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ECAT Mathematics Chapter 18 Basic Concepts & Definitions Online Test MCQs With Answers
Question # 1
If x =1 -t
2
and y =3t
2
- 2t
3
then dy/dx =
Choose an answer
(1-t)
3(1+t)
3(t-1)
3/1-t
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Question # 2
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Question # 3
Choose an answer
zero at x
differentiable at x
continuous at x
none of these
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Question # 4
d/dx [tan
2
x]
Choose an answer
2tan x sec
2
x
2tan x sec x
2 cot x tan x
2sec
2
x cos
2
x
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Question # 5
d / dx (cot x) =
Choose an answer
Sec x tan x
-csc
2
x
Sec
2
x
1/cot
2
x
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Question # 6
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Question # 7
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1
0
cx
c
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Question # 8
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Question # 9
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Question # 10
d/dx(x
3
+ 2x +3)=
Choose an answer
x
2
+ 2
3x + 2
3x
2
+ 5
3x2 + 2
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Question # 11
If ∱(x) = x
2/3
then∱
1
(x) at x = 8 equals:
Choose an answer
8
1/8
1/3
2/3
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Question # 12
If∱(x) = 2x
3
+ 1 then∱
1
(0) =
Choose an answer
0
1
6
None of these
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Question # 13
d/dx (cos x sin x) =
Choose an answer
cos
2
x - sin
2
x
2cos
2
x + sin
2
x
2cos
2
x - sin
2
x
1 - sin
2
x
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Question # 14
if x∈ D∱ and∱
1
(x) exists, then
∱ is said to be
Choose an answer
zero at x
Differentiable at x
Continuous at x
None of these
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Question # 15
If c is a constant, then d/dx (c) =
Choose an answer
0
c
cx
1
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Question # 16
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Question # 17
The derivative of 1/x
m
is:
Choose an answer
x
m+1
/ m
m(x)
m-1
(m-1) x
-m
m/x
m+1
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Question # 18
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Question # 19
If y = 3 x + 2cos x, then dy/dx =
Choose an answer
3-2 sin x
3-t sin x
3x
2
- 2sin x
3(1-4 sin x)
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Question # 20
Choose an answer
x
n-1
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Question # 21
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Question # 22
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Question # 23
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Question # 24
Choose an answer
8
1/8
1/3
2/3
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Question # 25
If x
2
+ y
2
= 1, then dy/dx
Choose an answer
y/x
-x/y
1/x
None of these
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Question # 26
Choose an answer
-2x
x
-3
-2x
3
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Question # 27
Let∫ be real valued function continuous in the interval (x,x
1
)⊆ D∫ (the domain of∫),
then∱(x
1
) -∱ (x)/x
1
-x represents:
Choose an answer
Instantaneous rate
Average rate of change
Differential coefficient
None of these
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Question # 28
If y = 1/x
2
then dy/dx equals:
Choose an answer
-2x
x
-3
-2/x
3
-2x
3
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Question # 29
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Question # 30
If∱(x) = x
-100
the value of∱
1
(1) is:
Choose an answer
100
-100
0
-101
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