MCQs of સાતત્ય અને વિકલન | GUJCET MCQ

સાતત્ય અને વિકલન MCQs

MCQs of સાતત્ય અને વિકલન

Showing 11 to 20 out of 178 Questions

11.

f (x) = \{\begin{matrix} \frac{x^{2}}{a} - a & x < a \\ 0 & x = a \\ a - \frac{x^{2}}{a} & x > a માટે \end{matrix}

(a)	$\lim_{x \to a +} f (x) = a$
(b)	$\underset{x \to a}{l i m} f (x) = - a$
(c)	f એ x = a આગળ સતત છે.
(d)	f એ x = a આગળ વિકલનીય છે.

12.

\frac{d}{d x} \frac{1}{l o g |x|} =_____.

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

13.

જો y = a \sin x + b \cos x, તો y^{2} + {(y_{1})}^{2} =_____. (a^{2} + b^{2} \neq 0)

(a)	acosx - bsinx
(b)	$(a \sin x - b \cos x)^{2}$
(c)	$a^{2} + b^{2}$
(d)	0

14.

\frac{d}{d x} {(x^{2} + s i n^{2} x)}^{3} =_____.

(a)	$3 (x^{2} + \sin^{2} x)$
(b)	$3 {(x^{2} + \sin^{2} x)}^{2} (2 x + \sin 2 x)$
(c)	2x + 2sinx cosx
(d)	0

15.

\frac{d}{d x} \sqrt{x s i n x} =_____0 < x < π

(a)	$\frac{x \sin x + \cos x}{\sqrt{x s i n x}}$
(b)	$\frac{xcosx}{2 \sqrt{xsinx}}$
(c)	$\frac{xcosx + sinx}{2 \sqrt{xsinx}}$
(d)	$\frac{1}{2 \sqrt{xsinx}}$

16.

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

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

17.

\frac{d}{d x} \tan^{- 1} \sqrt{\frac{1 - \cos x}{1 + \cos x}} =_____. π < x < 2 π

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

18.

જો x = e^{\tan - 1 \frac{y - x^{2}}{x^{2}}}, તો \frac{dy}{dx} =_____.

(a)	2x (tan (log x) + 1)
(b)	$2 x (\tan (\log x) + 1) + {xsec}^{2} (logx)$
(c)	$2 x (\tan (\log x) + 1) + x^{2} \sec (logx)$
(d)	0

19.

\frac{d}{d x} x^{2} =_____(x > 0)

(a)	$\frac{3}{5} + \frac{1}{\sqrt{1 - x^{2}}}$
(b)	$\frac{4}{5} \frac{1}{\sqrt{1 - x^{2}}}$
(c)	$\frac{1}{\sqrt{1 - x^{2}}}$
(d)	$\frac{1}{\sqrt{1 + x^{2}}}$

20.

\frac{d}{d x} t a n^{- 1} (\frac{x + a}{1 - x a}) =_____. (x, a \in R^{+}, x a > 1)

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

Showing 11 to 20 out of 178 Questions