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232 questions · 231 auto-graded MCQ + 1 self-marked written.

MCQ 11 Mark
tan$^{-1}$ $\left(\frac{x}{y}\right)$ - tan$^{-1}$ $\frac{x-y}{x+y}$ का मान है:
  • A
    $\frac \pi 2$
  • B
    $\frac \pi 3$
  • C
    $-\frac{3 \pi}{4}$
  • $\frac \pi 4$
Answer
Correct option: D.
$\frac \pi 4$
$\tan ^{-1}\left(\frac{x}{y}\right)$$-\tan ^{-1}\left(\frac{x-y}{x+y}\right)$= $\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}$ $\left(\frac{\frac{x}{y}-1}{\frac{x}{y}+1}\right)$
= $\tan ^{-1}\left(\frac{x}{y}\right)$ - $\left(\tan ^{-1} \frac{x}{y}-\tan ^{-1} 1\right)$ [$\because $ tan$^{-1}$ x - tan$^{-1}$y = tan$^{-1}$ $(\frac{x-y}{1+x y})$]
= tan$^{-1}$ 1 = $\frac{\pi}{4}$
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MCQ 21 Mark
यदि $\sin ^{-1}(1-x)$ $2 \sin ^{-1} x$ = $\frac{\pi}{2} $, तो x का मान बराबर है:
  • A
    $0, \frac{1}{2}$
  • $0$
  • C
    $\frac 1 2$
  • D
    $1, \frac{1}{2}$
Answer
Correct option: B.
$0$
ज्ञात है, $\sin ^{-1}(1-x)-2 \sin ^{-1} $ x = $\frac{\pi}{2}$
$\Rightarrow$ $-2 \sin ^{-1} x$ = $\frac{\pi}{2}-\sin ^{-1}(1-x)$ $ \Rightarrow$ $-2 \sin ^{-1} x$ = $\cos ^{-1}(1-x)$ [$\because$ $ \sin ^{-1}(1-x)$ + $\cos ^{-1}(1-x)$ = $\frac{\pi}{2}$]
$\Rightarrow $ $ \cos \left(-2 \sin ^{-1} x\right)$ = 1 - x (दोनों पक्षों में cos x की गुणा करने पर)
$ \Rightarrow$ $ \cos \left(2 \sin ^{-1} x\right)$ = 1 - x [$ \because$ cos (-x) = + cos x]
$\Rightarrow $ $\left[1-2 \sin ^{2}\left(\sin ^{-1} x\right)\right]$ = 1 - x [$\because$ $ \sin ^{2} x$ = $(\sin x)^{2}$]
$\Rightarrow $1 - 2x$^2$ = 1 - x $\Rightarrow$ 2x$^2$ - x = 0
$\Rightarrow $ x(2x - 1) = 0 $ \Rightarrow $ x = 0 या 2x - 1 = 0 $\Rightarrow$ x = 0 या $\frac{1}{2}$
किन्तु x = $ \frac{1}{2}$ ज्ञात समीकरण को सन्तुष्ट नहीं करता है, इसलिए x = 0 सही है।
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MCQ 31 Mark
sin ($\tan ^{-1}$ x), |x| < 1 का मान बराबर है:
  • A
    $\frac{1}{\sqrt{1-x^{2}}}$
  • $\frac{x}{\sqrt{1+x^{2}}}$
  • C
    $\frac{1}{\sqrt{1+x^{2}}}$
  • D
    $\frac{x}{\sqrt{1-x^{2}}}$
Answer
Correct option: B.
$\frac{x}{\sqrt{1+x^{2}}}$
$\left(\sin \tan ^{-1} x\right)=\sin \left[\sin ^{-1} \frac{x}{\sqrt{1+x^2}}\right]\left(\because \tan ^{-1} x=\sin ^{-1} \frac{x}{\sqrt{1+x^2}}\right)$
$=\frac{x}{\sqrt{1+x^2}}$
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MCQ 41 Mark
$\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$ बराबर है
  • A
    $\frac{1}{3}$
  • 1
  • C
    $\frac{1}{4}$
  • D
    $\frac{1}{2}$
Answer
Correct option: B.
1
$\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$= $\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\sin \frac{\pi}{6}\right)\right]$ $\left(\because \sin \frac{\pi}{6}=\frac{1}{2}\right)$
= $\sin \left[\frac{\pi}{3}-\sin ^{-1}\left\{\sin \left(-\frac{\pi}{6}\right)\right\}\right]$ $[\because \sin (-x)=-\sin x]$
= $\sin \left[\frac{\pi}{3}-\left(-\frac{\pi}{6}\right)\right]$ = $\sin \left(\frac{\pi}{3}+\frac{\pi}{6}\right)$ = $\sin \frac{\pi}{2}$ = 1

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MCQ 51 Mark
cos$^{-1}$ $\left(\cos \frac{7 \pi}{6}\right) $ बराबर है
  • $\frac{5 \pi}{6}$
  • B
    $\frac{7 \pi}{6}$
  • C
    $\frac{ \pi}{3}$
  • D
    $\frac{ \pi}{6}$
Answer
Correct option: A.
$\frac{5 \pi}{6}$
$\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$ = $\cos ^{-1}\left[\cos \left(2 \pi-\frac{5 \pi}{6}\right)\right]$
जहाँ, $\frac{5 \pi}{6} \in[0, \pi] $ $ \therefore$ cos$^{-1}$$\left(\cos \frac{7 \pi}{6}\right)$ = cos$^{-1}$ $ \left[\cos \left(\frac{5 \pi}{6}\right)\right]=\frac{5 \pi}{6}$ $[\because \cos (2 \pi-\theta)=\cos \theta]$
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MCQ 61 Mark
$\tan ^{-1} \sqrt{3}-\sec ^{-1}(-2) $ का मान बराबर है
  • $-\frac{\pi}{3}$
  • B
    $\frac{2 \pi}{3}$
  • C
    $\frac{\pi}{3}$
  • D
    $\pi$
Answer
Correct option: A.
$-\frac{\pi}{3}$
मान लीजिए $ \tan ^{-1} \sqrt{3}$ = x $ \Rightarrow$ $ \tan x=\sqrt{3} $ $\Rightarrow$ $ \tan x$ = $\tan \frac{\pi}{3}$
$\Rightarrow$ x = $ \frac{\pi}{3} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $ (मुख्य अंतराल)
मान लीजिए $ \sec ^{-1}(-2)$ = y $ \Rightarrow$ sec y = - 2 $[\because \sec (\pi-\theta)=-\sec \theta]$
$\Rightarrow$ sec y = sec $ \left(\frac{2 \pi}{3}\right) $
$\Rightarrow$ y = $\frac{2 \pi}{3} \in$ [0, $\pi$] - $\left(\frac{\pi}{2}\right)$ (मुख्य अंतराल)
$\therefore$ $ \tan ^{-1} \sqrt{3}-\sec ^{-1}(-2)$ = x - y = $ \frac{\pi}{3}-\frac{2 \pi}{3}$ = $-\frac{\pi}{3}$
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MCQ 71 Mark
यदि $sin^{-1} x = y,$ तब
  • $-\frac{\pi}{2}$ < y < $\frac{\pi}{2}$
  • B
    0 < y < $\pi$
  • C
    $\frac{\pi}{2} \leq$ y $ \leq \frac{\pi}{2}$
  • D
    $0 \leq y \leq \pi$
Answer
Correct option: A.
$-\frac{\pi}{2}$ < y < $\frac{\pi}{2}$
चूँकि sin$^{-1}$ x का परिसर $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ है, इसलिए $-\frac{\pi}{2} \leq$ y $ \leq \frac{\pi}{2}$
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MCQ 81 Mark
$2 \cot ^{-1} 3+\cot ^{-1} 7=$
  • A
    $\frac{\pi}{2}$
  • $\frac{\pi}{4}$
  • C
    $\pi$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: B.
$\frac{\pi}{4}$
(B)
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MCQ 91 Mark
$\cos ^{-1}(2 x-1)=$
  • A
    $2 \cos ^{-1} x$
  • B
    $\cos ^{-1} \sqrt{x}$
  • $2 \cos ^{-1} \sqrt{x}$
  • D
    None of these
Answer
Correct option: C.
