For all real x, the minimum value of 1 -  x&n

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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


Advertisement
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


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


Advertisement

8.

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

  • 0

  • 1/3

  • 1

  • 3


B.

1/3

Let y = 1 -  x + x21 +  x + x2 = 1 - 2x1 +  x + x2        = 1 - 21x + 1 + x y = 1 - 2twhere t = 1x + 1 + xNow, y is minimum, when 2t is max  t is min. dtdx = - 1x2 + 1 = 0   x = ± 1  d2tdx2 = 2x3 > 0, for x = 1  Minimum value of y is1 - 21 + 1 + 1 = 1 - 23                           = 13


Advertisement
Advertisement
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


Advertisement