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NDA (SEP 2011) MATHEMATICS
1.
2.
3.
4.
5.
6.
7.
What is the value of (1 + i)5 + (1 – i)5 where
i = √−1 ?
(a) – 8 (b 8
(c) i
(d) –8i
What is the value of tan 9° – tan 27° – tan 63° + tan
81° ?
(a) 1
(b) 2 (c) 3 (d) 4
2
4
If x = y ( 3 ) = z cos ( 3 ), then what is xy + yz + zx
equal to ?
(a) –1
(b) 0 (c) 1 (d) 2
If sin A + sin B + sin C = 3 then what is cos A + cos
B + cos C equal to ?
(a) –1
(b) 0 (c) 1 (d) 3
At a point 15 m away from the base of a 15 m high
house, the angle of elevation of the top is
(a) 90°
(b) 60°
(c) 45°
(d) 30°
The simultaneous equations 3x + 5y = 7 and
6x + 10y = 18 have
(a) no solution
(b) infinitely many solutions
(c) unique solution
(d) any finite number of solutions
2
What is the principal value of sec–1 ( 3) ?

8.
9.
10.
11.
12.
13.
ORC CADEMY


√
16.
(c) ± i
(d) 1
1
1
dy
If y = (1 + x 4 ) (1 + x 2 ) (1-x 4 ), then what is
dx
equal to ?
1
18.
19.
20.
21.
(a) 1
(b) –1
(c) x
(d) x 2
In binary system the decimal number 03 can be
expressed as
(a) (001001….)2
(b) (010110……)2
(c) (011001….)2
(d) (010101……)2
Two letters are drawn at random from the word
‘HOME’. What is the probability that both the
letters are vowels ?
(a) 1/6
(b) 5/6
(c) 1/2
(d) 1/3
3
If z = 1 + tan α where  < α < 2 , then what is | z |
equal to
(a) sec α (b) – sec α
(c) sec2 α
(d) – sec2α
There are 4 candidates for the post of a lecturer in
Mathematics and one is to be selected by votes of 5
men. What is the number of ways in which the votes
can be given ?
(a) 1048
(b) 1072
(c) 1024
(d) 625
n

22.
23.
24.
P(n,r)
What is the value of r 1
?
r!
n
(a) 2n – 1
(b) 2
(c) 2 n–1
(d) 2n + 1
What are the co-ordinates of the foot of the
perpendicular from the point (2, 3) on the line
x + y – 11 = 0 ?
(a) (2, 9)
(b) (5, 6)
(c) (– 5, 6)
(d) (6,5)
What is the degree of the differential equation
d3 y
2
3
d2 y
dy
(dx3 ) + 4 – 3 (dx2 ) + 5 (dx) = 0
26.
(b) ±(1 – i)
1
(c) 3 square unit 1
(d) 4 square unit
At an extreme point of a function f(x), the tangent to
the curve is
(a) parallel to the x-axis
(b) perpendicular to the x-axis
(c) inclined'at an angle 45° to the x-axis
(d) inclined at an angle 60° to the x-axis
1
17.
(a) 2
(b) 5
(c) 2 + 5i
(d) 2 – 5i
What are the square roots of –2i ?
(a) ± (1 + i)
(b) 2 square unit
1
25.
(i = √-1)
1
(a) 1 square unit

(a) 2
(b) 3
(c) 4
(d) 6
What is the 10th common term between the series
2 + 6 + 10 +……. and 1 + 6 + 11 +…… ?
(a) 180
(b) 186
(c) 196
(d) 206
If the 10th term of a GP is 9 and 4th term is 4, then
what is its 7th term ?
(a) 6
(b) 14
(c) 27/14
(d) 56/15
The function y = f(x) = mx + c has
(a) maximum point but no minimum point
(b) minimum point but no maximum point
(c) both maximum and minimum points
(d) neither maximum point nor minimum point
If log10 2, Iogl0 (2x – l), log10 (2x + 3) are three
consecutive terms of an AP, then which one of the
following is correct?
(a) x = 0
(b) x – 1
(c) x = log2 5
(d) x = log5 2
What is the locus of points of intersection of a
sphere and a plane ?
(a) Circle
(b) Ellipse
(c) Parabola
(d) Hyperbola
The equation x2 – 4x + 29 = 0 has one root 2 + 5i.
What is the other root
(i = √-1
14.
15. What is the area between the curve y = cos 3x,

