MCQs of સાતત્ય અને વિકલન | GUJCET MCQ

સાતત્ય અને વિકલન MCQs

MCQs of સાતત્ય અને વિકલન

Showing 21 to 30 out of 159 Questions

21.

જો f (x) = \log_{7} (\log_{3} x), તો f' (x) =_____.

(a)	$\frac{1}{xlog 7 \log 3}$
(b)	$\frac{1}{\log 3 \log x}$
(c)	$\frac{1}{x logx \log 7}$
(d)	$\frac{1}{xlogx}$

22.

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

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

23.

જો x = \frac{2 t}{1 + t^{2}}, y = \frac{1 - t^{2}}{1 + t^{2}}, તો \frac{dy}{dx} =_____

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

24.

\frac{d}{dx} e^{x \log x} =_____

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

25.

\frac{\tan^{- 1} x}{1 + \tan^{- 1} x} નો \tan^{- 1} x ને સાપેક્ષ વિકલિત =_____

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

26.

જો x = {at}^{2}, y = 2 at, તો \frac{d^{2} y}{{dx}^{2}} =_____

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

27.

\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)	$- \frac{1}{1 + x^{2}}$

28.

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

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

29.

જો x = secθ - cosθ, y = \sec^{n} θ - \cos^{n} θ, તો_____

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

30.

\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)	$\frac{x^{2}}{1 - x^{4}}$

Showing 21 to 30 out of 159 Questions