NET
Mathematics MCQs
These 100 MCQs which will give you a good idea of how to take entry test.Mathematics is most important portion in any engineering test.It holds special position in NET as it alone constitutes 80 out of 200 marks.
1) If a die
is rolled twice then what is the probability that the sum of the number of dots
shown is 8?
A. 5/36
(Correct)
B. 4/36
C. 1/12
D. 1/2
B. 4/36
C. 1/12
D. 1/2
2) What is
the sine inverse of sin(pi/2)?
A. 1
B. pi/2 radians
C. 90 degrees
A. 1
B. pi/2 radians
C. 90 degrees
D. Both B and
C (Correct)
3) What is
the derivative of the inverse cosecant function?
A. (1)/[x*sqrt(x^21)] (Correct)
B. (1)/[x*sqrt(x^2+1)]
C. 1/[x*sqrt(x^21)]
D. 1/sqrt(x^21)
A. (1)/[x*sqrt(x^21)] (Correct)
B. (1)/[x*sqrt(x^2+1)]
C. 1/[x*sqrt(x^21)]
D. 1/sqrt(x^21)
4) What is
the domain of the inverse cosecant function?
A. [1,1]
B. R
C. R(1,1) (Correct)
D. (1,1)
B. R
C. R(1,1) (Correct)
D. (1,1)
5) Evaluate:
[sin^1][3/4]+[sin^1][sqrt(7)/4]
A.
[cos^1](0)
B. [sin^1](1)
C. [tan^1](infinity)
D. All of these (Correct)
B. [sin^1](1)
C. [tan^1](infinity)
D. All of these (Correct)
6) How many
hours are there in 360 degrees?
A. 21600
A. 21600
B. 360
(Correct)
C. 60
D. 3.14
7) How many
terms are there in the expansion of (1+x)^n; considering that ‘n’ is positive?
A. n+1 (Correct)
B. n
C. Infinite
D. n1
A. n+1 (Correct)
B. n
C. Infinite
D. n1
8) What is
the derivative of 2t^3 with respect to 3t^2?
A. 2t^3
B. t (Correct)
C. t^2
D. 1/t
B. t (Correct)
C. t^2
D. 1/t
9) 1, 1/3,
1/5, 1/7... is a/an ________ sequence.
A. Fibonnaci
A. Fibonnaci
B. Harmonic
(Correct)
C. Geometric
D. Arithmetic
C. Geometric
D. Arithmetic
10) What is
the difference between the arithmetic mean and the geometric mean of 5 and 7?
A. 0.8
B. 0.08 (Correct)
C. 0.008
D. 0.0008
A. 0.8
B. 0.08 (Correct)
C. 0.008
D. 0.0008
11) What is
the real component of the complex number (4i)^2?
A. 8
B. 17
C. 15 (Correct)
D. Missing information
A. 8
B. 17
C. 15 (Correct)
D. Missing information
12) Which one
of the following properties of sets is said to be the commutative property?
A. AUB=BUA (Correct)
B. A=B
C. AU(BUC)=(AUB)UC
D. A’=UA
A. AUB=BUA (Correct)
B. A=B
C. AU(BUC)=(AUB)UC
D. A’=UA
13) If x^43x^2+4=0
then its roots are:
A. 2, 2, i and –i (Correct)
B. 1, 1, i and i
C. iota only
D. Impossible to determine
A. 2, 2, i and –i (Correct)
B. 1, 1, i and i
C. iota only
D. Impossible to determine
14) What are
the cube roots of unity?
A. 1, 1, i and i
B. 1, 1 and i
C. There doesn’t exist such entities in mathematics
D. 1, [1+sqrt(3)*i]/2 and [1sqrt(3)*i]/2 (Correct)
A. 1, 1, i and i
B. 1, 1 and i
C. There doesn’t exist such entities in mathematics
D. 1, [1+sqrt(3)*i]/2 and [1sqrt(3)*i]/2 (Correct)
15) If
4x/(x1)(x+1)=A/(x1)+B/(x+1) then the values of ‘A’ and ‘B’ are:
A. 2 and 2 (Correct)
A. 2 and 2 (Correct)
B. 2 and 2
C. 1 and 1
D. Impossible to determine
C. 1 and 1
D. Impossible to determine
16) What is
the nth term of the sequence: 1, 3, 5, 7…?
A. 2n1 (Correct)
A. 2n1 (Correct)
B. 2n+3
C. 2n
D. It is
impossible to find the nth term for such a sequence
17) What are
the two numbers whose sum is 20 but their product is minimum?
A. 10, 10
B. 15, 5
C. 0, 20 (Correct)
D. 1, 19
B. 15, 5
C. 0, 20 (Correct)
D. 1, 19
18) The set
of points P(x,y) in which x and y both are less than zero, lie in which quadrant?
A. I
A. I
B. II
C. III
(Correct)
D. IV
19) What is
the same as sin(a)?
A. –sin(a)
B. sin(a)
C. –tan(a)/sec(a)
D. Both A and C (Correct)
A. –sin(a)
B. sin(a)
C. –tan(a)/sec(a)
D. Both A and C (Correct)
20) What is
the domain of the function f(x)=1/sqrt(x^2+3x+2)?
A. (1,+infinity)U(2, +infinity) (Correct)
A. (1,+infinity)U(2, +infinity) (Correct)
B. (1,2)
C. Set of
real numbers
D.
(infinity, +infinity)
21) If
f(x)=x^3, then what is its inverse?
A. x^(1/3)
A. x^(1/3)
B. 3^x
C.
[x^(2/3)]^0.5
D. Both A and
C (Correct)
22) If in a
triangle, a=200, b=120 and γ=150 degrees, then what is the area of the
triangle?
A. 10932
B. Impossible
to determine
C. 7050
D. 6000
(Correct)
23) Use
analytical geometry to determine to classify the quadrilateral ABCD with
vertices A(1,0), B(3,3), C(6,1), and D(2,4).
A.
Parallelogram
C. Rhombus
D. Trapezium
24) Tell the
relationship between x and y.
x

