At the point x = 1, the functionfx = x3 - 1,&

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The multiplicative inverse of A = cosθ- sinθsinθcosθ is

  • - cosθsinθ- sinθ- cosθ

  • cosθsinθ- sinθcosθ

  • - cosθ- sinθsinθ- cosθ

  • cosθsinθsinθ- cosθ


2.

The value of 'a' for which the system of equations

a3x + (a + 1)3y + (a + 2)3z = 0

     ax + (a - 1)y + (a + 2)z = 0

                          x + y + z = 0

  • 1

  • 0

  • - 1

  • None of these


3.

If f(x) = 1 + sinxasinx, - π6 < x < 0etan2xtan3x,                        0 < x < π6 is continuous at x = 0, find the values of a and b.

  • 3/2, e3/2

  • - 2/3, e- 3/2

  • 2/3, e2/3

  • None of these


4.

If f(x) = exg(x), g(0) = 2, g'(0) = 1 then f'(0) is

  • 1

  • 3

  • 2

  • 0


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5.

At the point x = 1, the function

fx = x3 - 1,    1 < x < x - 1, -  < x  1

  • continuous and differentiable

  • continuous and not differentiable

  • discontinuous and differentiable

  • discontinuous and not differentiable


B.

continuous and not differentiable

LHL = limx1-fx =  limx1x - 1 = 0RHL = limx1+fx        = limx1+x3 - 1Also, f1 = 1 - 1 = 0 f is continuous at x = 1 

Now, Lf'1 = limh0f1 - h - f1- h                 = limh01 - h - 1 - 0- h                = limh0- h- h = 1and Rf'1 = limh0f1 + h - f1h                = limh01 + h3 - 1 - 0h                = limh01 + h3 + 3h + 3h2 - 1h                = limh0h2 + 3 + 3h = 3Clearly, Lf'1  Rf'1Thus, f (x) is not differentiable at x = 1


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6.

If x = 2cos(t) - cos(2t), y = 2sin(t) - sin(2t), then the value of d2ydx2t = π2

  • 3/2

  • 5/2

  • 5/3

  • - 3/2


7.

y = logtanx2 + sin-1cosx, then dy/dx is

  • csc(x) - 1

  • cs(x)

  • csc(x) + 1

  • x


8.

For all real x, the minimum value of 1 -  x + x21 +  x + x2 is

  • 0

  • 1/3

  • 1

  • 3


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9.

If x + y = k is normal to y2 = 12x, then k is

  • 3

  • 9

  • - 9

  • - 3


10.

A particle moves along a straight line according to the law s = 16 - 2t + 3t3, where s metres is the distance of the particle from a fixed point at the end of t second. The acceleration of the particle at the end of 2s is

  • 3.6 m/s2

  • 36 m/s2

  • 36 km/s2

  • 360 m/s2


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