0 ≤ x ≤ 6 and the co-ordinate axes ?
(a) 3
(b) 2
(c) 2/3
(d) Not defined
What is the area enclosed .by the equation
x2 + y2 = 2 ?
(a) 4 square units
(b) 2 square units
(c) 42 square units
(d) 4 square units
𝑑𝑥
What is equal ∫ 2
equal to ?
sin 𝑥 cos2 𝑥
(a) tan x + cot x + c
(b) tan x – cot x + c
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
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NDA (SEP 2011) MATHEMATICS
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
ORC CADEMY
(c) (tan x + cot x)2 + c
(d) (tan x – cot x)2 + c
where c is the constant of integration.
𝑥 𝛼 l
The roots of the equation |𝛽 𝑥 l| = 0
𝛽 𝛾 l
are independent of
(a) α
(b) β (c) γ (d) α, β, γ
Which one of the following is the mean of the data
given below ?
xi
6 10 14 18 24 28 30
Fi 2 4
7
12 8
4
3
(a) 17
(b) 18
(c) 19
(d) 20
If 𝑎⃗ and 𝑏⃗⃗ are two vectors such that 𝑎⃗ • 𝑏⃗⃗ = 0 and
𝑎⃗  𝑏⃗⃗ = 0, then which one of the following is
correct?
(a) 𝑎⃗ is parallel to 𝑎⃗.
(b) 𝑏⃗⃗ is perpendicular to 𝑏⃗⃗.
(c) Either 𝑎⃗ or 𝑏⃗⃗ is a null vector.
(d) None of the above
dy
38.
39.
40.
41.
If tan  = √𝑚 where m is a non-square natural
number m, then sec 2 is
(a) a negative number
(b) a transcendental number
(c) an irrational number
(d) a rational number
If any triangle ABC, the sides are 6 cm, 10 cm and
14 cm. Then the triangle is obtuse angled with the
obtuse angle equal
(a) 150°
(b) 135°
(c) 120°
(d) 105°
–1
In a triangle ABC, if A = tan 2 and B = tan–1 3,
then C is equal to




(a) 3
(b) 4
(c) 6
(d) 2
Let α, β be the roots of the equation
(x – a) (x – b) = c, c ≠ 0. Then the roots of the
equation (x – a) (x – β) + c = 0 are
(a) a, c
(b) b, c (c) a, b (d) a + b, a + c
If the equations x2 – px + q = 0 and x2 – ax + b = 0
have a common root and the roots of the second
equation are equal, then which one of the following
is correct ?
(a) aq = 2(b + p)
(b) aq = b + p
(c) ap = 2(b + q)
(d) ap = b + q
If n, !, 3  (n !) and (n + 1)! are in GP, then the value
of n will be
(a) 3
(b) 4
(c) 8
(d) 10
1−𝑖 𝑛
which(1 + 𝑖) is purely imaginary with positive
imaginary part is
(a) 1
(b) 3
(c) 4
(d) 5
What is the area of the triangle formed by the lines
joining the vertex of the parabola x2 = 12y to the
ends of the latus rectum ?
(a) 9 square units
(b) 12 square units
(c) 14 square units
(d) 18 square units
What is the angle between two planes 2x – y + z = 4
and x + y + 2z = 6?




