The range in which y = - x2 + 6x - 3 is increasing is from Mathe

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The solution of tan-1x + 2cot-1x = 2π3 is

  • - 13

  • 13

  • - 3

  • 3


2.

The value of sin2cos-153 is

  • 53

  • 253

  • 459

  • 259


3.

If A = 1- 1121- 3111, 10B = 422- 50α1- 23 and B is the inverse of A, then the value of α is

  • 2

  • 0

  • 5

  • 4


4.

If A = 1- 2202 - 33- 24, then A . adj (A) is equal to

  • 511151115

  • 500050005

  • 800080008

  • 000000000


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5.

If f : R  R is defined by f(x) = lxl, then

  • f-1(x) = - x

  • f-11x

  • the function f-1(x) does not exist

  • f-1x = 1x


6.

If A = 0x16x5 709xis singular, then the possible values of x are

  • 0, 12, - 12

  • 0, 1, - 1

  • 0, 4, - 4

  • 0, 5, - 5


7.

The value of xpqpxqpqx is

  • x(x - p)(x - q)

  • (x - p)(x - q)(x + p + q)

  • (p - q)(x - q)(x - p)

  • pq(x - p)(x - q)


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8.

The range in which y = - x2 + 6x - 3 is increasing is

  • x < 3

  • x > 3

  • 7 < x < 8

  • 5 < x < 6


B.

x > 3

Given, y = - x2 + 6x - 3

 dydx = - 2x + 6 = y'y is increasing, if y' > 0 - 2x + 6 > 0        - 2x > - 6            2x > 6              x > 3


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9.

OA and OB are two roads enclosmng an angle of 120°. X and Y start from 'O' at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h.The rate at which the shortest distance between X and Y is increasing after 1 h is

  • 37 km /h

  • 37 km/h

  • 13 km/h

  • 13 km/h


10.

If the function f(x) = 1 - cosxx2, x  0k,                  x = 0 is continuous at x = 0, then the value of k is

  • 1

  • 0

  • 12

  • - 1


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