MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 111 to 120 out of 440 Questions

111.

\int \sqrt{cosec x + 1} d x

=_____ + c

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

112.

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

= _____ + c

(a)	$\frac{1}{2} \log \|e^{\frac{x}{2}} + e^{\frac{- x}{2}}\|$
(b)	$2 \log \|e^{\frac{x}{2}} + e^{\frac{- x}{2}}\|$
(c)	$2 \log \|e^{x} + 1\|$
(d)	આપેલ પૈકી એક પણ નહી.

113.

\int \frac{(\sqrt{1 + x^{2}} + x)^{n}}{\sqrt{1 + x^{2}}} d x

= _____ + c

(a)	$\frac{1}{n} (\sqrt{1 + x^{2}} + x)^{n}$
(b)	$\frac{1}{x} (\sqrt{1 + x^{2}} + x)^{n}$
(c)	$(\sqrt{1 + x^{2}} + x)^{n + 1}$
(d)	આપેલ ઉકેલમાંથી એક પણ નહી.

114.

\int \frac{x^{5}}{\sqrt{1 - x^{3}}} d x

= _____ + c

(a)	$\frac{2}{3} \sqrt{1 - x^{3}} - \frac{2}{9} (1 - x^{3})^{\frac{3}{2}}$
(b)	$\frac{2}{3} (2 + x^{3}) \sqrt{1 - x^{3}}$
(c)	$- \frac{2}{9} (2 + x^{3}) \sqrt{1 - x^{3}}$
(d)	આપેલ પૈકી એક પણ નહી.

115.

\int \frac{d x}{1 + \sqrt[3]{x}}

= _____ + c

(a)	$\frac{1}{2} x^{\frac{2}{3}} - \sqrt[3]{x} + \log \|\sqrt[3]{x} + 1\|$
(b)	$\frac{3}{2} x^{\frac{2}{3}} + 3 \sqrt[3]{x} + 3 \log \|\sqrt[3]{x} + 1\|$
(c)	$\frac{3}{2} x^{\frac{2}{3}} - 3 \sqrt[3]{x} + 3 \log \|\sqrt[3]{x} + 1\|$
(d)	આપેલ પૈકી એક પણ નહી.

116.

\int \frac{1}{(x - a) \sqrt{x - b}} d x, x > a > b

=

k \log |\frac{\sqrt{x - b} - \sqrt{a - b}}{\sqrt{x - b} + \sqrt{a - b}}| + c

તો k = _____

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

117.

\int \frac{\sin x + \cos x}{\sqrt{\sin 2 x}} d x

(a)	sin^-1(sinx-cosx)
(b)	sin^-1(sinx+cosx)
(c)	sin^-1(cosx-sinx)
(d)	આપેલ પૈકી એક પણ નહી.

118.

\int \frac{1}{(\sin x)^{\frac{3}{5}} (\cos x)^{\frac{7}{5}}} d x

= _____ + c

(a)	$\frac{5 (\tan x)^{\frac{7}{5}}}{7}$
(b)	$\frac{5 (\tan x)^{\frac{2}{5}}}{2}$
(c)	$\frac{5 (\cot x)^{\frac{2}{5}}}{2}$
(d)	$\frac{5 (\cot x)^{\frac{7}{5}}}{7}$

119.

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

= tan^-1x+f(x)+c તો f(x) = _____

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

120.

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

= _____ + c

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

Showing 111 to 120 out of 440 Questions