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QUESTION: 1

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

The gradient of the curve y = 2x^{3} –3x^{2} – 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 = 2x^{3} –5x^{2} – 3x at x = 0 is

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QUESTION: 3

The derivative of y =

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QUESTION: 4

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QUESTION: 5

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QUESTION: 6

If y = x (x –1) (x – 2) then is

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QUESTION: 7

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

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QUESTION: 8

The curve y^{2} = ux^{3} + v passes through the point P(2, 3) and = 4 at P. The values of u and v are

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QUESTION: 9

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

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QUESTION: 10

If xy = 1 then y^{2} + dy/dx is equal to

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QUESTION: 11

The derivative of the function

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QUESTION: 12

Given e^{-}^{xy} –4xy = 0, can be proved to be

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QUESTION: 13

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QUESTION: 14

If log (x / y) = x + y, may be found to be

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QUESTION: 15

If f(x, y) = x^{3 }+ y^{3} – 3axy = 0, can be found out as

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QUESTION: 16

Given x = at^{2}, y = 2at; is calculated as

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QUESTION: 17

Given x = 2t + 5, y = t^{2} – 2; is calculated as

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QUESTION: 18

If y =

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QUESTION: 19

If x = 3t^{2} –1, y = t^{3} –t, then is equal to

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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 = x^{2} –x at the point, where the line y = 2 cuts the curve in the Ist quadrant, is

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QUESTION: 22

For the curve x^{2} + y^{2} + 2gx + 2hy = 0, the value of at (0, 0) is

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QUESTION: 23

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QUESTION: 24

If x^{y}.y^{x} = M, M is constant then is equal to

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QUESTION: 25

Given x = t + t^{–1} and y = t – t^{–1} the value of at t = 2 is

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QUESTION: 26

If x^{3} –2x^{2 }y^{2} + 5x +y –5 =0 then at x = 1, y = 1 is equal to

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QUESTION: 27

The derivative of x^{2} log x is

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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) = 3x^{2}, 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) = x^{2} – 6x+8 then f ’(5) – f ’(8) is equal to

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QUESTION: 37

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QUESTION: 38

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QUESTION: 39

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QUESTION: 40

If f(x) = x^{k} and f’(1) = 10 the value of k is

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