(a)
(b)
(c)
(d)
2
3
4
6
What is the equation of the curve passing through

the point (0, 3) satisfying the differential equation
sin x cos y dx + cos x sin y dy = 0 ?
√3
2
√3
2
1
=
2
(a) cos x cos y = –

If y = ln √tan x, then what is the value of at x =
dx
4
(a) 0
(b) –l
(c) 1/2
(d) 1
The point in the interval (0, 2) where f(x) = ex sin x
has maximum slope is


3
(a) 4
(b) 2
(c) 
(d) 2
The smallest positive integral value of n for
1
42.
43.
44.
45.
(c) sin x sin y =
(d) cos x cos y
2
A husband and wife appear in an interview for two
vacancies in the same post. The probability of
husband’s selection is 1/5 and that of wife’s
selection is 1/3, What is the probability that only
one of them will be selected ?
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
If α and β are the complex cube roots of unity, then
what is the value of (1 + α) (1 + β) (1 + α2) (1 + β2)?
(a) –1
(b) 0
(c) 1
(d) 4.
A tower of height 15 m stands vertically on the
ground. From a point on the ground the angle of
elevation of the top of the tower is found to be 30°.
What is the distance of the point from the foot of the
tower ?
(a) 15√3 m
(b) 10√3m
(c) 5√3 m
(d) 30 m
If tan A – tan B = x and cot B – cot A = y, then what
is cot (A – B) equal to ?
1 1
1 1
1 1
1 1
(a) –
(b) –
(c) +
(d) – –
𝑦
46.
47.
48.
(b) sin x sin y =
𝑥
𝑥
𝑦
𝑥
𝑦
𝑥
𝑦
There is a point inside a circle. What is the
probability that this point is close to the
circumference than to the centre ?
(a) 3/4
(b) 1/2
(c) 1/4
(d) 1/3
How many diagonals will be there in an n-sided
regular polygon ?
𝑛(𝑛−1)
𝑛(𝑛−3)
𝑛(𝑛 + 1)
(a)
(b)
(c) n2 – n (d)
2
2
2
Students of three sections of a class, having 30, 30
and 40 students appeared for a test of 100 marks.
The arithmetic means of the marks of the three
sections are 722, 69 0 and 641 in that order. What
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
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NDA (SEP 2011) MATHEMATICS
49.
50.
51.
is the arithmetic mean of the marks of all the
students of the three sections ?
(a) 66 6
(b) 673
(c) 680
(d) 706
What is the focal distance of any point P(x1, y1) on
the parabola y2 = 4ax ?
(a) x1 + yl
(b) x1 y1
(c) ax1
(d) a + x1
If the vectors –і̂ –2xј̂ – 3y𝑘̂ and і̂ – 3xј̂ – 2y𝑘̂ are
orthogonal to each other, then what is the locus of
the point (x, y) ?
(a) a straight line
(b) an ellipse
(c) a parabola
(d) a circle
What is the value of the determinant
𝑎−𝑏 𝑏+𝑐 𝑎
|𝑏 − 𝑐
52.
53.
54.
𝑐+𝑎
𝑏| ?
(c)
(d)
58.
If 𝑐⃗ is the unit vector perpendicular to both the
vectors 𝑎⃗ and 𝑏⃗⃗, then what is another unit vector
perpendicular to both the vectors 𝑎⃗ and 𝑏⃗⃗ ?
⃗⃗  ⃗b⃗)
⃗⃗  ⃗b⃗)
(a
(a
(a) c⃗  a⃗⃗
(b) c⃗  ⃗⃗
b
(c) –
(d)
59.
If p is the length of the perpendicular drawn from
𝑥 𝑦
the origin to the line + = 1, then which one of the
𝑎 𝑏
following is correct ?
1
1
1
1
1
1
(a) 𝑝2 = 𝑎2 + 𝑏2 (b) 𝑝2 = 𝑎2 – 𝑏2
⃗⃗  ⃗b⃗|
|a
1
tan α+ tan β
ℎ
cos (α− β)
61.
62.
63.
64.
65.
If |0 𝑝 𝑞 | = 0, then which one of the following is
𝑞 0 𝑝
correct ?
(a) p is one of the cube roots of unity
(b) q is one of the cube roots of unity
𝑝
(c) 𝑞 is one of the cube roots of unity
56.
57.
(d) None of the above
If (p, q) is the point on the x-axis equidistant from
the points (1, 2) and (2, 3), then which one of the
following is correct ?
(a) p = 0, q = 4 (b) p = 4, q = 0
(c) p = 3/2, q = 0 (d) p = 1, q = 0
If the variance of the data 2, 4, 5, 6, 17 is v, then
what is the variance of the data 4, 8, 10, 12, 34?
(a) v
(b) 4v
(c) v2
(d) 2v
1
(d)
1
𝑝
1
⃗⃗  ⃗b⃗|
|a
1
=𝑎–𝑏
If the sides of a triangle arc in the ratio
2 : √6:1 + √3, then what is the smallest angle of the
triangle ?
(a) 75°
(b) 60°
(c) 45°
(d) 30°
What is the value of
√8 + 2√8 + 2√8 + 2√8 + ⋯ ∞ ?
𝑝 −𝑞 0
55.
1
(c) 𝑝 = 𝑎 + 𝑏
60.
𝑐−𝑎 𝑎+𝑏 𝑐
(a) a3 + b3 + c3
(b) 3bc
(c) a3 + b3 + c3 – 3abc
(d) 0
If a, b, c, d, e, f are in AP, then (e – c) is equal to
which one of the following ?
