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This mock test of Test: Basic Concepts Of Differential And Integral Calculus- 2 for CA Foundation helps you for every CA Foundation entrance exam.
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QUESTION: 1

then y y_{1} (where y_{1} = dy/dx) is equal to

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QUESTION: 2

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QUESTION: 3

The derivative of (x^{2}–1)/x is

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QUESTION: 4

The differential coefficients of (x^{2} +1)/x is

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QUESTION: 5

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QUESTION: 6

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QUESTION: 7

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

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QUESTION: 8

f(x) = x^{2}/e^{x} 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 ∫ 5x^{2} dx and the answer will be

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QUESTION: 12

Integration of 3 – 2x – x^{4} will become

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QUESTION: 13

Given f(x) = 4x^{3} + 3x^{2} – 2x + 5, ∫ f(x) dx is

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QUESTION: 14

Evaluate ∫ (x 2 -1) 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 px^{3} + qx^{2} + 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 (x^{2} + 4)^{5}dx 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

∫ 8x^{2}/ (x^{3} + 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/x^{2} – a^{2} and the answer is

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QUESTION: 23

Use integration by parts to evaluate ∫ x^{2} e^{3x }dx and the answer is

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QUESTION: 24

∫ logx dx is equal to

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QUESTION: 25

∫ x e^{x} 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

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QUESTION: 32

then ∫ f(x)dx is

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QUESTION: 33

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QUESTION: 34

∫ (e^{x} – e^{–x})2 (e^{x} – e^{–x}) dx is

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QUESTION: 35

^{a}∫_{0} [ f(x) + f(–x) ] dx is equal to

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QUESTION: 36

∫ xe^{x}/(x + 1)^{2} dx is equal to

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QUESTION: 37

∫ (x^{4} + 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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