0

1

2

3

4

5

6

7

8

y

Undefined

0

0.693

1.099

1.386

1.609

1.792

1.946

2.079

A. y=ln x
(Correct)
B. y=log x
C. y=1/x
D. y=e^x
25) The
feasible solution which maximizes or minimizes the objective function is
called:
A. Optimal
solution (Correct)
B. Feasible
solution
C. Linear
solution
D. Quintic
solution
26) Evaluate:
(sin(θ)1)^2+(sin(θ)+1)^2
A.
2[1+[sin^2](θ)] (Correct)
B.
1+[sin^2](θ)
C. 1
D.
2+(sin^2)(θ)
27) If one of
the lengths of the sides of an equilateral triangle is 10, then what is the
area of the triangle?
A. 25*sqrt(3)
B. 43.30
C. Both A and
B (Correct)
D. Missing
information
28) Iota
expressed in the form of coordinates is:
A. (0,1)
(Correct)
B. (1,0)
C. (0,0)
D. It is
impossible to express a complex number in the form of coordinates
29) What is
the sum of angles in a quadrilateral?
A. 120
B. 180
C. 270
D. 360
(Correct)
30) What is the
power of fourth power of ‘x’ in the sixth power of (2x)?
A. 24
(Correct)
B. 10
C. 6/4
D. 2
31) What is
the sum of the first 50 real numbers?
A. 500
B. 1275
(Correct)
C. 1200
D. 8900
32) Orders of
some matrices are given in the following. Which one of them cannot be
multiplied?
A. mxn, nxp
where m, n and p are all positive integers
B. axb, bxc
where a, b and c are all positive integers
C. 1x2, 2x6
D. 3x5, 4x1
(Correct)
33) sin
(pi/3) is equal to?
A. 0.866
(Correct)
B. 0.500
C. 0.707
D. 0.966
34) What is
the formula for tan θ?
A. sin θ/cos
θ
B. 1/cot θ
C. tan(180+ θ)
D. All of
these (Correct)
35) What is
the formula for cos 2θ?
A.
[1[tan^2](θ)]/[1+[tan^2](θ)]
B. 12sin^2(θ)
C. Both A and
B (Correct)
D. None of
these
36) Evaluate:
cos θ+tan θ*sin θ
A. sec θ
B. 1/cos θ
C. sqrt[1sin^2(θ)]
D. All of
these (Correct)
37) Solve:
(22/7)*sqrt(3)
A. 5.44
(Correct)
B. 5.20
C. 5.85
D. 5.69
38) What is
the cosine inverse of cos(0.5)?
A. 1/6
B. 1/2
(Correct)
C. 1/3
D. 1/4
39) Probability
of any event cannot have the value of:
A. 1/5
B. 1/8
C. 1/2
D. 3/2
(Correct)
40) If
A={1,2,3}, B={0,4,5} and U={0,3,6}, then find n(AUB).
A. 64
(Correct)
B. 8
C. 16
D. 32
41) When both
nappes of a doublenapped cone are intersected by a plane (not passing through
the vertex), the cross section produces a/an:
A. Hyperbola
(Correct)
C. Ellipse
D. Parabola
42) Find the
value of cos[(tan^1)(1)].
A. 0.766
B. 0.707
(Correct)
C. 0.500
D. 0.087
43) Evaluate:
tan (θ/2)
A.
sqrt[(1cos θ)/(1+cos θ)]
B. 1/cot
(θ/2)
C. tan(180+θ/2)
D. All of
these (Correct)
44) Evaluate:
[tan^1][1/sqrt(3)]
A. pi/6
radians
B. pi/3
radians
C. 13pi/6
radians
D. Both A and
C (Correct)
45) Find the
distance AB between the two points: A(3,1) and B(2,4).
A. sqrt(50)
(Correct)