$2 \cos ^{-1} \sqrt{x}$
(C)
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MCQ 101 Mark
$\cos ^{-1}\left(\cos \frac{8 \pi}{5}\right)=$
  • A
    $\frac{8 \pi}{5}$
  • B
    $\frac{12 \pi}{5}$
  • $\frac{2 \pi}{5}$
  • D
    $\frac{4 \pi}{5}$
Answer
Correct option: C.
$\frac{2 \pi}{5}$
(C)
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MCQ 111 Mark
$\sin \left(\sin ^{-1} \frac{1}{2}+\cos ^{-1} \frac{1}{2}\right)=$
  • A
    $0$
  • B
    -1
  • 1
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
1
(C)
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MCQ 121 Mark
$\sec ^2\left(\tan ^{-1} 5\right)+\operatorname{cosec}^2\left(\cot ^{-1} 5\right)$ का मान है :
  • A
    10
  • B
    50
  • C
    51
  • 52
Answer
Correct option: D.
52
(D)
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MCQ 131 Mark
$\sec ^{-1} x+\operatorname{cosec}^{-1} x$ का मान है :
  • $\frac{\pi}{2}$
  • B
    $\frac{\pi}{4}$
  • C
    1
  • D
    $-\frac{\pi}{2}$
Answer
Correct option: A.
$\frac{\pi}{2}$
(A)
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MCQ 141 Mark
$\tan ^{-1} x+\cot ^{-1} x$ का मान है :
  • A
    $-\pi$
  • B
    $-\frac{\pi}{2}$
  • $\frac{\pi}{2}$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: C.
$\frac{\pi}{2}$
(C)
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MCQ 151 Mark
$\sin ^{-1} x+\cot ^{-1} x$ का मान है :
  • A
    $\pi$
  • $\frac{\pi}{2}$
  • C
    $-\frac{\pi}{2}$
  • D
    1
Answer
Correct option: B.
$\frac{\pi}{2}$
(B)
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MCQ 161 Mark
$\operatorname{cosec}^{-1}(-2)$ का मुख्य मान है :
  • A
    $-\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{2 \pi}{3}$
  • $-\frac{\pi}{6}$
Answer
Correct option: D.
$-\frac{\pi}{6}$
(D)
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MCQ 171 Mark
यदि $\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}$ तो $\cos ^{-1} x+\cos ^{-1} y=$
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{4}$
  • $\frac{\pi}{3}$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: C.
$\frac{\pi}{3}$
(C)
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MCQ 181 Mark
$4 \tan ^{-1} \frac{1}{5}-\tan ^{-1} \frac{1}{239}=$
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{3}$
  • $\frac{\pi}{4}$
Answer
Correct option: D.
$\frac{\pi}{4}$
(D)
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MCQ 191 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=$
  • $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{3}$
  • D
    $\pi$
Answer
Correct option: A.
$\frac{\pi}{4}$
(A)
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MCQ 201 Mark
यदि $|x| \leq 1$ तो $\tan \left(\cos ^{-1} x\right)=$
  • $\frac{\sqrt{1-x^2}}{x}$
  • B
    $\frac{x}{1+x^2}$
  • C
    $\frac{\sqrt{1+x^2}}{x}$
  • D
    $\sqrt{1-x^2}$
Answer
Correct option: A.
$\frac{\sqrt{1-x^2}}{x}$
(A)
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MCQ 211 Mark
$\sin ^{-1}\left(\sin \frac{\pi}{3}\right)+\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)$ का मान है :
  • A
    $\frac{17}{12} \pi$
  • B
    $\frac{5}{12} \pi$
  • $\frac{\pi}{12}$
  • D
    $-\frac{7 \pi}{12}$
Answer
Correct option: C.
$\frac{\pi}{12}$
(C)
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MCQ 221 Mark
$\tan \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)$ का मान है :
  • $\frac{17}{6}$
  • B
    34
  • C
    18
  • D
    -18
Answer
Correct option: A.
$\frac{17}{6}$
(A)
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MCQ 231 Mark
$\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})$ के बराबर है :
  • A
    $\pi$
  • $-\frac{\pi}{2}$
  • C
    $0$
  • D
    $2 \sqrt{3}$
Answer
Correct option: B.
$-\frac{\pi}{2}$
(B)
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MCQ 241 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{2}{11}=\tan ^{-1} a$ तब $a=$ ?
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • $\frac{3}{4}$
  • D
    1
Answer
Correct option: C.
$\frac{3}{4}$
(C)
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MCQ 251 Mark
$\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$ के बराबर है :
  • A
    $\frac{1}{2}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{4}$
  • 1
Answer
Correct option: D.
1
(D)
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MCQ 261 Mark
$\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$ के बराबर है :
  • A
    $\frac{7 \pi}{6}$
  • $\frac{5 \pi}{6}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: B.
$\frac{5 \pi}{6}$
(B)
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MCQ 271 Mark
$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)=$
  • A
    $0$
  • B
    $\frac{\pi}{4}$
  • $\frac{3 \pi}{4}$
  • D
    कोई नहीं
Answer
Correct option: C.
$\frac{3 \pi}{4}$
(C)
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MCQ 281 Mark
$\tan ^{-1} \sqrt{3}-\sec ^{-1}(-z)$ के बराबर है :
  • A
    $\pi$
  • $-\frac{\pi}{3}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{2 \pi}{3}$
Answer
Correct option: B.
$-\frac{\pi}{3}$
(B)
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MCQ 291 Mark
$\sin ^{-1} x=y$ तब :
  • A
    $0 \leq y \leq \pi$
  • $-\frac{\pi}{2} \leq \sin y \leq \frac{\pi}{2}$
  • C
    $0\lt y\lt\pi$
  • D
    $-\frac{\pi}{2}$
Answer
Correct option: B.
$-\frac{\pi}{2} \leq \sin y \leq \frac{\pi}{2}$
(B)
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MCQ 301 Mark
$\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$ का मुख्य मान है :
  • $\frac{3 \pi}{4}$
  • B
    $\frac{5 \pi}{4}$
  • C
    $-\frac{\pi}{4}$
  • D
    कोई नहीं
Answer
Correct option: A.
$\frac{3 \pi}{4}$
(A)
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MCQ 311 Mark
$\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)$ का मुख्य मान है :
  • $\frac{\pi}{4}$
  • B
    $\frac{3 \pi}{4}$
  • C
    $\frac{5 \pi}{4}$
  • D
    कोई नहीं
Answer
Correct option: A.
$\frac{\pi}{4}$
(A)
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MCQ 321 Mark
$\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)$ समान है :
  • A
    $\frac{1}{2} \cos ^{-1}\left(\frac{3}{5}\right)$
  • B
    $\frac{1}{2} \sin ^{-1}\left(\frac{3}{2}\right)$
  • C
    $\frac{1}{2} \tan ^{-1}\left(\frac{3}{5}\right)$
  • $\tan ^{-1}\left(\frac{1}{2}\right)$
Answer
Correct option: D.
$\tan ^{-1}\left(\frac{1}{2}\right)$
(D)
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MCQ 331 Mark
यदि $\cot ^{-1}\left[(\cos \alpha)^{1 / 2}\right]-\tan ^{-1}\left[(\cot \alpha)^{1 / 2}\right]=x$ तब $\sin x=$
  • $\tan ^2 \frac{\alpha}{2}$
  • B
    $\cot ^2 \frac{\alpha}{2}$
  • C
    $\tan \alpha$
  • D
    $\cot \frac{\alpha}{2}$
Answer
Correct option: A.
$\tan ^2 \frac{\alpha}{2}$
(A)
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MCQ 341 Mark
$\cos ^{-1}\left(\cos \frac{5 \pi}{3}\right)+\sin ^{-1}\left(\sin \frac{5 \pi}{3}\right)$ का मान है :
  • A
    $\frac{\pi}{2}$
  • B
    $\frac{5 \pi}{3}$
  • C
    $\frac{10 \pi}{3}$
  • $0$
Answer
Correct option: D.
