If y = emsin-1x and 1 - x2dydx2&nbs

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If A = 110215121, then a11A21 + a12A22 + a13A23 is equal to

  • 1

  • 0

  • - 1

  • 2


2.

If Rolle's theorem for f(x) = exsinx - cosx is verified on π4, 5π4, then the value of c is

  • π3

  • π2

  • 3π4

  • π


3.

If 2tan-1cosx = tan-12cscx, then sinx + cosx is equal to

  • 22

  • 2

  • 12

  • 12


4.

The approximate value of f(x) = x3 + 5x2 - 7x + 9 at x = 1.1 is

  • 8.6

  • 8.5

  • 8.4

  • 8.3


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5.

The point on the curve 6y = x3 + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is

  • (4, 11)

  • (4, - 11)

  • (- 4, 11)

  • (- 4, - 11)


6.

If the function f(x) defined by

fx = xsin1x, for x  0k,            for x  = 0

is continuous at x = 0, then k is equal to

 

  • 0

  • 1

  • - 1

  • 12


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7.

If y = emsin-1x and 1 - x2dydx2 = Ay2, then A is equal to

  • m

  • - m

  • m2

  • - m2


C.

m2

Given, y = emsin-1x      ...iOn differentiating both sides w.r. t. x, we get       dydx = emsin-1xddxm sin-1x  dydx = emsin-1xm × 11 - x2 1 - x2dydx = my        from Eq. (i)On squaring both sides, we get                        1 - x2dydx2 = m2y2But it is given  1 - x2dydx2 = Ay2                                        A = m2


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8.

tan-13 - sec-1- 2csc-1- 2 + cos-1- 12 is equal to

  • 45

  • - 45

  • 35

  • 0


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9.

For what value of k, the function defined by

f(x) = log1 + 2xsinx°x2, for x  0k                             , for x = 0

is continuous at x = 0 ?

  • 2

  • 12

  • π90

  • 90π


10.

If log10x2 - y2x2 + y2 = 2, then dydx is equal to

  • - 99x101y

  • 99x101y

  • - 99y101x

  • 99y101x


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