B. sqrt(26)
C. sqrt(34)
D. sqrt(10)
46) What are
three AMs between 18 and 4?
A. 12.5, 7 and 1.5
A. 12.5, 7 and 1.5
B. AM can’t
be found between a negative and a positive number
C. 12.5, 7
and 1.5 (Correct)
D. 1, 2 and 3
47) Find the
sum: 1+3+5…+(2n+1)
A. n^2
(Correct)
B. ln e^2
C. 2^n
D. n^e
48) What is
the domain of tan x?
A. R –
(2n+1)(pi/2) where ‘n’ cannot be zero
B. R –
(2n+1)(pi/2) where ‘n’ can be zero (Correct)
C. R – n(pi)
where ‘n’ cannot be zero
D. R
49) Which one
of the following pairs has the same period?
A. Tangent
function and cotangent function (Correct)
B. Sine
function and tangent function
C. Cosine
function and cotangent function
D. Cosecant
function and tangent function
50) 30
degrees, 45 minutes and 47 seconds are equal to _____ degrees:
A. 30.56
B. 30.66
C. 30.67
D. 30.86
(Correct)
51) Tickets
numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the
probability that the ticket drawn has a number which is a multiple of 3 or 5?
A. 1/2
B. 2/5
C. 8/15
D. 9/20
(Correct)
52) If α and
β are the roots of the equation x^2x+1=0, then find 2α and 2β.
A.
1+sqrt(3)*i, 1sqrt(3)*i (Correct)
B. only i
C. Impossible
to determine
D. i and i
53) If
A={a,b,c} then the number of possible subsets is:
A. 3
B. 8
(Correct)
C. 6
D. None of
these
54) How many
6digit numbers can be formed without repeating any digit from the digits 0, 1,
2, 3, 4 and 5?
A. 120
B. 720
(Correct)
C. 96
D. 4920
55) If a
parabola has an equation of y^2=4x, then find its focus.
A. (1,0)
(Correct)
B. (0,1)
C. (4,0)
D. (0,4)
56) Any line
parallel to xaxis has a slope of:
A. 0 (Correct)
A. 0 (Correct)
B. infinity
C. 1
D. 1
57) The
product of all the three cube roots of unity is:
A. 1
(Correct)
B. 1
C.
1+sqrt(3)*i
D. 0
58) 2/3 is
a/an ________ number.
A. Irrational
B. Rational
C. Positive
D. Both B and
C (Correct)
59) How many
radians are there in a degree?
A. 0.07145
(Correct)
B. 0.06250
C. 0.06145
D. 0.07135
60) Which one
of the following things a hyperbola has?
A. One focus and
two directrices
B. Two foci
and two directrices (Correct)
C. Two foci
and one directrix
D. None of
these
61) A line
segment that touches two points on the outside of the circle but doesn't pass
through the center is called:
A. Chord
(Correct)
B. Diameter
C. Radius
D. None of
these
62) In a
rightangled triangle, if a median drawn from the right angle to the hypotenuse
has a length of 6 meters, then what is the length of the hypotenuse?
A. 12 meters
(Correct)
B. 6 meters
C. 3 meters
D. 36 meters
63) If we
have a function f(x,y)=c, then we differentiate it using the method of:
A. Chain Rule
B. Implicit differentiation (Correct)