(a) 2(c – a)
(b) 2(d – c)
(c) 2(f – d)
(d) (d – c)
Let α and β be the roots of the equation
x2 + x + 1 = 0. The equation whose roots are α19 and
β7 is
(a) x2 – x – 1 = 0
(b) x2 – x + 1 = 0
2
(c) x + x – 1 = 0
(d) x2 + x + 1 = 0
A vertical tower stands on a horizontal plane and is
surmounted by a vertical flag staff of height h. At a
point P on the plane, the angle of elevation of the
bottom of the flag staff is P and that of the top is a.
What is the height of the tower ?
ℎ tan β
ℎ tan β
(a)
(b)
tan α− tan β
ℎ cos 𝛽
tan α − cos β
ORC CADEMY
(a) 10
.(b) 8
(c) 6
(d) 4
If A = {a, b, c}, then what is the number of proper
subsets of A ?
(a) 5
(b) 6
(c) 7
(d) 8
In a random arrangement of the letters of the word
‘UNIVERSITY’, what is the probability that two I’s
do not come together ?
(a) 4/5 (b) 1/5
(c) 1/10
(d) 9/10
If tan A = 1/2 and tan B = 1/3. then what is the value
of 4A + 4B ?
(a) /4
(b) /2
(c)  (d) 2
An aeroplane flying at a height of 300 m above the
ground passes vertically above another plane at an
instant when the angles of elevation of two planes
from the same point on the ground are 60° and 45°
respectively. What is the height of the lower plane
from the ground ?
100
(a) 50 m
(b) 3 m
√
66.
67.
68.
(c) 100 √3m
(d) 150(√3 +1) m
For what value of m are the points with position
vectors 10і̂ + 3ј̂, 12і̂ – 5ј̂ and mі̂ + 11ј̂ collinear ?
(a) –8
(b) 4
(c) 8
(d) 12
The mean of 7 observations is 10 and that of 3
observations is 5. What is the mean of all the 10
observations?
(a) 15
(b) 10
(c) 85
(d) 75
What is the ratio of coefficient of x15 to the term
2 15
independent of x in (x 2 + ) ?
x
(a) 1/64
(b) 1/32
(c) 1/16
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
(d) 1/4
Page 3
NDA (SEP 2011) MATHEMATICS
1+a
69.
70.
71.
72.
73.
74.
75.
–1
–1
–1
If a + b + c = 0 such | 1
1
1+b
1
1 | = λ,
1
1 1+c
then what is λ equal to ?
(a) – abc
(b) abc
(c) 0
(d) 1
In a class of 125 students 70 passed in Mathematics,
55 passed in Statistics and 30 passed in both. What
is the probability that a student selected at random
from the class has passed in only one subject?
(a) 13/25
(b) 3/25
(c) 17/25
(d) 8/25
For what value of m are the vectors 2і̂ –3ј̂ + 4k̂,
̂і + 2ј̂ – k̂ and mі̂ – ̂ј + 2k̂ coplanar ?
(a) 0
(b) 5/3
(c) 1
(d) 8/5
In a triangle ABC, a = 8, b = 10 and c = 12. What is
angle C equal to ?
(a) A/2
(b) 2A
(c) 3A
(d) 3A/2
𝑥
If sin  = x + 𝑎 for all x  R – {0}, then which one of
the following is correct ?
1
1
1
(a) a ≥ 4
(b) a ≥ 2
(c) a ≤ 4
(d) a ≤ 2
The equation tan4 x – 2 sec2 x + a2 = 0 will have at
least one real solution if,
(a) | a) | ≤ 4
(b) | a | ≤ 2
(c) | a | ≤ √3
(d) None of the above
The sides a, b, c of a triangle ABC are in arithmetic
progression and ‘a’ is the smallest side. What is cos
A equal to ?
(a)
3𝑐 – 4𝑏
2𝑐
(b)
3𝑐 – 4𝑏
2𝑏
(c)
4𝑐 – 3𝑏
2𝑐
(c)
3𝑏 – 4𝑐
2𝑐
2
82. If the rate of change in volume of spherical
soap bubble is uniform, then the rate of change
of surface area varies as
(a) square of radius
(b) square root of radius
(c) inversely proportional to radius
(d) cube of the radius
sin 𝑥
1 + cos 𝑥
83. What is l +cos 𝑥 + sin 𝑥 equal to ?
(a) 2 tan x
(b) 2 cosec x
(c) 2 cos x
(d) 2 sin x
84. Some measures of central tendency for n discrete
observations are given below,:
(a) Arithmetic mean
(b) Geometric mean
(c) Harmonic mean
(d) Median
A desirable property of a measure of central
tendency is if every observation is multiplied by c,
then the measure of central tendency is also
multiplied by c, where c > 0. Which of the above
measures satisfy the property ?
(a) 1, 2 and 3 only
(b) 1, 2 and 4 only
(c) 3 and 4 only
(d) 1, 2, 3 and 4
85. If f(x) = x ln x, then f(x) attains minimum value at
which one of the following points ?
(a) x = e–2
(b) x = e
(c) x = e–1
(d) x = 2e–1
86. A variate X takes values 2, 3, 4, 2, 5, 4, 3, 2, 1. What
is the mode ?
(a) 2
(b) 3
(c) 4
(d) 5
87.

