MCQs of Continuity and Differentiability | GUJCET MCQ

Continuity and Differentiability MCQs

MCQs of Continuity and Differentiability

Showing 21 to 30 out of 117 Questions

21.

\frac{d}{d x} x |x| =_____. (x < 0)

(a)	$2 x$
(b)	$- 2 x$
(c)	$\|x\|$
(d)	0

22.

If x = \frac{2 t}{1 + t^{2}}, y = \frac{1 - t^{2}}{1 + t^{2}}, then \frac{d y}{d x} =_____.

(a)	$\frac{2 t^{2}}{1 - t^{2}}$
(b)	$\frac{2 t}{1 + t^{2}}$
(c)	$2 t$
(d)	$\frac{- 2 t}{1 - t^{2}}$

23.

\frac{d}{d x} e^{x l o g x} =_____

(a)	$x^{x} (1 + l o g x)$
(b)	$x^{x}$
(c)	$1 + l o g x$
(d)	$x^{x - 1}$

24.

\frac{d}{d x} \frac{t a n^{- 1} x}{1 + t a n^{- 1} x} w . r . t . t a n^{- 1} x =_____

(a)	$\frac{1}{1 + t a n^{- 1} x}$
(b)	$\frac{1}{{(1 + \tan^{- 1} x)}^{2}}$
(c)	$\frac{1}{1 + x^{2}}$
(d)	$\frac{- 1}{1 + x^{2}}$

25.

If x = a t^{2}, y = 2 a t, then \frac{d^{2} y}{d x^{2}}

(a)	$\frac{- 1}{t^{2}}$
(b)	$\frac{1}{t^{2}}$
(c)	$\frac{- 1}{2 a t^{3}}$
(d)	$\frac{1}{2 a t^{3}}$

26.

\frac{d}{d x} c o t^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x} =_____(x \in R - {0})

(a)	$\frac{1}{1 + x^{2}}$
(b)	$\frac{1}{2 (1 + x^{2})}$
(c)	$\frac{2}{1 + x^{2}}$
(d)	$- \frac{1}{1 + x^{2}}$

27.

\frac{d^{2} x}{d y^{2}} =_____

(a)	$\frac{1}{\frac{d^{2} y}{d x^{2}}}$
(b)	$\frac{1}{{(\frac{d y}{d x})}^{2}}$
(c)	$- \frac{1}{{(\frac{d y}{d x})}^{2}}$
(d)	$- \frac{1}{{(\frac{d y}{d x})}^{3}} \frac{d^{2} y}{d x}$

28.

If x=secθ - cosθ, y=secⁿθ - cosⁿθ, then _____

(a)	$(x^{2} + 4) {(\frac{d y}{d x})}^{2} = n^{2} (y^{2} + 4)$
(b)	$(x^{2} - 4) {(\frac{d y}{d x})}^{2} = n^{2} (y^{2} - 4)$
(c)	$(x^{2} + 4) {(\frac{d y}{d x})}^{2} = 1$
(d)	$(x^{2} + 4) {(\frac{d y}{d x})}^{2} = y^{2} + 4$

29.

\frac{d}{d x} t a n^{- 1} \frac{\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}}{\sqrt{1 - x^{2}} + \sqrt{1 + x^{2}}} =_____|x| < 1

(a)	$\frac{1}{\sqrt{1 - x^{4}}}$
(b)	$\frac{- x}{\sqrt{1 - x^{4}}}$
(c)	$\frac{1}{2 \sqrt{1 - x^{4}}}$
(d)	$\frac{x^{2}}{1 - x^{4}}$

30.

\frac{d}{d x} (\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} s i n^{- 1} \frac{x}{a}) =_____(a > 0)

(a)	$\frac{1}{\sqrt{a^{2} - x^{2}}}$
(b)	$\sqrt{a^{2} - x^{2}}$
(c)	$\sqrt{x^{2} - a^{2}}$
(d)	$\sqrt{x^{2} + a^{2}}$

Showing 21 to 30 out of 117 Questions