$0$
(D)
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MCQ 351 Mark
यदि $\cot ^{-1} \sqrt{\cos \theta}-\tan ^{-1} \sqrt{\cos \theta}=x$ तब $\sin x=$ :
  • $\frac{1-\cos \theta}{1+\cos \theta}$
  • B
    $\frac{1+\cos \theta}{1-\cos \theta}$
  • C
    $\frac{2 \sqrt{\cos \theta}}{1+\cos \theta}$
  • D
    $\frac{2 \sqrt{\cos \theta}}{1-\cos \theta}$
Answer
Correct option: A.
$\frac{1-\cos \theta}{1+\cos \theta}$
(A)
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MCQ 361 Mark
यदि $\cos ^{-1} x-\cos ^{-1}\left(\frac{y}{2}\right)=a$ तब $4 x^2-4 x y \cos \alpha+y^2$ समान है :
  • $4 \sin ^2 \alpha$
  • B
    $-4 \sin ^2 \alpha$
  • C
    $2 \sin ^2 \alpha$
  • D
    4
Answer
Correct option: A.
$4 \sin ^2 \alpha$
(A)
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MCQ 371 Mark
$x$ का मान जिसके लिए $\sin \left(\cot ^{-1}(1-x)\right)=\cos \left(\tan ^{-1} x\right)$ :
  • A
    $\frac{2}{1}$
  • B
    1
  • C
    $0$
  • $\frac{1}{2}$
Answer
Correct option: D.
$\frac{1}{2}$
(D)
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MCQ 381 Mark
यदि $\sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}$ तब $x$ का मान है :
  • $0$
  • B
    $0,-\frac{1}{2}$
  • C
    $0, \frac{1}{2}$
  • D
    कोई नहीं
Answer
Correct option: A.
$0$
(A)
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MCQ 391 Mark
$\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)$ बराबर है :
  • A
    $\frac{\pi}{3}$
  • $\frac{\pi}{4}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{-3 \pi}{4}$
Answer
Correct option: B.
$\frac{\pi}{4}$
(B)
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MCQ 401 Mark
$\tan ^{-1}\left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right)$ का मान है :
  • A
    $\frac{6}{17}$
  • B
    $\frac{7}{16}$
  • $\frac{17}{6}$
  • D
    कोई नहीं (None)
Answer
Correct option: C.
$\frac{17}{6}$
(C)
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MCQ 411 Mark
$\tan ^{-1}(-1)$ का मान है :
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{-\pi}{2}$
  • C
    $\frac{5 \pi}{4}$
  • $\frac{-\pi}{4}$
Answer
Correct option: D.
$\frac{-\pi}{4}$
(D)
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MCQ 421 Mark
$\cos ^{-1}\left(4 x^3-3 x\right)$ का सरल रूप है :
  • A
    $3 \sin ^{-1} x$
  • $3 \cos ^{-1} x$
  • C
    $\pi-3 \sin ^{-1} x$
  • D
    कोई नहीं (None)
Answer
Correct option: B.
$3 \cos ^{-1} x$
(B)
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MCQ 431 Mark
$\sin \left(\cot ^{-1} x\right)$ के लिए बीजीय व्यंजक है :
  • A
    $\frac{1}{1+x^2}$
  • $\frac{1}{\sqrt{1+x^2}}$
  • C
    $\frac{x}{\sqrt{1+x^2}}$
  • D
    कोई नहीं (None)
Answer
Correct option: B.
$\frac{1}{\sqrt{1+x^2}}$
(B)
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MCQ 441 Mark
$\tan ^{-1}(1)+\cot ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{3}\right)$ का मान है :
  • $0$
  • B
    1
  • C
    $\pi$
  • D
    $-\pi $.
Answer
Correct option: A.
$0$
(A)
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MCQ 451 Mark
$\cos ^{-1}\left(\frac{1}{2}\right)+2 \sin ^{-1}\left(\frac{1}{2}\right)$ का मान है :
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{6}$
  • $\frac{2 \pi}{3}$
  • D
    $\frac{5 \pi}{6}$
Answer
Correct option: C.
$\frac{2 \pi}{3}$
(C)
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MCQ 461 Mark
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$ का मुख्य मान है :
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{3}$
  • $\frac{-\pi}{6}$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: C.
$\frac{-\pi}{6}$
(C)
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MCQ 471 Mark
$\cos ^{-1} \frac{1-x^2}{1+x^2}=$
  • A
    $2 \cos ^{-1} x$
  • B
    $2 \sin ^{-1} x$
  • $2 \tan ^{-1} x$
  • D
    $\cos ^{-1} 2 x$
Answer
Correct option: C.
$2 \tan ^{-1} x$
(C)
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MCQ 481 Mark
$\sin \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)=$
  • 1
  • B
    -1
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{3}$
Answer
Correct option: A.
1
(A)
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MCQ 491 Mark
$\sin ^{-1} x=$
  • A
    $\cot ^{-1} x$
  • B
    $\frac{1}{\cot ^{-1} x}$
  • $\operatorname{cosec}^{-1} \frac{1}{x}$
  • D
    $-\cot ^{-1} x$
Answer
Correct option: C.
$\operatorname{cosec}^{-1} \frac{1}{x}$
(C)
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MCQ 501 Mark
$\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ का मुख्य मान है :
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{\pi}{4}$
  • $\frac{\pi}{3}$
Answer
Correct option: D.
$\frac{\pi}{3}$
(D)
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MCQ 511 Mark
$\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})=$
  • A
    $\pi$
  • B
    $0$
  • C
    $2 \sqrt{3}$
  • $-\frac{\pi}{2}$
Answer
Correct option: D.
$-\frac{\pi}{2}$
(D)
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MCQ 521 Mark
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=$
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{4 \pi}{3}$
  • $\frac{\pi}{3}$
Answer
Correct option: D.
$\frac{\pi}{3}$
(D)
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MCQ 531 Mark
$\sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}$ तो $x=$ ?
  • $0, \frac{1}{2}$
  • B
    $1, \frac{1}{2}$
  • C
    $\frac{1}{2}$
  • D
    $0$
Answer
Correct option: A.
$0, \frac{1}{2}$
(A)
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MCQ 541 Mark
$\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)=$
  • A
    $\frac{7 \pi}{6}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{6}$
  • $\frac{5 \pi}{6}$
Answer
Correct option: D.
$\frac{5 \pi}{6}$
(D)
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MCQ 551 Mark
$2 \tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{7}=$
  • A
    $\tan ^{-1} \frac{44}{29}$
  • B
    $\frac{\pi}{2}$
  • C
    $0$
  • $\frac{\pi}{4}$
Answer
Correct option: D.
$\frac{\pi}{4}$
(D)
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MCQ 561 Mark
$\tan ^{-1} \frac{2 x}{1-x^2}=$ प्रतिलोम त्रिकोणमितीय फलन :
  • A
    $2 \sin ^{-1} x$
  • B
    $\sin ^{-1} 2 x$
  • C
    $\tan ^{-1} 2 x$
  • $2 \tan ^{-1} x$
Answer
Correct option: D.
$2 \tan ^{-1} x$
(D)
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MCQ 571 Mark
$\cos ^{-1}\left(-\frac{1}{2}\right)$ का मुख्य मान है :
  • A
    $\frac{\pi}{3}$
  • B
    $\frac{\pi}{6}$
  • $\frac{2 \pi}{3}$
  • D
    $\frac{3 \pi}{4}$
Answer
Correct option: C.
$\frac{2 \pi}{3}$
(C)
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MCQ 581 Mark
$\sin ^{-1} x+\cos ^{-1} x=$
  • $\frac{\pi}{2}$
  • B
    $\pi$
  • C
    $\frac{\pi}{4}$
  • D
    $2 \pi$
Answer
Correct option: A.
$\frac{\pi}{2}$
(A)
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MCQ 591 Mark
$2 \tan ^{-1} x=$
  • $\sin ^{-1} \frac{2 x}{1+x^2}$
  • B
    $\sin ^{-1} \frac{2 x}{1-x^2}$
  • C
    $\sin ^{-1} \frac{1-x^2}{1+x^2}$
  • D
    $\sin ^{-1} \frac{1+x^2}{1-x^2}$
Answer
Correct option: A.
$\sin ^{-1} \frac{2 x}{1+x^2}$
(A)
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MCQ 601 Mark
$\sin ^{-1}\left(\sin \frac{7 \pi}{6}\right)=$
  • A
    $\frac{7 \pi}{6}$
  • B
    $\frac{\pi}{6}$
  • $\frac{-\pi}{6}$
  • D
    $\frac{5 \pi}{6}$
Answer
Correct option: C.
