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Mathematics ECAT Pre Engineering Chapter 18 Basic Concepts & Definitions Online Test MCQs With Answers
Question # 1
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 # 2
If y = (7x + 9)
2
, then dy/dx equals:
Choose an answer
98x +126
14x
14x +18
14x+81
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Question # 3
If 3x + 4y +7 = 0 , then dy / dx =
Choose an answer
-1/2
-4/3
7/2
-3/4
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Question # 4
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 # 5
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Question # 6
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Question # 7
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Question # 8
Choose an answer
None of these
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Question # 9
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Question # 10
Choose an answer
x
2
+ 2
3x + 2
3x
2
+ 5
3x
2
+ 2
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Question # 11
Choose an answer
1
0
cx
c
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Question # 12
Differentiation of sin x w.r.t. cot x is:
Choose an answer
-sin
2
x sec x
-cos x sin
2
x
-cos
2
x tan x
-sin
2
x
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Question # 13
If y=x
m
then dy/dx equals:
Choose an answer
mx
x/m
mx
m-1
xm
m-1
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Question # 14
d/dx (cosec x)
Choose an answer
-sec x tan x
sin x cos x
-csc x cot x
2sin x cos x
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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
If∱(x) = 2x
3
+ 1 then∱
1
(0) =
Choose an answer
0
1
6
None of these
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Question # 18
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 # 19
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Question # 20
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 # 21
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Question # 22
The derivative of√x at x =a is:
Choose an answer
1/2a
2 / √a
2√x
1 / 2√x
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Question # 23
If∱(x) = x
5
+ x
3
+ x the value of∱
1
(1) is:
Choose an answer
0
8
5
9
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Question # 24
∱(x) = ax
2
-3x -5, and∱
1
(2) = 9, a is equal to
Choose an answer
2
3
-2
4
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Question # 25
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Question # 26
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 # 27
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Question # 28
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Question # 29
If y = x
n
then dy/dx equals:
Choose an answer
nx
x
n-1
nx
n-1
n
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Question # 30
if y=x
2
then dy/dx equals:
Choose an answer
2x
x/2
2x
3
x
3
/2
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Question # 31
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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