A. Chain Rule
B. Implicit differentiation (Correct)
C. Product
Rule
D. Newton ’s method
64) The sum
of coefficients in the expansion of (x+y)^5 is:
A. 128
B. 64
C. 32
(Correct)
D. 16
65) If the
sum of two consecutive integers is ‘x’, then what is the product of them?
A. (x^21)/4
(Correct)
B. (x^21)/2
C. x^21
D. None of
these
66) What
fraction is the result of the sum of the series: 0.2+0.02+0.002…
A. 1/3
B. 1/6
C. 2/9
(Correct)
D. 1/7
67)
Differentiate ‘sin 2x’ with respect to x.
A. 2cos 2x
B. 2sin 2x
C.
2[12[sin^2](x)]
D. Both A and
C (Correct)
68) Men and
women are in a ratio of P:Q. What is the percentage of men?
A. P/P+Q
(Correct)
B. Q/P+Q
C. 100/P+Q
D. 50/50
69) Which of
the following is the biggest number?
A. 1
B. 2*sqrt(2)
C. 3*sqrt(3)
D. 4*sqrt(4)
(Correct)
70) What is
the geometric mean of 32 and 64?
A. 32*sqrt(2)
B.
sqrt(32*64)
C. Geometric
mean of positive numbers isn’t possible to determine
D. Both A and
B (Correct)
71) Differentiate
ln (e) with respect to ‘x’.
A. 1/e
B. 0
(Correct)
C. 1/x
D. e
72) Evaluate:
cos x * sin x * tan x * cot x * csc x
A. cos x
B. 1/sec x
C. Both A and
B (Correct)
D. sin x
73) Evaluate:
w^23+w^28
A. 1
(Correct)
B. 1
C. w
D. w^2
74) The
derivate of f(x) with respect to ‘x’ is defined as:
A. The rate
of change in f(x) with respect to ‘x’ (Correct)
B. The
increase in the relevance rate of f(x) with respect to ‘x’
C. The
decrease in the relevance rate of f(x) with respect to ‘x’
D. None of
these
75) Which one
of the following is the additive inverse for 2+sqrt(3)?
A. sqrt(3)
B. 2+sqrt(3)
C. 2sqrt(3)
(Correct)
D. 2+sqrt(3)
76) What are
the angles of an equilateral triangle?
A. 45
degrees, 45 degrees and 90 degrees
B. 45
degrees, 90 degrees and 45 degrees
C. 120
degrees, 30 degrees and 30 degrees
D. 60
degrees, 60 degrees and 60 degrees (Correct)
77) If a
square has a side of 2 units, then what is the length of its diagonal?
A. 2*sqrt(2)
(Correct)
B. 8
C. 4
D. 16
78) In an
ellipse, what is the name for the line through the focus and perpendicular to
the major axis ending at the ellipse?
A. Focal
chord
B. Minor axis
B. Minor axis
C. Latus
rectum (Correct)
D. Vertical
asymptote
79) The
length of all the sides of a square and an equilateral triangle is 5 units.
What is the ratio of the area of the square to the area of the triangle?
A. 8/sqrt(3)
B.
[8*sqrt(3)]/5
C. 4/sqrt(3)
(Correct)
D. sqrt(3)/8
80) Two
figures having the same shape but different sizes are called:
A. Congruent
figures
B. Similar figures
(Correct)
C. Equal
figures
D. All of
these
81) Evaluate:
cos(θ)*cos(θ)*[cos(θ)]*cos(θ)*[cos(θ)]
A. [cos^5](θ)
(Correct)
B.
[cos^5](θ)
