MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 131 to 140 out of 440 Questions

131.

\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}} d x

= _____

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

132.

\int \frac{d x}{(x + 1)^{\frac{3}{4}} (x - 2)^{\frac{5}{4}}}

= _____

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

133.

જો

\int \frac{\log (1 + \sqrt{1 + t^{2}})}{\sqrt{1 + t^{2}}} d t = \frac{1}{2} {(g (t))}^{2} + C

જ્યાં C એ અચળ હોય, તો g(2) = _____

(a)	$2 \log (2 + \sqrt{5})$
(b)	$\log (2 + \sqrt{5})$
(c)	$\frac{1}{\sqrt{5}} \log (2 + \sqrt{5})$
(d)	$\frac{1}{2} \log (2 + \sqrt{5})$

134.

\int \frac{d x}{x [(\log x)^{2} + (\log x) + 1]}

=_____ + c

(a)	$\sqrt{3} \tan^{- 1} (1 + \log x)$
(b)	$\frac{2}{\sqrt{3}} \tan^{- 1} (\frac{2 \log x + 1}{\sqrt{3}})$
(c)	$\frac{1}{\sqrt{3}} \tan^{- 1} (\frac{\log x + 1}{\sqrt{3}})$
(d)	$\frac{1}{\sqrt{3}} \sec^{- 1} (\frac{2 \log x + 1}{\sqrt{3}})$

135.

\int \frac{1}{e^{x} + 1} d x

= _____

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

136.

\int \frac{x^{3} + 4 x - 3}{x^{2} + 4} d x = A x^{2} + {Btan}^{- 1} \frac{x}{2} + c

તો A+B = _____ જ્યાં A, B ∈ R

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

137.

\int \frac{d x}{(2 x + 3) \sqrt{x^{2} + 3 x + 2}}

= _____ + c જ્યાં x >

- \frac{3}{2}

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

138.

\int \frac{\sin x - x \cos x}{x^{2} + x \sin x} d x

= _____ + c

(a)	$\log \|\frac{x + \sin x}{x}\|$
(b)	$\log \|\frac{x}{x + \sin x}\|$
(c)	$\log \|x^{2} + x \sin x\|$
(d)	$\log \|x + \sin x\|$

139.

\int \frac{x - 1}{\sqrt{x + 4}} d x

= _____ + c જ્યાં x+4 > 0

(a)	$\frac{2}{3} (x + 1)^{\frac{3}{2}} + 5 \sqrt{x + 4}$
(b)	$\frac{2}{3} (x + 4)^{\frac{3}{2}} + 10 \sqrt{x + 4}$
(c)	$\frac{2}{3} (x + 4)^{\frac{3}{2}} - 5 \sqrt{x + 4}$
(d)	$\frac{2}{3} (x + 4)^{\frac{3}{2}} - 10 \sqrt{x + 4}$

140.

\int \frac{(x - 1)^{2}}{(x^{2} + 1)^{2}} d x = \tan^{- 1} x + f (x) + c

તો f(x) = _____

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

Showing 131 to 140 out of 440 Questions