If 1 {k2 +{4 – 4k)x + 4x3} dx ≤ 12, then which one of
the following is correct ?
(a) k = 3 (b) 0 ≤ k < 3
(c) k ≤ 4 (d) k = 0
77. If p, q, r are positive integers and ω is the cube root
of unity and f(x) = x3p + x3q+2 + x3r+2, then what is
f(ω) equal to ?
(a) ω
(b) – ω2 (c) – ω
(d) 0
78. What is the maximum value of 3 cos x + 4 sin x + 5?
(a) 5
(b) 7
(c) 10
(d) 12
79. If sin  = cos2 , then what is cos2  (1 + cos2 )
equal to ?
(a) I
(b) 0
(c) cos2 
(d) 2 sin 
80. What is the equation of the plane passing through
the point (1, –l, –1) and perpendicular to each of the
planes x – 2y – 8z – 0 and 2x + 5y – z = 0 ?
(a) 7x – 3y + 2z = 14
(b) 2x + 5y – 3z = 12
(c) x – 7y + 3z = 4
(d) 14x – 5y + 3z = 16
81. What is the value of tan 15°  tan 195° ?
(a) 7 – 4√3
(b) 7 + 4√3
(c) 7 + 2√3
(d) 7 + 6√3
76.
ORC CADEMY
If z =
1 +2i
2-i
2-i
– 1 + 2i, then what is the value of
z2 + zz ? (i = √-1)
88.
89.
(a) 0
(b) –1
(c) 1
(d) 8
What is the argument of (I – sin ) + i cos  ?
(i = √−1)
 
