -1 (b) 1 (c) 2 (d) -2 ax 2  bx  c  0 by 2 is x 2  36x  24  0 .
Q.44 If  and  are the roots of the equation Q.53 What is the value of b : c?
(a) 3 : 1 (b) 1 : 2 (c) 1 : 3 (d) 3 : 2
x 2  q 1  x   r  0 , then what is the value Q.54 Which one of the following is correct?
(a) bc  a 2 (b) bc  36a 2
of 1    a    ?
(c) bc  72a 2 (d) bc  108a 2
(a) 1  r (b) q  r (c) 1  r (d) q  r
Directions (Q.Nos. 55-57) Let sin (A + B) = 1
Q.45 If 1/4, 1/x, 1/10 are in HP, then what is the vale
of x?  
(a) 5 (b) 6 (c) 7 (d) 8 and sin (A - B) = 1/2, where AB  0,  .
2  
Q.46 If p, q and r are in AP as well as GP, then which Q.55 What is the value of A?
one of the following is correct?
(a) p  q  r (b) p  q  r    
(a) (b) (c) (d)
(c) p  q  r (d) p  q  r 6 3 4 8
Q.47 What is the perimeter of the triangle of the with Q.56 What is the value of tan(A + 2B).tan(2A + B)?
(a) -1 (b) 0 (c) 1 (d) 2
verticle A  4, 2  , B  0, 1 and C  3,3 ? Q.57 What is the value of sin 2 A  sin 2 B ?
(a) 7  3 2 (b) 10  5 2 (a) 0 (b) 1/2 (c) 1 (d) 2
Q.58 If the latusrectum of an ellipse in equal to half
(c) 11  6 2 (d) 5  2 of the minor axis, then what is its eccentricity?
Q.48 If the mid point between the point  a  b, a  b  (a) 2 / 3 (b) 1/ 3 (c) 3 / 2 (d) 1/ 2
Q.59 What is the probability that a leap year selected
adn  a, b  lies on the line ax  by  k , what at random contains 53 Mondays?
is th value of k? (a) 1/7 (b) 2/7 (c) 7/366 (d) 26/183
(a) a/b (b) a + b (c) ab (d) a - b Q.60 What is the decimal nuimber representation of
Q.49 The acute angle which the perpendicular form the binary number (11101.001)2?
origin onthe lien 7x  3y  4 makes with the (a) 30.125 (b) 29.025
(c) 29.125 (d) 28.025
x-axis is
(a) zero Q.61 If a  2,1, 1 , b  1, 1,0  , c   5, 1,1 ,
(b) positive but not  / 4 them what is the unit vector parallel to a + b - c
(c) negative in the opposite direction?
(d)  / 4 i  j  2k i  2 j  2k
Q.50 Out of 500 first year student, 260 passed inthe (a) (b)
3 3
first semester and 210 passed inth second se-
mester. If 170 and did not pass in either semeste,.

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Q.70 If A is a equal matrix such that A2 = I, where, I
2i  j  2k
(c) (d) None of these is the identity matrix, then what is teh value of
3 A -1 ?
Q.62 If the magnitudesof two vectos a and b are equal, (a) A  I (b) Null matrix
then which one of the following is correct? (c) A (d) Transpose of A
(a)  a  b  is parallel to  a  b  Q.71 What is the escentricity of the conic
4x 2  9y 2  144 ?
(b)  a  b  . a  b   1
5 5 3 2
(c)  a  b  is perpendicular to  a  b  (a) (b) (c) (d)
3 4 5 3
(d) None of the above
Q.72 If two rows of a deteminant are identical, then
Q.63 Consider the following in respect of the func-
what is the value of the determinant?
tion f  x   x  3 (a) 0 (b) 1
(c) -1
1. f  x  is continuous at x = 3 (d) Can be any real value
Q.73 If A = {0, 1} adn B={1, 0} then what is the
2. f  x  is differential at x = 0 value of A × B
Which of the above statements is.are correct? (a) {0,1} {1, 0} (b) {0, 0} {1, 1}
(a) Only 1 (b) Only 2 (c) {0, 1}{1,0} {1,1} (d) A × A
(c) Both 1 and 2 (d) neither 1 nor 2 Q.74 What is the perpendicular distance of the point
Q.64 If four dice are down together, then what is the (x, y) from x-axis?
probabilityb that the sum of the numbers appear- (a) x (b) y (c) |x| (d) |y|
ing on them is5? Q.75 If ABCD is a cyclic quadrilateral, then what is
(a) 0 (b) 1/2 (c) 1 (d) 1/1296 the value of sin A + sin B - sin C - sin D?
Q.65 Let O be the origin and P,Q, and R be the poitns (a) 0 (b) 1
such that PQ + OQ = OR. Then, which one of (c) 2 (d) 2(sinA + sinB)
the following is correct?
Q.76 If  xy   f  x  y  , then f  t  may be of th
(a) P,Q and R are the vertices of an equiliateral
triangle form
(b) P,Q adn R are the vertices of an isocleles (a) t + k (b) ct + k (c) tk + c (d) tk
triangle 4  2i
(c) P,Q and R are collinear Q.77 If A  iB  , where i  1 , then what
1  2i
(d) None of these
is the value of A?
1 (a) -8 (b) 0 (c) 4 (d) 8
Q.66 What is the value of 2 log 8 2  log 3 9 ?
2 Q.78 If z = -z, then which one of the following is cor-
(a) 0 (b) 1 (c) 2 (d) 1/3 rect?
(a) the real part of z is zero.
Q.67 What is the value of m, if the vectors 2i  j  k ,
(b) The imaginary part of z is zero.
i  2 j  3k adn 3i  mj  5k are coplanar? (c) The real part of z is equal to imaginary part
(a) -2 (b) 2 (c) -4 (d) 4 of z.
(d) the sum of real and imaginary part of z is z.
Q.68 If a  10, b  2 and a.b  12 , then what is
Q.79 If A and B are two non-empty sets having n
the value of a  b ? elements in common, then what is the number
of common elements in the sets A × B and B ×
(a) 12 (b) 16 (c) 20 (d) 24 A?
Q.69 If the vector i  xj  yk and i  xj  yk are or- (a) n (b) n2 (c) 2n (d) zero
thogonal to each other, then what is the locus of Q.80 If A and B are any two sets, then What is the

