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Test: Basic Concepts Of Differential And Integral Calculus- 1


40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Basic Concepts Of Differential And Integral Calculus- 1


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This mock test of Test: Basic Concepts Of Differential And Integral Calculus- 1 for CA Foundation helps you for every CA Foundation entrance exam. This contains 40 Multiple Choice Questions for CA Foundation Test: Basic Concepts Of Differential And Integral Calculus- 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Basic Concepts Of Differential And Integral Calculus- 1 quiz give you a good mix of easy questions and tough questions. CA Foundation students definitely take this Test: Basic Concepts Of Differential And Integral Calculus- 1 exercise for a better result in the exam. You can find other Test: Basic Concepts Of Differential And Integral Calculus- 1 extra questions, long questions & short questions for CA Foundation on EduRev as well by searching above.
QUESTION: 1

Choose the most appropriate option (a) (b) (c) or (d)

The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 is

Solution:

ANSWER :- a

Solution :- 2x^3 - 3x^2 -12x + 8 = 0 

dy/dx = 6x^2 - 6x -12 = 0

(At x=0) = 6(0)^2 - 6(0) - 12 

        = -12

QUESTION: 2

The gradient of the curve y = 2x3 –5x2 – 3x at x = 0 is

Solution:
QUESTION: 3

The derivative of y = 

Solution:
QUESTION: 4

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QUESTION: 5

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QUESTION: 6

If y = x (x –1) (x – 2) then  is
Solution:
QUESTION: 7

The gradient of the curve y – xy + 2px + 3qy = 0 at the point (3, 2 ) is and q are
Solution:



QUESTION: 8

The curve y2 = ux3 + v passes through the point P(2, 3) and  = 4 at P. The values of u and v are 
Solution:

QUESTION: 9

The gradient of the curve y + px +qy = 0 at (1, 1) is 1/2. The values of p and q are
Solution:

y+px+qy=0
y+qy=-px
(1+q)y=-px
y=-[p/(1+q)]x
This is a linear function, so has constant gradient at all points on the curve. Hence
-p/(1+q)=1/2
2p=-(1+q)
But there is an issue: you have stated that the curve's gradient is 1/2 at the point (1,1) but the curve does not cross through this point! Regardless of our choices for p and q satisfying the expressions above this paragraph, the equation of the curve will always simplify to y=0.5x, which crosses through the origin (0,0), as well as (1,0.5) and (2,1) - but not (-1,1).
For your curve to pass through (-1,1), we would need to add a constant term, like so:
y+px+qy=1/2
 

QUESTION: 10

If xy = 1 then y2 + dy/dx is equal to
Solution:
QUESTION: 11

The derivative of the function 
Solution:
QUESTION: 12

Given e-xy –4xy = 0,  can be proved to be
Solution:
QUESTION: 13

Solution:

QUESTION: 14

If log (x / y) = x + y,   may be found to be
Solution:
QUESTION: 15

If f(x, y) = x3 + y3 – 3axy = 0,  can be found out as
Solution:
QUESTION: 16

Given x = at2, y = 2at;  is calculated as
Solution:
QUESTION: 17

Given x = 2t + 5, y = t2 – 2;  is calculated as 
Solution:
QUESTION: 18

If y = 
Solution:
QUESTION: 19

If x = 3t2 –1, y = t3 –t, then   is equal to
Solution:
QUESTION: 20

The slope of the tangent to the curve y = at the point, where the ordinate and the abscissa are equal, is
Solution:

so the point is (√2,√2)

= -1

QUESTION: 21

The slope of the tangent to the curve y = x2 –x at the point, where the line y = 2 cuts the curve in the Ist quadrant, is
Solution:
QUESTION: 22

For the curve x2 + y2 + 2gx + 2hy = 0, the value of  at (0, 0) is
Solution:
QUESTION: 23

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QUESTION: 24

If xy.yx = M, M is constant then is equal to
Solution:
QUESTION: 25

Given x = t + t–1 and y = t – t–1 the value of  at t = 2 is
Solution:
QUESTION: 26

If x3 –2x2 y2 + 5x +y –5 =0 then  at x = 1, y = 1 is equal to
Solution:
QUESTION: 27

The derivative of x2 log x is
Solution:
QUESTION: 28

The derivative of 
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QUESTION: 29

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QUESTION: 30

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QUESTION: 31

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QUESTION: 32

If f(x) = 3x2, then F(x) = 
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QUESTION: 33

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QUESTION: 34

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QUESTION: 35

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QUESTION: 36

If f(x) = x2 – 6x+8 then f ’(5) – f ’(8) is equal to
Solution:
QUESTION: 37

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QUESTION: 38

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QUESTION: 39

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QUESTION: 40

If f(x) = xk and f’(1) = 10 the value of k is
Solution:

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