C. [cos^3](θ)
D. cos (θ)
82) Evaluate:
[sin^1][3/5]
A.
[cos^1][4/5]
B.
[sec^1][5/4]
C.
[csc^1][5/3]
D. All of
these (Correct)
83) What is
the period of sin 3x?
A. (2*pi)/3 (Correct)
B. 2*pi
C. 3*pi
D. (3*pi)/2
84) What is
the formula of cos 3α?
A. cos 2α*cos
α
B.
4[cos^3](α)3cos α (Correct)
C. (1+cos α)/sin
α
D. Both A and C
D. Both A and C
85) Differentiate
3^2x with respect to ‘x’.
A. 2*ln
2*(3^2x) (Correct)
B. ln
2*(3^2x)
C. 3^2x
D. 2x/3
86) Find the
integral with respect to x: e^x/(e^x+1)
A. ln
e^x+1+c (Correct)
B. ln e^x+c
C. Impossible
to determine
D. e^x+c
87) If two
coordinates of a rectangle are present in the first quadrant, then which one of
the following coordinates is NOT to be of that rectangle?
A. (2, 8)
B. (2, 8)
C. (8, 2)
D. (2, 8)
(Correct)
88) Calculate
the exact value of the decimal 0.4545…
A. 5/11
(Correct)
B. 50/11
C. 500/11
D. 5000/11
89) What is
the cosine inverse of cos(1/2)?
A. 1/2
(Correct)
B. 1/2
C. 1/4
D. (2*pi)/3
radians
90) An
equation of a parabola is (x2)^2=4(y+2), then its vertex is:
A. (2, 2)
(Correct)
B. (2, 2)
C. (0, 0)
D. Missing information
D. Missing information
91) If ‘x’ is
real, then which one of the following is an odd function?
A. –sin (x)
(Correct)
B. –cos (x)
C. x
D.
(e^x1)/(e^x1)
92) If cos θ
= 1, then what is the possible value of θ?
A. 0 degrees
B. 360
degrees
C. 720
degrees
D. All of
these are possible (Correct)
93) If an
equation of hyperbola is: x^2/4y^2/9=1, then find its eccentricity.
A. sqrt(13)/4
(Correct)
B. 9/4
C. sqrt(5)/4
D.
sqrt(9)*sqrt(5)
94) Every
homogenous second degree equation ax^2+2hxy+by^2 represents a pair of lines
through the origin. When are these lines coincident?
A. (a*b) <
h^2
B. h^2 = 0
C. h^2 <
(a*b)
D. h^2 = a*b
(Correct)
95) Which one
of the following is the real part of the complex number: 6(23i)?
A. 2
B. 12
(Correct)
C. 3
D. 6
96) Simplify:
(1+tan x)/(1tan x)
A. tan(45+x)
(Correct)
B. Can’t be
further simplified
C. tan(45x)
D. tan(x+1)
97) If in a
triangle, α=49 degrees, b=5 inches and c=7 inches, then what is the length of
‘a’?
A. 5.29
(Correct)
B. 7.31
C. 12.07
D. 9.65
98) The
equation which doesn’t change by replacing ‘x’ with ‘1/x’ is called:
A. Linear
B. Quadratic
C.
Proportional
D. None of
these (Correct)
99) Differentiate
tan[sqrt(x)] with respect to ‘x’.
A.
[sec^2][x]/[2sqrt(x)]
B.
[sec^2][sqrt(x)]/[2sqrt(x)]
C.
[sec^2][sqrt(x)]/[2sqrt(x)] (Correct)
D. None of
these
100) Which
one of the following is the same as sin (75)?
A.
[sqrt(3)+1]/sqrt(8) (Correct)
B. It is
impossible to determine
C.
[sqrt(3)1]/sqrt(8)
D.
[sqrt(3)+1]/8
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