f(x) is a polynomial of degree 2, f(0) = 4, f (0) = 3 and f (0)

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

dxxx7 + 1 is equal to

  • logx7x7 + 1

  • 17logx7x7 + 1 + c

  • logx7 + 1x7 + c

  • 17logx7 +1x7


22.

The solution of the differential equation dxx + dyy = 0 is

  • xy = c

  • x + y = c

  • log(x)log(y) = c

  • x2 + y2 = c


23.

The differential equation obtained by eliminating arbitrary constants from y = a . ebx, is

  • yd2ydx2 + dydx = 0

  • yd2ydx2 - dydx = 0

  • yd2ydx2 - dydx2 = 0

  • yd2ydx2 + dydx2 = 0


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24.

f(x) is a polynomial of degree 2, f(0) = 4, f'(0) = 3 and f''(0) = 4, then f(- 1) is equal to

  • 3

  • - 2

  • 2

  • - 3


A.

3

Let the polynomial equation be

f(x) = ax2 + bx + c       ...(i)

f'(x) = 2ax + b

and f''(x) = 2a

Given, f(0) = 4, f'(0) = 3 and f''(0) = 4

     c = 4              ...(ii)

        b = 3              ...(iii)

and 2a = 4

    a = 2             ...(iv)

On putting these values in Eq. (i), we get

       f(x) = 2x2 + 3x + 4

 f(- 1) = 2(- 1)2 + 3(- 1) + 4

             = 2 - 3 + 4 = 3


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25.

Solution of differential equation sec(x)dy - cosec(y)dx = 0 is

  • cos(x) + sin(y) = c

  • sin(x) + cos(y) = 0

  • sin(y) - cos(x) = c

  • cos(y) - sin(x) = c


26.

The point P(9/2, 6) lies on the parabola y2 = 4ax, then parameter of the point P is

  • 3a2

  • 23a

  • 23

  • 32


27.

Using Trapezoidal rule and following table 08fxdx is equal to
x 0 0 4 6 8
f(x) 2 5 10 17 26

 

  • 184

  • 92

  • 46

  • - 36


28.

Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then a . b  + b . c + c . a is

  • 47

  • 25

  • 50

  • - 25


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29.

Unbiased die is thrown, probability that outcome is greater than 4, is

  • 3/4

  • 4/5

  • 1/3

  • 5/6


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