$\frac{-\pi}{6}$
(C)
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MCQ 611 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{4}=\ldots \ldots$
  • A
    $\tan ^{-1} \frac{3}{2}$
  • $\tan ^{-1} \frac{6}{7}$
  • C
    $\tan ^{-1} \frac{5}{6}$
  • D
    $\tan ^{-1} \frac{1}{2}$
Answer
Correct option: B.
$\tan ^{-1} \frac{6}{7}$
(B)
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MCQ 621 Mark
$\tan ^{-1}(1)=\ldots .$. ?
  • $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{8}$
Answer
Correct option: A.
$\frac{\pi}{4}$
(A)
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MCQ 631 Mark
$\tan ^{-1} \frac{4 \sqrt{x}}{2-2 x}$
  • $2 \tan ^{-1} \sqrt{x}$
  • B
    $\cos ^{-1} \frac{1-x}{1+x}$
  • C
    $\sin ^{-1} \frac{2 x}{1+x^2}$
  • D
    $\sqrt{2} \tan ^{-1} x$
Answer
Correct option: A.
$2 \tan ^{-1} \sqrt{x}$
(A)
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MCQ 641 Mark
$\cos ^{-1}\left(\frac{-1}{2}\right)=$
  • $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{-\pi}{3}$
  • D
    $\frac{-2 \pi}{3}$
Answer
Correct option: A.
$\frac{2 \pi}{3}$
(A)
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MCQ 651 Mark
$\cot ^{-1}(-x)=$
  • $-\cot ^{-1} x$
  • B
    $\cot ^{-1} x$
  • C
    $\pi+\cot ^{-1} x$
  • D
    $\pi-\cot ^{-1} x$
Answer
Correct option: A.
$-\cot ^{-1} x$
(A)
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MCQ 661 Mark
$3 \sec ^{-1} \frac{1}{x}-\sin ^{-1}\left(4 x^3-3 x\right)=$
  • A
    $\pi$
  • B
    $\frac{\pi}{2}$
  • $\frac{3 \pi}{2}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{3 \pi}{2}$
(C)
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MCQ 671 Mark
समीकरण $\sqrt{1+\cos 2 x}=\sqrt{2} \cos ^{-1}(\cos x)$ in $\left[\frac{\pi}{2}, \pi\right]$ के  वास्तविक हलों की संख्या है
  • $0$
  • B
    1
  • C
    2
  • D
    अनंत
Answer
Correct option: A.
$0$
A
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MCQ 681 Mark
व्यंजक $\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{5}}\right)$ का मान है
  • A
    $2+\sqrt{5}$
  • $\sqrt{5}-2$
  • C
    $\frac{\sqrt{5}+2}{2}$
  • D
    $5+\sqrt{2}$
Answer
Correct option: B.
$\sqrt{5}-2$
B
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MCQ 691 Mark
व्यंजक $2 \sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right)$ का मान है
  • A
    $\frac{\pi}{6}$
  • $\frac{5 \pi}{6}$
  • C
    $\frac{7 \pi}{6}$
  • D
    1
Answer
Correct option: B.
$\frac{5 \pi}{6}$
B
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MCQ 701 Mark
यदि $|x| \leq 1$, तब $2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ बराबर है
  • $4 \tan ^{-1} x$
  • B
    $0$
  • C
    $\frac{\pi}{2}$
  • D
    $\pi$
Answer
Correct option: A.
$4 \tan ^{-1} x$
A
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MCQ 711 Mark
यदि $\tan ^{-1} x+\tan ^{-1} y=\frac{4 \pi}{5}$, तो $\cot ^{-1} x+$$\cot ^{-1} y$ बराबर है
  • $\frac{\pi}{5}$
  • B
    $\frac{2 \pi}{5}$
  • C
    $\frac{3 \pi}{5}$
  • D
    $\pi$
Answer
Correct option: A.
$\frac{\pi}{5}$
A
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MCQ 721 Mark
यदि $\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\cos ^{-1}\left(\frac{1-a^2}{1+a^2}\right)$ $=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$ जहाँ $a, x \in] 0,1[$, तब x बराबर है
  • A
    $0$
  • B
    $\frac{a}{2}$
  • C
    a
  • $\frac{2 a}{1-a^2}$
Answer
Correct option: D.
$\frac{2 a}{1-a^2}$
D
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MCQ 731 Mark
यदि $\cos \left(\sin ^{-1} \frac{2}{5}+\cos ^{-1} x\right)=0$, तो x का मान है
  • A
    $\frac{1}{5}$
  • $\frac{2}{5}$
  • C
    $0$
  • D
    1
Answer
Correct option: B.
$\frac{2}{5}$
B
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MCQ 741 Mark
यदि $\cos ^{-1} x>\sin ^{-1} x$, हो तो
  • A
    $\frac{1}{\sqrt{2}} < x \leq 1$
  • B
    $0 \leq x<\frac{1}{\sqrt{2}}$
  • $-1 \leq x<\frac{1}{\sqrt{2}}$
  • D
    $x>0$
Answer
Correct option: C.
$-1 \leq x<\frac{1}{\sqrt{2}}$
C
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MCQ 751 Mark
यदि $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, तब$\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ बराबर है
  • A
    $0$
  • B
    1
  • 6
  • D
    12
Answer
Correct option: C.
6
C
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MCQ 761 Mark
यदि $3 \tan ^{-1} x+\cot ^{-1} x=\pi$, तब x बराबर है?
  • A
    $0$
  • 1
  • C
    -1
  • D
    $\frac{1}{2}$
Answer
Correct option: B.
1
B
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MCQ 771 Mark
निम्नलिखित में से कौन सा $\operatorname{cosec}^{-1} x$ की मुख्य शाखा है?
  • A
    $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$
  • B
    $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
  • C
    $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
  • $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
Answer
Correct option: D.
$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
D
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MCQ 781 Mark
निम्न में से कौन सा $\cos ^{-1} x$ की मुख्य शाखा है ?
  • A
    $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
  • B
    $(0, \pi)$
  • $[0, \pi]$
  • D
    $(0, \pi)-\left\{\frac{\pi}{2}\right\}$
Answer
Correct option: C.
$[0, \pi]$
C
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MCQ 791 Mark
The domain of the function $\cos ^{-1}(2 x-1)$ is
  • $[0,1]$
  • B
    $[-1,1]$
  • C
    $(-1,1)$
  • D
    $[0, \pi]$
Answer
Correct option: A.
$[0,1]$
A
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MCQ 801 Mark
$\sin \left[2 \tan ^{-1}(0.75)\right]$ का मान है
  • A
    $0.75$
  • B
    $1.5$
  • $0.96$
  • D
    $\sin 1.5$
Answer
Correct option: C.
$0.96$
C
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MCQ 811 Mark
$\sin ^{-1}\left[\cos \left(\frac{33 \pi}{5}\right)\right]$ का मान है-
  • A
    $\frac{3 \pi}{5}$
  • B
    $-\frac{7 \pi}{5}$
  • C
    $\frac{\pi}{10}$
  • $-\frac{\pi}{10}$
Answer
Correct option: D.
$-\frac{\pi}{10}$
D
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MCQ 821 Mark
$f(x)=\sin ^{-1} \sqrt{x-1}$ द्वारा परिभाषित फलन का प्रांत है
  • $[1,2]$
  • B
    $[-1,1]$
  • C
    $[0,1]$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$[1,2]$
A
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MCQ 831 Mark
$\cot \left[\cos ^{-1}\left(\frac{7}{25}\right)\right]$ का मान है
  • A
    $\frac{25}{24}$
  • B
    $\frac{25}{7}$
  • C
    $\frac{24}{25}$
  • $\frac{7}{24}$
Answer
Correct option: D.
$\frac{7}{24}$
D
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MCQ 841 Mark
$\cos ^{-1}\left(\cos \frac{3 \pi}{2}\right)$ का मान है
  • $\frac{\pi}{2}$
  • B
    $\frac{3 \pi}{2}$
  • C
    $\frac{5 \pi}{2}$
  • D
    $\frac{7 \pi}{2}$
Answer
Correct option: A.
