The function f(x) = [x], where [x] denotes the greatest integer n

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

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

281.

If f(x5) = 5x3, then f'(x) is equal to

  • 3x25

  • 3x5

  • 3x

  • x5


282.

f(x) = 2a - x   in - a < x < a3x - 2a in a  x

Then, which of the following is true ?

  • f(x) is discontinuous at x = a

  • f(x) is not differentiable at x = a

  • f(x) is differentiable at x   a

  • f(x) is continuous at all x <a


283.

If f(x) = beax + aebx, then f''(0) is equal to

  • 0

  • 2ab

  • ab(a + b)

  • ab


284.

Th function f(x) = log1 +ax - log1 - bxxis not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuousat x = 0 is 

  • a - b

  • a + b

  • log(a) + log(b)

  • 0


Advertisement
285.

If f(x) = 1 + nx + nn - 12x2 + nn - 1n - 26x3 + ... + xn, then f''(1) is equal to

  • n(n - 1)2n - 1

  • (n - 1)2n - 1

  • n(n - 1)2n - 2

  • n(n - 1)2n


286.

If f(x) = logx2logex, then f'(x) at x = e is

  • 1

  • 1e

  • 12e

  • 0


287.

If f(x) = gx + g- x2 + 2hx + h- x- 1 where g and h are differentiable function, then f'(0)

  • 1

  • 12

  • 32

  • 0


Advertisement

288.

The function f(x) = [x], where [x] denotes the greatest integer not greater than x , is

  • continuous for all non-integral values of x

  • continuous only at positive integral values of x

  • continuous for all real values of x

  • continuous only at rational values of x


A.

continuous for all non-integral values of x

Given, f(x) = [x] from the graph we observe that f(c) = [x] discontinuous at every integral value of x. That means, f(x) = [x]. Continuous only for all non-integral values of x


Advertisement
Advertisement
289.

If the three function f(x), g(x) and h(x) are such that h(x) = f(x) g(x) and f'(x) g'(x) = c where c is constant, then

f''xfx + g''xgx + 2cfx . gx is equal to

  • h'(x) . h''(x)

  • hxh''x

  • h''xhx

  • hxh'x


290.

The derivative of eax cos(bx) with respect x is reax cos(bx) tan-1ba when a>0,b>0, then a value of r, is

  • a2 + b2

  • 1ab

  • ab

  • a + b


Advertisement