 
 
 
(a) –
(b) +
(c) –
(d) +
2 2
2 2
4 2
2 2
What is the area bounded .by the curve
√𝑥 +√𝑦 = √𝑎, (x, y ≥ 0) and the coordinate axes ?
5𝑎2
90.
91.
92.
𝑎2
𝑎2
𝑎2
(a) 6
(b) 3
(c) 2
(d) 6
Consider the following statements in respect of the
square matrices A and B of same order :
1. A and B are non-zero and AB = 0 ⇒ either
| A | = 0 or | B | = 0
2. AB – 0 ⇒ A = 0 or B = 0
Which of the above statements is/are correct ?
(a) 1 only
(b) 2 only
(c) Both 1 and 2 (d) Neither 1 nor 2
For what value of k, are the lines x + 2y – 9 = 0 and
kx + 4y + 5 = 0 parallel ?
(a) 2
(b) –1
(c) 1
(d) 0
What are the points on the curve x2 + y2 – 2x – 3 = 0
where the tangents are parallel to x-axis ?
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
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NDA (SEP 2011) MATHEMATICS
93.
94.
95.
96.
97.
98.
(a) (1, 2) and (1, –2)
(b) (0, √3) and (0, –√3)
(c) (3, 0) and (–3, 0)
(d) (2, 1) and (2, –1)
If sin 3A = 1, then how many distinct values can sin
A assume ?
(a) 1
(b) 2
(c) 3
(d) 4
What is the radius of the circle touching x-axis at
(3, 0) and y-axis at (0, 3) ?
(a) 3 units (b) 4 units (c) 5 units (d) 6 units
For all n  N, 24n – 15n–1 is divisible by
(a) 125
(b) 225
(c) 450
(d) None of the above
If the roots of the equation xz – 4x – log3 N = 0 are
real, then what is the minimum value of N ?
(a) 1/256
(b) 1/27
(c) 1/64
(d) 1/81
The equation to sphere passing through origin and
the points (–1, 0, 0), (0, –2, 0) and (0, 0, –3) is
x2 + y2 + z2 + f(x, y, z) = 0. What is f(x, y, z) equal to?
(a) –x – 2y – 3z
(b) x + 2y + 3z
(c) x + 2y + 3z – 1
(d) x – 2y + 3z + 1
What is the area of the triangle with vertices
(1, 2, 3), (2, 5, –1) and (–1, 1, 2) ?
(a)
√155
2
√155
4
square units
(b)
√175
2
√175
4
square units
(c)
square units
(d)
square units
99. For what value of x does
1 3 0 0
(1 3 2) (3 0 2) (3) = (0) hold ?
2 0 1 𝑥
(a) –1
(b) 1
(c) 9/8
(d) –9/8
100. If one of the roots of the equation
a(b – c)x2 + b(c – a)x + c(a – b) = 0 is 1, what is the
second root ?
𝑏(𝑐−𝑎)
𝑏(𝑐 − 𝑎)
(a) – 𝑎(𝑏−𝑐)
(b) 𝑎(𝑏 − 𝑐)
𝑐(𝑎−𝑏)
(c) 𝑎(𝑏−𝑐)
𝑏(𝑎 − 𝑏)
(d) – 𝑎(𝑏 − 𝑐)
101. What are the roots of the equation
2(y + 2)2 – 5(y + 2) = 12 ? .
(a) –7/2, 2
(b) – 3/2, 4
(c) – 5/3, 3
(d) 3/2, 4
102. What is the value of log2 (log3 81) ?
(a) 2
(b) 3
(c) 4
(d) 9
2
103. If the roots of the equation 3x – 5x + q = 0 are
equal, then what is the value of q ?
(a) 2
(b) 5/12
(c) 12/25
(d) 25/12
104. If  is a null set, then which one of the following is
correct ?
(a)  = 0
(b)  = { 0 }
(c)  = {  }
(d)  = {  }
