74. यदि \( x=4 t, y=\frac{-}{t} \) तो \( \frac{{ }^{2}}{d x}= \)
(A) \( \frac{1}{t^{2}} \)
(B) \( \frac{4}{t^{2}} \)
(C) \( \frac{t}{4} \)
(D) \( \frac{-1}{t^{2}} \)
75. \( \frac{d \cos ^{-1}(\sin x)}{d x}= \)
(A) -1
(B) \( \frac{1}{\sqrt{1-x^{2}}} \)
(C) 1
(D) 0
76. \( \frac{d \sin (\sqrt{x})}{d x}= \)
(A) \( \frac{2 \cos \sqrt{x}}{\sqrt{x}} \)
(B) \( \frac{\cos \sqrt{x}}{\sqrt{x}} \)
(C) \( \frac{\cos \sqrt{x}}{2 \sqrt{x}} \)
(D) \( \frac{\cos \sqrt{x}}{2} \)
77. \( \frac{d(2+\cos 2 x)}{d x}= \)
(A) \( 1-\sin 2 x \)
(B) \( 2 \sin 2 x \)
(C) \( -2 \sin 2 x \)
(D) \( 2 \sin ^{2} x \)
78. \( \int_{2}^{3} \frac{1}{x} d x= \)
(A) \( \log 6 \)
(B) \( \log \frac{3}{2} \)
(C) \( \log \frac{2}{3} \)
(D) 0
79. \( \int \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}} d x \)
(A) \( \frac{1}{2}\left(\sin ^{-1} x\right)^{2}+C \)
(B) \( \frac{-1}{2}\left(\sin ^{-1} x\right)^{2}+C \)
(C) \( 2\left(\sin ^{-1} x\right)^{2}+C \)
(D) \( -2\left(\sin ^{-1} x\right)^{2}+C \)
80. \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^{5}+x \cos x+\sin ^{7} x+1\right) d x= \)
(A) \( \pi \)
(B) 0
(C) 2
(D) 1
गणि