$\frac{\pi}{2}$
A
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MCQ 851 Mark
$\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})=$
  • A
    $\pi$
  • B
    $0$
  • C
    $2 \sqrt{3}$
  • $-\frac{\pi}{2}$
Answer
Correct option: D.
$-\frac{\pi}{2}$
D
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MCQ 861 Mark
यदि $\sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}$, तब x बराबर है
  • A
    $0, \frac{1}{2}$
  • B
    $1, \frac{1}{2}$
  • $0$
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
$0$
C
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MCQ 871 Mark
$\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$ का मुख्य मान निम्न है:
  • A
    $\frac{-\pi}{5}$
  • B
    $\frac{\pi}{3}$
  • $\frac{5 \pi}{6}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{5 \pi}{6}$
C
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MCQ 881 Mark
$\tan ^{-1}(\sqrt{3})-\sec ^{-1}(-2)$ बराबर है
  • A
    $\pi$
  • $-\frac{\pi}{3}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{2 \pi}{3}$
Answer
Correct option: B.
$-\frac{\pi}{3}$
B
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MCQ 891 Mark
यदि $\sin ^{-1} x=y$, तब
  • A
    $0 \leq y \leq \pi$
  • $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
  • C
    $0 < v<\pi$
  • D
    $-\frac{\pi}{2}< y< \frac{\pi}{2}$
Answer
Correct option: B.
$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
B
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MCQ 901 Mark
$\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)=$
  • A
    $\frac{\pi}{2}$
  • B
    $\frac{\pi}{3}$
  • $\frac{\pi}{4}$
  • D
    $\frac{\pi}{4}$ या $\frac{3 \pi}{4}$
Answer
Correct option: C.
$\frac{\pi}{4}$
C
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MCQ 911 Mark
$\sin \left(\tan ^{-1} x\right) ;|x|<1$ बराबर है
  • A
    $\frac{x}{\sqrt{1-x^2}}$
  • B
    $\frac{1}{\sqrt{1-x^2}}$
  • C
    $\frac{1}{\sqrt{1+x^2}}$
  • $\frac{x}{\sqrt{1+x^2}}$
Answer
Correct option: D.
$\frac{x}{\sqrt{1+x^2}}$
D
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MCQ 921 Mark
$\sin \left\{\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right\}$ का मान है
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{2}$
  • 1
Answer
Correct option: D.
1
D
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MCQ 931 Mark
$\tan \left\{\frac{1}{2}\left(\tan ^{-1} x+\tan ^{-1} \frac{1}{x}\right)\right\}=$
  • 1
  • B
    $\sqrt{3}$
  • C
    $0$
  • D
    $\infty$
Answer
Correct option: A.
1
A
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MCQ 941 Mark
$\tan ^{-1}(\sqrt{3})-\cot ^{-1}(-\sqrt{3})=$
  • A
    $0$
  • $-\frac{\pi}{2}$
  • C
    $\pi$
  • D
    $\frac{\pi}{2}$
Answer
Correct option: B.
$-\frac{\pi}{2}$
B
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MCQ 951 Mark
$\tan ^{-1}(-\sqrt{3})=$
  • A
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{2 \pi}{3}$
  • $-\frac{\pi}{3}$
Answer
Correct option: D.
$-\frac{\pi}{3}$
D
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MCQ 961 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=$
  • A
    $\pi$
  • $\frac{\pi}{4}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{3}$
Answer
Correct option: B.
$\frac{\pi}{4}$
B
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MCQ 971 Mark
$\sin \left(\sin ^{-1} \frac{2 \pi}{3}\right)+\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)=$
  • A
    $\frac{17 \pi}{12}$
  • B
    $\frac{5}{12} \pi$
  • $\frac{\pi}{12}$
  • D
    $-\frac{\pi}{12}$
Answer
Correct option: C.
$\frac{\pi}{12}$
C
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MCQ 981 Mark
$\sin \left\{\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right\}=1, \Rightarrow x=$
  • A
    1
  • B
    $0$
  • C
    $\frac{4}{5}$
  • $\frac{1}{5}$
Answer
Correct option: D.
$\frac{1}{5}$
D
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MCQ 991 Mark
$\cot ^{-1}\left(\tan \frac{\pi}{7}\right)=$
  • A
    $\frac{\pi}{7}$
  • $\frac{5 \pi}{14}$
  • C
    $\frac{9 \pi}{14}$
  • D
    $\frac{3 \pi}{14}$
Answer
Correct option: B.
$\frac{5 \pi}{14}$
B
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MCQ 1001 Mark
$\cos ^{-1} x+\sec ^{-1} \frac{1}{x}=$
  • A
    $\frac{\pi}{2}$
  • $\cos ^{-1}\left(2 x^2-1\right)$
  • C
    $\cos ^{-1}\left(1-2 x^2\right)$
  • D
    $\cos ^{-1} 2 x$
Answer
Correct option: B.
$\cos ^{-1}\left(2 x^2-1\right)$
B
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MCQ 1011 Mark
$\cos ^{-1}\left(\cos \frac{8 \pi}{5}\right)=$
  • A
    $\frac{8 \pi}{5}$
  • $\frac{2 \pi}{5}$
  • C
    $\frac{\pi}{5}$
  • D
    $\frac{3 \pi}{5}$
Answer
Correct option: B.
$\frac{2 \pi}{5}$
B
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MCQ 1021 Mark
$x \in[-1,1], \sin ^{-1}(-x)=$
  • $-\sin ^{-1} x$
  • B
    $\sin ^{-1} x$
  • C
    $-\cos ^{-1} x$
  • D
    $\cos ^{-1} x$
Answer
Correct option: A.
$-\sin ^{-1} x$
A
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MCQ 1031 Mark
$x \in[-1,1], \cos ^{-1} x=$
  • A
    $\frac{\pi}{2}-\cot ^{-1} x$
  • $\frac{\pi}{2}-\sin ^{-1} x$
  • C
    $\frac{\pi}{2}-\tan ^{-1} x$
  • D
    $\frac{\pi}{2}-\sec ^{-1} x$
Answer
Correct option: B.
$\frac{\pi}{2}-\sin ^{-1} x$
B
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MCQ 1051 Mark
$\tan ^{-1} \sqrt{3}-\sec ^{-1}(-2)=$
  • $-\frac{\pi}{3}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{2 \pi}{3}$
  • D
    $\pi$
Answer
Correct option: A.
$-\frac{\pi}{3}$
A
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MCQ 1061 Mark
$\sin \left(\cot ^{-1} x\right)=$
  • A
    $\sqrt{1+x^2}$
  • B
    x
  • C
    $\left(1+x^2\right)^{-3 / 2}$
  • $\frac{1}{\sqrt{1+x^2}}$
Answer
Correct option: D.
$\frac{1}{\sqrt{1+x^2}}$
D
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MCQ 1071 Mark
$\operatorname{cosec}^{-1} x= ........... ; x \geq 1$ or $\leq-1$.
  • A
    $\sin ^{-1} x$
  • $\sin ^{-1} \frac{1}{x}$
  • C
    $\cos ^{-1} x$
  • D
    $\cos ^{-1} \frac{1}{x}$
Answer
Correct option: B.
$\sin ^{-1} \frac{1}{x}$
B
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MCQ 1091 Mark
$\cos ^{-1}\left(-\frac{1}{2}\right)=$
  • $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{6}$
  • D
    $\frac{\pi}{2}$
Answer
Correct option: A.
$\frac{2 \pi}{3}$
A
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MCQ 1101 Mark
$\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)=$
  • A
    $\frac{7 \pi}{6}$
  • $\frac{5 \pi}{6}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: B.
$\frac{5 \pi}{6}$
B
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MCQ 1111 Mark
$|x| \leq 1,2 \tan ^{-1} x=$
  • A
    $\tan ^{-1} 2 x$
  • $\sin ^{-1} \frac{2 x}{1+x^2}$
  • C
    $\cos ^{-1} \frac{2 x}{1+x^2}$
  • D
    $\tan ^{-1} \frac{2 x}{1+x^2}$
Answer
Correct option: B.
