# Test: Basic Concepts Of Differential And Integral Calculus- 2

## 40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Basic Concepts Of Differential And Integral Calculus- 2

Description
Attempt Test: Basic Concepts Of Differential And Integral Calculus- 2 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions
QUESTION: 1

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QUESTION: 2
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QUESTION: 3

### The derivative of (x2–1)/x is

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QUESTION: 4

The differential coefficients of (x2 +1)/x is

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QUESTION: 5

If y = then  is equal to _____.

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QUESTION: 6

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QUESTION: 7

If x = (1 – t2 )/(1 + t2) y = 2t/(1 + t2) then dy/dx at t =1 is _____________.

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QUESTION: 8

f(x) = x2/ex then f ’(1) is equal to _____________.

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QUESTION: 9

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QUESTION: 10

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QUESTION: 11

Evaluate ∫ 5x2 dx  and the answer will be

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QUESTION: 12

Integration of 3 – 2x – x4 will become

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QUESTION: 13

Given f(x) = 4x3 + 3x2 – 2x + 5, ∫ f(x) dx   is

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QUESTION: 14

Evaluate ∫ () dx . The value is

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QUESTION: 15

∫ (1 - 3x) (1 + x) dx is equal to

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QUESTION: 16

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QUESTION: 17

The integral of px3 + qx2 + rk + w/x is equal to

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QUESTION: 18

Use method of substitution to integrate the function f(x) = (4x + 5)6 and the answer is

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QUESTION: 19

Use method of substitution to evaluate ∫ x (x2 + 4)5dx and the answer is

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QUESTION: 20

Integrate (x + a)n and the result will be

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QUESTION: 21

∫ 8x2/ (x3 + 2)3 dx is equal to

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QUESTION: 22

Using method of partial fraction find the integration of f(x) when f(x) = 1/x2 – a2 and the answer is

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QUESTION: 23

Use integration by parts to evaluate ∫ x2 e3x dx and the answer is

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QUESTION: 24

​∫ logx dx is equal to

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QUESTION: 25

∫ x ex dx is

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QUESTION: 26

∫ (logx)2 dx and the result is

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QUESTION: 27

Using method of partial fraction to evaluate ∫ (x + 5) dx/(x + 1) (x + 2)2 and the final answer becomes

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QUESTION: 28

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QUESTION: 29

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QUESTION: 30

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QUESTION: 31

Solution:

Let x
x = t. Then,d(xx) = dt
d(exlogx) = dt
exlogx (logx+1)dx = dt
xx(1+logx)dx=dt
Therefore, I = ∫xx(1+logx) dx
I= ∫dt = t+C = x+ C

QUESTION: 32

then ∫ f(x)dx is

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QUESTION: 33

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QUESTION: 34

∫ (ex – e–x)2 (ex – e–x) dx is

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QUESTION: 35

a0 [ f(x) + f(–x) ] dx is equal to

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QUESTION: 36

∫ xex/(x + 1)2 dx is equal to

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QUESTION: 37

∫ (x4 + 3/x ) dx is equal to

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QUESTION: 38

Evaluate the integral ∫ (1 − x)3/ x dx and the answer is equal to

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QUESTION: 39

The equation of the curve in the form y = f(x) if the curve passes through the point (1, 0) and f’(x) = 2x – 1 is

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QUESTION: 40

Evaluate  dx and the value is

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