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Mathematics ECAT Pre Engineering Online Test MCQs With Answers
Question # 1
Cos
-1
12/13 =
Choose an answer
tan
-1
3/5
cot
-1
13/12
Sec
-1
13/12
sin
-1
5/13
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Question # 2
If A and B are two matrices such that AB = B and BA = A then A2 + B2 =
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2 AB
2 BA
A + B
AB
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Question # 3
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0
undefined
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Question # 4
If S
r
denotes the sum of the first r terms of a G.P., then S
n
, S
2n
- S
n
, S
3n
- S
2n
are in
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A.P.
G.P.
H.P.
None of these
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Question # 5
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None of these
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Question # 6
The domain of the principle cos function is
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Question # 7
The eccentricity e of an ellipse is always
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Rational
Real
Irrational
Integer
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Question # 8
∀x,y,z ∈ R and z 0,then
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x > y ⇒ xz > yz
x<y ⇒ xz < yz
x < y ⇒ xz > yz
None of these
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Question # 9
A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is
Choose an answer
50
25
10
100
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Question # 10
Choose an answer
none of these
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Question # 11
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Question # 12
What is the period of tan 4/3 x =?
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π/4
4π/3
7π/4
3π/4
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Question # 13
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cos 2x
2 cos 2x
2 sin2x
-2 cos2x
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Question # 14
The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are
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Question # 15
The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if
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Question # 16
The factorial of a positive integers is a (an)
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Rational number
Positive integer
Real number
None
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Question # 17
The number of solution of the equation tan x + sec x = 2 cos x lying in the interval [0, 2
π
] is
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0
1
2
3
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Question # 18
If the vector 2i + 4j - 7k and 2i + 6j + xk are perpendicular then x = ?
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0
2
4
7
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Question # 19
Choose an answer
Hermitian matrix
Skew-hermitian matrix
Symmetric matrix
Identity matrix
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Question # 20
If E = { } , then P(E)
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∅
{ }
{(2),(4),(6)....}
(∅)
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Question # 21
Ifπ≤x≤2π, then cos-1 (cos x)=
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cos x
-x
1/x
-x
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Question # 22
The middle term(s) of (a+x)11 is
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6th term
6thor 7th
7th term
6thand7th
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Question # 23
Intersection of two parabolas
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parabola
Two points
Four points
Hyperobla
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Question # 24
Choose an answer
z is purely imaginary
a is any complex number
z is real
None of these
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Question # 25
x = 0 is in the solution of the inequality
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x > 0
3x + 4 < 0
x + 3 < 0
x - 2 < 0
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Question # 26
The sum of the cubes of three consecutive natural number is divisible by
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9
6
5
10
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Question # 27
Any whole number can be written as a product of factors which are
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Even number
Odd numbers
Prime number
Rational number
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Question # 28
Domain of sec x is ______
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Question # 29
The maximum value of the quadratic function f(x) = -2x2+20x,is
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4
3
50
7
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Question # 30
For a set A, A∪Ac= ---------------------
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A
∅
Ac
U
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Question # 31
If A⊆ B, and B is a finite set, then
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n (a) < n(B)
n(B)<(A)
n(A)≤ n (B)
n(A)≥ n(B)
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