$\sin ^{-1} \frac{2 x}{1+x^2}$
B
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MCQ 1121 Mark
$x \in R$, $\operatorname{cosec}\left(\tan ^{-1} x+\cot ^{-1} x\right)=$
  • A
    $0$
  • 1
  • C
    $\frac{2}{\sqrt{3}}$
  • D
    2
Answer
Correct option: B.
1
B
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MCQ 1131 Mark
$x \in R, \cot ^{-1} x=$
  • A
    $\frac{\pi}{2}-\sin ^{-1} x$
  • B
    $\frac{\pi}{2}-\cos ^{-1} x$
  • $\frac{\pi}{2}-\tan ^{-1} x$
  • D
    $\frac{\pi}{2}-\sec ^{-1} x$
Answer
Correct option: C.
$\frac{\pi}{2}-\tan ^{-1} x$
C
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MCQ 1141 Mark
$x \in[-1,1], \sin \left[2\left(\sin ^{-1} x+\cos ^{-1} x\right)\right]=$
  • $0$
  • B
    1
  • C
    -1
  • D
    $\frac{1}{2}$
Answer
Correct option: A.
$0$
A
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MCQ 1151 Mark
$|x| \geq 1, \tan \left[\frac{2}{3}\left(\tan ^{-1} x+\cot ^{-1} x\right)\right]=$
  • A
    $\frac{1}{\sqrt{3}}$
  • $\sqrt{3}$
  • C
    $0$
  • D
    1
Answer
Correct option: B.
$\sqrt{3}$
B
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MCQ 1161 Mark
$\tan ^{-1}\left(\frac{x+y}{1-x y}\right)=$
  • A
    $\sin ^{-1}(x+y)$
  • B
    $\cos ^{-1}(x+y)$
  • C
    $\tan ^{-1}(x+y)$
  • $\tan ^{-1} x+\tan ^{-1} y$
Answer
Correct option: D.
$\tan ^{-1} x+\tan ^{-1} y$
D
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MCQ 1171 Mark
$\sin \left(\sin ^{-1} \frac{1}{2}\right)=$
  • A
    1
  • $\frac{1}{2}$
  • C
    $\frac{\sqrt{3}}{2}$
  • D
    $0$
Answer
Correct option: B.
$\frac{1}{2}$
B
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MCQ 1181 Mark
$\sin ^{-1} x+\sin ^{-1} y=$
  • A
    $\sin ^{-1}\left\{x \sqrt{1-y^2}-y \sqrt{1-x^2}\right\}$
  • $\sin ^{-1}\left\{x \sqrt{1-y^2}+y \sqrt{1-x^2}\right\}$
  • C
    $\sin ^{-1}\left\{x \sqrt{1+y^2}+y \sqrt{1+x^2}\right\}$
  • D
    $\sin ^{-1}\left\{x \sqrt{1+y^2}-y \sqrt{1+x^2}\right\}$
Answer
Correct option: B.
$\sin ^{-1}\left\{x \sqrt{1-y^2}+y \sqrt{1-x^2}\right\}$
B
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MCQ 1191 Mark
यदि $x=\frac{24}{25}$, तब $\sin \left(3 \sin ^{-1} x+2 \cos ^{-1} x\right)$ का मान है
  • A
    $\frac{7}{25}$
  • B
    $\frac{-7}{25}$
  • $\frac{-24}{25}$
  • D
    $\frac{24}{25}$
Answer
Correct option: C.
$\frac{-24}{25}$
C
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MCQ 1201 Mark
$\tan ^{-1} \frac{4}{3}+\tan ^{-1} \frac{1}{7}=$
  • $\tan ^{-1} \frac{31}{17}$
  • B
    $\tan ^{-1} \frac{31}{21}$
  • C
    $\tan ^{-1} \frac{12}{19}$
  • D
    $\tan ^{-1} \frac{3}{4}$
Answer
Correct option: A.
$\tan ^{-1} \frac{31}{17}$
A
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MCQ 1211 Mark
$\cos ^{-1} \frac{4}{5}-\cos ^{-1} \frac{60}{61}=$
  • $\cos ^{-1} \frac{273}{305}$
  • B
    $\cos ^{-1} \frac{240}{305}$
  • C
    $\frac{\pi}{2}$
  • D
    $\cos ^{-1} \frac{57}{305}$
Answer
Correct option: A.
$\cos ^{-1} \frac{273}{305}$
A
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MCQ 1221 Mark
$2 \tan ^{-1} \frac{1}{9}=$
  • $\tan ^{-1} \frac{9}{40}$
  • B
    $\tan ^{-1} \frac{2}{9}$
  • C
    $\tan ^{-1} \frac{1}{81}$
  • D
    $\tan ^{-1} \frac{5}{9}$
Answer
Correct option: A.
$\tan ^{-1} \frac{9}{40}$
A
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MCQ 1231 Mark
$\tan \left[\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{13}\right]=$
  • $\frac{2}{9}$
  • B
    $\frac{9}{2}$
  • C
    $\frac{7}{9}$
  • D
    $\frac{9}{7}$
Answer
Correct option: A.
$\frac{2}{9}$
A
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MCQ 1241 Mark
$\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{12}{13}=$
  • A
    $\sin ^{-1} \frac{36}{65}$
  • $\sin ^{-1} \frac{63}{65}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: B.
$\sin ^{-1} \frac{63}{65}$
B
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MCQ 1251 Mark
$\operatorname{cosec}^{-1}(2)$ का मुख्य मान है
  • A
    $\frac{\pi}{3}$
  • $\frac{\pi}{6}$
  • C
    $\frac{2 \pi}{3}$
  • D
    $\frac{5 \pi}{6}$
Answer
Correct option: B.
$\frac{\pi}{6}$
B
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MCQ 1261 Mark
If $x=\frac{1}{5}$, तब $\cos \left(\cos ^{-1} x+2 \sin ^{-1} x\right)$ का मान है-
  • A
    $\frac{1}{5}$
  • $-\frac{1}{5}$
  • C
    $\frac{\sqrt{24}}{5}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$-\frac{1}{5}$
B
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MCQ 1271 Mark
$2 \tan ^{-1}\left(\frac{1}{2}\right)=$
  • A
    $\tan ^{-1}\left(\frac{3}{4}\right)$
  • $\tan ^{-1}\left(\frac{4}{3}\right)$
  • C
    $\tan ^{-1}\left(\frac{7}{12}\right)$
  • D
    $\tan ^{-1}\left(\frac{12}{7}\right)$
Answer
Correct option: B.
$\tan ^{-1}\left(\frac{4}{3}\right)$
B
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MCQ 1281 Mark
यदि $x \in[-1,1]$, तब $\sin ^{-1}(-x)=$
  • $-\sin ^{-1} x$
  • B
    $\sin ^{-1} x$
  • C
    $\sin x$
  • D
    $\cos ^{-1} x$
Answer
Correct option: A.
$-\sin ^{-1} x$
A
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MCQ 1291 Mark
यदि $|x| \geq 1$, तब $\operatorname{cosec}^{-1}(-x)=$
  • A
    $\operatorname{cosec}^{-1} x$
  • $-\operatorname{cosec}^{-1} x$
  • C
    $\operatorname{cosec} x$
  • D
    $\sin x$
Answer
Correct option: B.
$-\operatorname{cosec}^{-1} x$
B
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MCQ 1301 Mark
$\tan ^{-1}\left(\frac{-1}{\sqrt{3}}\right)=$
  • A
    $\frac{\pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $-\frac{\pi}{3}$
  • $-\frac{\pi}{6}$
Answer
Correct option: D.
$-\frac{\pi}{6}$
D
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MCQ 1311 Mark
$\cot ^{-1} \frac{1}{x}=\ldots \ldots .(x>0)$
  • A
    $-\cot ^{-1} x$
  • B
    $\tan ^{-1} \frac{1}{x}$
  • $\tan ^{-1} x$
  • D
    $\cot ^{-1} x$
Answer
Correct option: C.
$\tan ^{-1} x$
C
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MCQ 1321 Mark
$\cos \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)=$
  • A
    1
  • B
    -1
  • $0$
  • D
    $\frac{1}{\sqrt{2}}$
Answer
Correct option: C.