105. What is the equation of a line parallel to x-axis at a
distance of 5 units below x-axis ?
(a) x = 5 (b) x = –5
(c) y = 5
(d) y = –5
ORC CADEMY
NOTE : STUDY THE FOLLOWING TABLE AND
ANSWER THE NEXT 08 (EIGHT) QUESTIONS
THAT FOLLOW :
Year
Male
Female
Total
14. Urban 15.
Rural Total Urban Rural Total
1995 280 16.
350
310
1350
1996 370 17.
670 180
450
1997
18.
130 440
190
1998 400 19.
280
290
Total
20.
1060 850
106. What is the total population in the year 1997 ?
(a) 810
(b) 830
(c) 970
(d) 1030
107. What is the female urban population in the year
1995 ?
(a) 390
(b) 410
(c) 430
(d) 470
108. What is the urban population in the year 1997 ?
(a) 400
(b) 460
(c) 490
(d) 510
109. What is the total population for the year 1998 ?
(a) 1000
(b) 1020
(c) 1040
(d) 1050
110. What is the difference between the number of
females and the number of males in the year 1995 ?
(a) 90
(b) 100
(c) 110
(d) 120
111. In which year is the male population minimum ?
(a) 1995 (b) 1996
(c) 1997 (d) 1998
112. In which year is the female population maximum ?
(a) 1995
(b) 1996
(c) 1997
(d) 1998
113. What is the percentage of rural male population
(over the whole population) in the year 1998 ?
80
100
(a) %
(b)
%
(c) 35 % (d) 40%
3
3
NOTE : STUDY THE PIE CHART GIVEN BELOW
AND ANSWER THE NEXT 04 (FOUR) QUESTIONS
THAT FOLLOW :
The following pie chart gives the distribution of funds in a
five year plan under the major heads of development
expenditures :
Agriculture (A), Industry (B), Education (C),
Employment (D) and Miscellaneous (E).
The total allocation is 36,000 (in crores of rupees),
114. Which head is allocated maximum funds ?
(a) Agriculture (b) Industry
(c) Employment (d) Miscellaneous
115. How much money (in crores) is allocated to
Education ?
(a) 3000
(b) 6000
(c) 9000
(d) 10800
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
Page 5
NDA (SEP 2011) MATHEMATICS
ORC CADEMY
116. How much money (in crores) is allocated to both
Agriculture and Employment?
(a) 20000
(b) 21000 (c) 24000
(d) 27000
117. How much excess money (in crores) is allocated to
Miscellaneous over Education ?
(a) 3600 (b) 4200 (c) 4500
(d) 4800
118. What is the geometric mean of 10, 40 and 60 ?
(a) 10
(b) 20
(c) 40
(d) 70
119. What is the median of the distribution 3, 7, 6, 9, 5, 4, 2 ?
(a) 5
(b) 6
(c) 7
(d) 8
120. If the arithmetic and geometric means of two
numbers are 10, 8 respectively, then one number
exceeds the other number by
(a) 8
(b) 10
(c) 12
(d) 16
SCO-371-373, 4TH FLOOR, SEC-34/A, CHD. CONTACT – 78140-11022, 78143-11022
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