the point  x, y  ? valueof A   A  B  ?

(a) A parabola (b) An ellipse (a) Completment of A (b) Complement of B
(c) A circle (d) A straight line (c) B (d) A

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Q.81 What is the cosine of angle between the planes Q.89 If y = cost and x = sin t, then what is the value
x  y  z  1  0 and 2x  2y  2z  1  0 ? dy
(a) 1/2 (b) 1/3 of ?
dx
(c) 2/3 (d) None of these
(a) xy (b) x / y (c)  y / x (d)  x / y
1 2  0  1
If A   and B  
5
  , then what is
x  1 2 xdx ?
Q.82
1 1  1 2 
2
Q.90 What is the value of
the value of B1A 1 ? 7
2 2
(b)  x  1 2  C
7

1  3  1 3  
(a) x  1 2
 2 C
7
(a)   (b)  
 1 2  1  2  1 2 7

(c)  x  1 2  C (d) None of these

 1 3   1  3 7
(c)   (d)   Q.91 What is the value of
 1  2   1  2
Q.83 Which one of the following functions is sin 420.cos 390  cos  300 
differntiable for all real vlaue of x? (a) 0 (b) 1 (c) 2 (d) -1
x 1 Q.92 Consider the following statements
1 (1) 1° in radina mesasure is less than 0.02 radi-
(a) x (b) x x (c) x (d)
x ans.
Q.84 Which one of the following defferential equa- (2) 1 radian in degree measure is greater than
tions is not linear? 45°.
What of the above statements is/are correct?
d2 y dy (a ) Only 1 (b) Only 2
(a)  4y  0 (b) x  y  x3
dx 2 dx (c) Both 1 and 2 (d) Neither 1 nor 2
Q.93 What is the maximum value of sin2x
dy
x  y
2
(c) 9 (a) -1 (b) 0 (c) 1 (d) Infinity
dx Q.94 the sum and product of matrices A and B exist.
dy Which of the following implications are
2
(d) cos x  y  tan x necessarilly true?
dx 1. A and B are square matrices of same order.
Q.85 What is the sum of the squares of direction co- 2. A and B are non-singular matrices
sines of the line joining the points (1, 2, -3) and Select the correct answer using the codes given
(-2,2,-3)? below.
2 (a) Only 1 (b) Only 2
(a) 0 (b) 1 (c) 3 (d) (c) Both 1 and 2 (d) Norther 1 nor 2
26
Q.95 What is the area of the rectangle having verices.
Q.86 What is the diameter of the sphere ? A, B, C and D with position vectors
x 2  y 2  z 2  4x  6y  8z  7  0 1 1 1
(a) 4 units (b) 5 units i  j  4k , i  j  4k , i  j  4k and
2 2 2
(c) 6 units (d) 12 units
Q.87 What is the slope of the tanger to the curves 1
i  j  4k ,
x  t 2  3t  8, y  2t  5 at t  2 ? 2
(a) 7/6 (b) 6/7 (c) 1 (d) 5/6 (a) 1/2 sq units (b) 1 sq units
Q.88 Which one of the following statements is cor- (c) 2 sq units (d) 4 sq units
rect? Q.96 The set A = {x : x + 4 = 4} can also be repre-
(a) ex is an increasing function sented by
(b) ex is decreasing function (a) 0 (b)  (c)  (d) {0}
(c) ex is neither increasing nor decreasing func- Q.97 If a line makes the angles ,  and  with the
tion
axes, then what is the value of 1+
(d) ex is a constant function

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cos2  1  cos 2  cos   cos 2  ?