$0$
C
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MCQ 1331 Mark
$\cos ^{-1}(2 x)+\sin ^{-1}(2 x)=\ldots \ldots \ldots . .2 x \in[-1,1]$
  • $\frac{\pi}{2}$
  • B
    $\frac{\pi}{4}$
  • C
    $\pi$
  • D
    $0$
Answer
Correct option: A.
$\frac{\pi}{2}$
A
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MCQ 1341 Mark
$3 \sin ^{-1} x=\ldots \ldots \ldots \ldots,|x| \leq \frac{1}{2}$
  • A
    $\sin ^{-1}\left(4 x^3-3 x\right)$
  • B
    $\sin ^{-1}\left(3 x+4 x^3\right)$
  • $\sin ^{-1}\left(3 x-4 x^3\right)$
  • D
    $\sin ^{-1}\left(3 x^3-4 x\right)$
Answer
Correct option: C.
$\sin ^{-1}\left(3 x-4 x^3\right)$
C
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MCQ 1351 Mark
$\tan ^{-1} 1+\tan ^{-1} \frac{1}{3}=$ ?
  • $\tan ^{-1} 2$
  • B
    $\tan ^{-1} 3$
  • C
    $\tan ^{-1} \frac{4}{3}$
  • D
    $\tan ^{-1} \frac{2}{3}$
Answer
Correct option: A.
$\tan ^{-1} 2$
A
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MCQ 1361 Mark
$\cot \left(\tan ^{-1} x+\cot ^{-1} x\right)=?$
  • $0$
  • B
    1
  • C
    $\frac{1}{2}$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: A.
$0$
A
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MCQ 1371 Mark
यदि $x \geq 1$ or $x \leq-1$, तब $\sin ^{-1} \frac{1}{x}=$
  • A
    $\sin ^{-1} x$
  • B
    $\cos ^{-1} x$
  • $\operatorname{cosec}^{-1} x$
  • D
    $\sin x$
Answer
Correct option: C.
$\operatorname{cosec}^{-1} x$
C
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MCQ 1381 Mark
यदि $-1< x<1$, तब $2 \tan ^{-1} x=$
  • A
    $\tan ^{-1} 2 x$
  • $\tan ^{-1} \frac{2 x}{1-x^2}$
  • C
    $\tan ^{-1} \frac{2 x}{1+x^2}$
  • D
    $\cot ^{-1} \frac{2}{x}$
Answer
Correct option: B.
$\tan ^{-1} \frac{2 x}{1-x^2}$
B
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MCQ 1391 Mark
$\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=?$
  • $\frac{\pi}{4}$
  • B
    $-\frac{\pi}{4}$
  • C
    $\frac{\pi}{2}$
  • D
    $-\frac{\pi}{2}$
Answer
Correct option: A.
$\frac{\pi}{4}$
A
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MCQ 1401 Mark
$3 \sec ^{-1} \frac{1}{x}-\sin ^{-1}\left(4 x^3-3 x\right)=$
  • A
    $\pi$
  • B
    $\frac{\pi}{2}$
  • $\frac{3 \pi}{2}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{3 \pi}{2}$
C
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MCQ 1411 Mark
$\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$ का मान है
  • A
    $\frac{\pi}{4}$
  • $\frac{3 \pi}{4}$
  • C
    $-\frac{\pi}{4}$
  • D
    $\frac{\pi}{2}$
Answer
Correct option: B.
$\frac{3 \pi}{4}$
B
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MCQ 1421 Mark
$\cos ^{-1}\left(\cos \frac{8 \pi}{5}\right)=$
  • A
    $\frac{8 \pi}{5}$
  • B
    $\frac{12 \pi}{5}$
  • $\frac{2 \pi}{5}$
  • D
    $\frac{4 \pi}{5}$
Answer
Correct option: C.
$\frac{2 \pi}{5}$
C
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MCQ 1431 Mark
$\cos ^{-1}(2 x-1)=$
  • A
    $2 \cos ^{-1} x$
  • B
    $\cos ^{-1} \sqrt{x}$
  • $2 \cos ^{-1} \sqrt{x}$
  • D
    ) इनमें से कोई नहीं
Answer
Correct option: C.
$2 \cos ^{-1} \sqrt{x}$
C
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MCQ 1441 Mark
$2 \cot ^{-1} 3+\cot ^{-1} 7=$
  • A
    $\frac{\pi}{2}$
  • $\frac{\pi}{4}$
  • C
    $\pi$
  • D
    $\frac{\pi}{6}$
Answer
Correct option: B.
$\frac{\pi}{4}$
B
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MCQ 1451 Mark
$\tan ^{-1}(1)=$............?
  • $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{8}$
Answer
Correct option: A.
$\frac{\pi}{4}$
A
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MCQ 1461 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{4}=\ldots \ldots$.
  • A
    $\tan ^{-1} \frac{3}{2}$
  • $\tan ^{-1} \frac{6}{7}$
  • C
    $\tan ^{-1} \frac{5}{6}$
  • D
    $\tan ^{-1} \frac{1}{2}$
Answer
Correct option: B.
$\tan ^{-1} \frac{6}{7}$
B
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MCQ 1471 Mark
$\sec ^2\left(\tan ^{-1} 5\right)+\operatorname{cosec}^2\left(\cot ^{-1} 5\right)=$
  • A
    10
  • B
    50
  • C
    51
  • 52
Answer
Correct option: D.
52
D
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MCQ 1481 Mark
यदि $x \in R$, तब $\tan ^{-1} x+\cot ^{-1} x=$
  • $\frac{\pi}{2}$
  • B
    $\pi$
  • C
    $-\frac{\pi}{2}$
  • D
    $2 \pi$
Answer
Correct option: A.
$\frac{\pi}{2}$
A
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MCQ 1491 Mark
यदि $|x| \geq 1$, तब $\sec ^{-1}(-x)=$
  • $\pi-\sec ^{-1} x$
  • B
    $\pi+\sec ^{-1} x$
  • C
    $\sec ^{-1} x$
  • D
    $-\sec ^{-1} x$
Answer
Correct option: A.
$\pi-\sec ^{-1} x$
A
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MCQ 1501 Mark
$\tan ^{-1} \frac{2 x}{1-x^2}=$
  • A
    $2 \sin ^{-1} x$
  • B
    $\sin ^{-1} 2 x$
  • C
    $\tan ^{-1} 2 x$
  • $2 \tan ^{-1} x$
Answer
Correct option: D.
$2 \tan ^{-1} x$
D
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MCQ 1511 Mark
$\cos ^{-1}\left(\frac{-1}{2}\right)$ का मुख्य मान है
  • A
    $\frac{-\pi}{3}$
  • $\frac{2 \pi}{3}$
  • C
    $\frac{4 \pi}{3}$
  • D
    $\frac{\pi}{3}$
Answer
Correct option: B.
$\frac{2 \pi}{3}$
B
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MCQ 1521 Mark
$\cos ^{-1} \frac{1-x^2}{1+x^2}=$
  • A
    $2 \cos ^{-1} x$
  • B
    $2 \sin ^{-1} x$
  • $2 \tan ^{-1} x$
  • D
    $\cos ^{-1} 2 x$
Answer
Correct option: C.
$2 \tan ^{-1} x$
C
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MCQ 1531 Mark
$\tan ^{-1} x=$
  • A
    $\cot ^{-1} x$
  • B
    $\frac{1}{\cot ^{-1} x}$
  • $\cot ^{-1} \frac{1}{x}$
  • D
    $-\cot ^{-1} x$
Answer
Correct option: C.
$\cot ^{-1} \frac{1}{x}$
C
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MCQ 1541 Mark
$\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ का मुख्य मान है-
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{\pi}{4}$
  • $\frac{\pi}{3}$
Answer
Correct option: D.
$\frac{\pi}{3}$
D
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MCQ 1551 Mark
$\sin \left(\sin ^{-1} \frac{1}{2}+\cos ^{-1} \frac{1}{2}\right)$ का मान है
  • A
    $0$
  • 1
  • C
    -1
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
1
B
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MCQ 1561 Mark
$\cot ^{-1}\left(\tan \frac{\pi}{7}\right)$ का मुख्य मान ज्ञात करें।
  • A
    $\frac{7}{\pi}$
  • $\frac{5 \pi}{14}$
  • C
    $\frac{\pi}{14}$
  • D
    $\frac{3 \pi}{14}$
Answer
Correct option: B.
