MCQs of સાતત્ય અને વિકલન | GUJCET MCQ

સાતત્ય અને વિકલન MCQs

MCQs of સાતત્ય અને વિકલન

Showing 121 to 130 out of 159 Questions

121.

જો f(x) =

\{\begin{cases} \frac{\sqrt{2 + \cos x} - 1}{{(π - x)}^{2}}, x \neq π \\ k, x = π \end{cases}

એ

x = π

આગળ સતત હોય ,તો k =_____

(a)	0
(b)	$\frac{1}{2}$
(c)	2
(d)	$\frac{1}{4}$

122.

\frac{d}{d x} [x^{(\cos e c^{- 1} x + s e c^{- 1} x)}]

= _____ જ્યાં

|x| \geq 1

(a)	$\frac{2}{π} x^{\frac{π - 1}{2}}$
(b)	$\frac{2}{π} x^{\frac{π}{2}}$
(c)	0
(d)	$\frac{π}{2} x^{\frac{π - 2}{2}}$

123.

x = a(

\cos t + \log \tan \frac{t}{2}

) , y =asint

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

=_____

(a)	$\frac{1}{a} s e c^{4} t . \cos e c t$
(b)	$\frac{1}{a} s e c^{4} t . \sin t$
(c)	sec²t
(d)	$\frac{1}{a} s e c^{4} t$

124.

જો y=

e^{m \cos^{- 1} x}

હોય તો m =_____

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

125.

જો

\frac{d}{d x}

(f' (x)) = g (x) હોય તો

\frac{d}{d x} (- \frac{1}{g (x)})

= _____ . જ્યાં g(x) ≠ 0

(a)	$\frac{g (x)}{{\{\frac{d}{d x} g (x)\}}^{2}}$
(b)	$\frac{\frac{d^{2}}{d x^{2}} (f (x))}{{\{\frac{d}{d x} (g' (x))\}}^{2}}$
(c)	$\frac{\frac{d}{d x} (f' (x))}{{\{\frac{d}{d x} (f' (x))\}}^{2}}$
(d)	$\frac{\frac{d^{2}}{d x^{2}} (f' (x))}{{\{\frac{d}{d x} (f' (x))\}}^{2}}$

126.

{[\frac{d}{d x} \cos e c^{- 1} x]}_{x = - 5}

= _____ .

(a)	$- \frac{1}{\|x\| \sqrt{x^{2} + 1}}$
(b)	$- \frac{1}{10 \sqrt{6}}$
(c)	$- \frac{1}{5 \sqrt{26}}$
(d)	$\frac{1}{10 \sqrt{6}}$

127.

\frac{d}{d x} \sin (x^{x})

= _____ .

(a)	x sin (x^x-1) cos x
(b)	x^x cos (x^x)
(c)	x^x (1 + log x) sin (x^x)
(d)	x^x (1 + log x) cos (x^x)

128.

x = cos θ + θ sin θ, y = sin θ - θ cos θ તો

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

= _____ .

(a)	$- \frac{\cos e c^{3} θ}{θ}$
(b)	$s e c^{2} θ$
(c)	$\frac{s e c θ}{θ}$
(d)	$\frac{s e c^{3} θ}{θ}$

129.

જો y =

\sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + . . . . . . \infty}}}

, તો

\frac{d y}{d x}

= _____ .

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

130.

જો y = x tan y, તો

\frac{d y}{d x}

= _____ .

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

Showing 121 to 130 out of 159 Questions