8 5 1
(a) -1 (b) 0 (c) 1 (d) 2
Q.98 What is the sum of the series 5 x 1 2
Q.107 If , then what is the value of
1 1 1 6 3 1
1     ......?
2 4 8 x?
(a) 1/2 (b) 3/2 (c) 2 (d) 2/3 (a) 4 (b) 5 (c) 6 (d) 8
Q.99 Consider the following statements Q.108 What is the order of the product
1. Two independent variable are always
uncorrelated. a h g x
2. The coefficient of correlation between two  xyz h b f  t  ?
variables X and Y is positive when X decreasess, g f c  z 
the Y decreases.
Which of the above statements is/are correct? (a) 3 1 (b) 1  1 (c) 1 3 (d) 3  3
(a) Only 1 (b) Only 2
 /2
(c) Both 1 and 2 (d) Neither 1 nor 2
Q.100 A variate X takes values 2, 9, 3,7,5,4,3,2,10.
Q.109 What is the value of / 2
sin x dx ?

What is the median? (a) 2 (b) 1 (c)  (d) 0

(a) 2 (b) 4 (c) 7 (d) 9 Q.110 The area bounded by the curve x  f  y  , y-
Q.101 What are the direction ratios of normal tot he
axis and the two lines y = a and y = b is equal to-
plane. 2  y  2 z  l  0 ?
b b

1 (a)  a
ydx (b) a
y 2dx
(a)  2,1, 2  (b)  1,  ,1 
2 b

(c)  1, 2,1  (d) None of these

(c)  a
xdx (d) None of these

Directions (Q.102-105) In a city, three daily x 1 dy

newspapers A, B and C are published, 42% read Q.111 If y  , then what is the value of ?
x 1 dx
A, 51% read B, 68% read B and C, 36% read A
and C, 8 do not read any of the three newspa- 2 2
pers. (a) (b) x  1 2
Q.102 What is the percentage of persons who read all x 1  
the three papers? 2 2
(a) 20% (b) 25% (c) 30% (d) 40%
Q.103 What is the percentage of persons who read
(c) x  1 2
   
(d) x  1
only two papers? Q.112 Which one of the following statements is cor-
(a) 19% (b) 31% rect?
(c) 44% (d) None of these (a) The dericative of a function f(x) at a point
Q.104 What is the percentage of persons who read will exist, if there is sone tangent to the curve =
only one paper? f(x) at theat point and the tangent is parallel to
(a) 38% (b) 39% y-axis.
(c) 51% (d) None of these (b) The derivative of a function f(x) at a point
Q.105 What is the percentage of persons who read will exist, if there is one tangent to the curve y =
only A but neither B nor C? f(x) at that point and the tnagently must be par-
(a) 4% (b) 3% allel to x-axis
(c) 1% (d) None of these (c) The derivative of a function f(x) at a point
Q.106 If f(x)x2 - 6x + 8 and there exists a point c in will exist, if there is one and only one tangent to
the interval [2, 4] such that f'(c) = 0, then what the curve y= f(x) at that point and teh tangent
is the value of c? isnot parallel to y-axis.
(a) 2.5 (b) 39% (d) None of the above
(c) 51% (d) None of these Q.113 Consider the following
1.  log10dx  x  C
OURS ACADEMY:Near Bus Stand, Rishi Nagar, Hisar. M.9467134541,9812130823
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(a) xy  C (b) x  Cy

2. 10 dx  10  C
x x

where C is the contant of integration. Which of (c) y  Cx (d) None of these

the above is/are correct? Q.118 What is the degree of the differential equation y
(a) Only 1 (b) Only 2
dy  dy 
(c) Both 1 and 2 (d) Neither 1 not 2 yx   ?
Q.114 How many tangents are parallel to x-axis for dx  dx 
the curve? y  x 2  4x  3 ? (a) 1 (b) 2
(c) -1
(a) 1 (b) 2 (d) Degree does not exist
(c) 3 where C is constant
(d) No tangent is parallel to x-axis
tan 1 x
1
 x2  Q.119 What is the value of 0 dx ?
Q.115 What is the value of xlim  ? 1 x2
 x 8
2 3

(a) 1/ 4 (b) 1/ 4 (c) 1/ 12 (d) 1/12   2 2

(a) (b) (c) (d)
4 8 8 32
1
Q.116 What is the value of lim x 2 sin  ? Q.120 What is the rate of change of
x 0
x x 2  16 with
(a) 0 (b) 1 respect to x 2 at x = 3?
(c) 1/2 (d) Limit does not exist (a) 1/5 (b) 1/10
Q.117 What is the solution of the differential equations? (c) 1/20 (d) none of these
dy d
 0
dx x

Answer Key
Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A.
Q. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
A.
Q. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A.
Q. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
A.
Q. 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
A.
Q. 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
A.

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 BOOKLET CODE: A

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