$\frac{5 \pi}{14}$
B
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MCQ 1571 Mark
$\sin ^{-1}\left[\sin \left(\frac{2 \pi}{3}\right)\right]$ का मुख्य मान निम्न है:
  • A
    $\frac{-2 \pi}{3}$
  • $\frac{\pi}{3}$
  • C
    $\frac{4 \pi}{3}$
  • D
    $\frac{5 \pi}{3}$
Answer
Correct option: B.
$\frac{\pi}{3}$
B
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MCQ 1581 Mark
$\sin \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)=$
  • 1
  • B
    -1
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{3}$
Answer
Correct option: A.
1
A
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MCQ 1591 Mark
$2 \tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{7}=$
  • A
    $\tan ^{-1}\left(\frac{49}{29}\right)$
  • B
    $\frac{\pi}{2}$
  • C
    $0$
  • $\frac{\pi}{4}$
Answer
Correct option: D.
$\frac{\pi}{4}$
D
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MCQ 1601 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{2}{11}=\tan ^{-1} a$ तब $a=$ ?
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • $\frac{3}{4}$
  • D
    1
Answer
Correct option: C.
$\frac{3}{4}$
C
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MCQ 1611 Mark
यदि $x \neq 0$ तब $\cos \left(\tan ^{-1} x+\cot ^{-1} x\right)=?$
  • A
    -1
  • B
    1
  • $0$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$0$
C
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MCQ 1621 Mark
यदि $x \in R$, तब $\tan \left(\tan ^{-1} x\right)=$
  • A
    $\frac{1}{x}$
  • B
    $x^2$
  • X
  • D
    $\frac{1}{x^2}$
Answer
Correct option: C.
X
C
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MCQ 1631 Mark
यदि $x \in R$ तब $\tan ^{-1}(-x)=$
  • $-\tan ^{-1} x$
  • B
    $\tan x$
  • C
    $\cot x$
  • D
    $\tan ^{-1} x$
Answer
Correct option: A.
$-\tan ^{-1} x$
A
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MCQ 1641 Mark
यदि $x \in R$, तब $\cot \left(\cot ^{-1} x\right)=$
  • X
  • B
    $\frac{1}{x}$
  • C
    $\frac{1}{x^2}$
  • D
    $x^2$
Answer
Correct option: A.
X
A
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MCQ 1651 Mark
यदि $x \in R-[-1,1]$ तब $\sec \left(\sec ^{-1} x\right)=$
  • x
  • B
    $\frac{1}{x}$
  • C
    $x^2$
  • D
    $\frac{1}{x^2}$
Answer
Correct option: A.
x
A
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MCQ 1661 Mark
यदि $x \in R-[-1,1]$, तब $\operatorname{cosec}\left(\operatorname{cosec}^{-1} x\right)$
  • A
    $\frac{1}{x}$
  • x
  • C
    $x^2$
  • D
    $\frac{1}{x^2}$
Answer
Correct option: B.
x
B
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MCQ 1671 Mark
यदि $x \in[-1,1]$, तब $\sin \left(\sin ^{-1} x\right)=$
  • A
    $\frac{1}{x}$
  • x
  • C
    $x^2$
  • D
    $\frac{1}{x^2}$
Answer
Correct option: B.
x
B
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MCQ 1681 Mark
यदि $x \in[-1,1]$, तब $\sin ^{-1} x+\cos ^{-1} x=$
  • $\frac{\pi}{2}$
  • B
    $\pi$
  • C
    $-\pi$
  • D
    $-\frac{\pi}{2}$
Answer
Correct option: A.
$\frac{\pi}{2}$
A
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MCQ 1691 Mark
यदि $x \in[-1,1]$, तब $\cos \left(\cos ^{-1} x\right)=$
  • x
  • B
    $\frac{1}{x}$
  • C
    $x^2$
  • D
    $\frac{1}{x^2}$
Answer
Correct option: A.
x
A
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MCQ 1701 Mark
यदि $x \in[-1,1]$, तब $\cos ^{-1}(-x)=$
  • A
    $\pi+\cos ^{-1} x$
  • $\pi-\cos ^{-1} x$
  • C
    $\cos ^{-1} x$
  • D
    $\cos x$
Answer
Correct option: B.
$\pi-\cos ^{-1} x$
B
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MCQ 1711 Mark
यदि $x \in] 0, \pi[$, तब $\cot ^{-1}(\cot x)=$
  • x
  • B
    $\frac{1}{x}$
  • C
    $x^3$
  • D
    $x^2$
Answer
Correct option: A.
x
A
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MCQ 1721 Mark
यदि $x \in[0, \pi]$, तब $\cos ^{-1}(\cos x)=$
  • A
    $\frac{1}{x}$
  • x
  • C
    $\frac{1}{x^2}$
  • D
    $x^2$
Answer
Correct option: B.
x
B
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MCQ 1731 Mark
यदि $x \in[0, \pi]-\left\{\frac{\pi}{2}\right\}$, तब $\sec ^{-1}(\sec x)=$
  • x
  • B
    $x^2$
  • C
    $x^3$
  • D
    $\frac{1}{x}$
Answer
Correct option: A.
x
A
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MCQ 1741 Mark
यदि $x>0, y>0, x y<1$ तब $\tan ^{-1} x+\tan ^{-1} y=$
  • A
    $\tan ^{-1}(x+y)$
  • $\tan ^{-1} \frac{x+y}{1-x y}$
  • C
    $\tan ^{-1}(x-y)$
  • D
    $\sin ^{-1}(x+y)$
Answer
Correct option: B.
$\tan ^{-1} \frac{x+y}{1-x y}$
B
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MCQ 1751 Mark
यदि $|x| \geq 1$, तब $\operatorname{cosec}^{-1} x+\sec ^{-1} x=$
  • A
    $\pi$
  • $\frac{\pi}{2}$
  • C
    $-\frac{\pi}{2}$
  • D
    $2 \pi$
Answer
Correct option: B.
$\frac{\pi}{2}$
B
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MCQ 1761 Mark
यदि $x \geq 1$ or $x \leq-1$, तब $\cos ^{-1} \frac{1}{x}=$
  • A
    $\cos ^{-1} x$
  • $\sec ^{-1} x$
  • C
    $\sec x$
  • D
    $\cos x$
Answer
Correct option: B.
$\sec ^{-1} x$
B
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MCQ 1771 Mark
यदि $\tan ^{-1} x=\frac{\pi}{4}-\tan ^{-1} \frac{1}{3}$, तब $x=$ ?
  • $\frac{1}{2}$
  • B
    $\frac{1}{4}$
  • C
    $\frac{1}{6}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{1}{2}$
A
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MCQ 1781 Mark
यदि $\tan ^{-1}\left(\frac{a}{x}\right)+\tan ^{-1}\left(\frac{b}{x}\right)=\frac{\pi}{2}$, तब x =
  • $\sqrt{a b}$
  • B
    $\sqrt{2 a b}$
  • C
    $2 a b$
  • D
    ab
Answer
Correct option: A.
$\sqrt{a b}$
A
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MCQ 1791 Mark
यदि $\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$, तब $x=$ ?
  • A
    1
  • B
    -1
  • $0$
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
$0$
C
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MCQ 1801 Mark
यदि $\sin \left[\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right]=1$ तब x होगा :
  • A
    1
  • B
    $0$
  • C
    $\frac{4}{5}$
  • $\frac{1}{5}$
Answer
Correct option: D.
$\frac{1}{5}$
D
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MCQ 1811 Mark
यदि $\sin \left(\frac{1}{2} \cos ^{-1} x\right)=1$, तब $x=$
  • A
    $0$
  • B
    1
  • -1
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
-1
C
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MCQ 1821 Mark
यदि $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{\pi}{2}$, तब $x^2+y^2$$+z^2+2 x y z=$
  • A
    $0$
  • 1
  • C
    -1
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
1
B
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MCQ 1831 Mark
यदि $\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}$, तब बराबर है
  • A
    $\frac{-1}{2}$
  • $\frac{\sqrt{3}}{2}$
  • C
    $\frac{1}{2}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\frac{\sqrt{3}}{2}$
B
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MCQ 1841 Mark
यदि $\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\sin ^{-1}\left(\frac{2 b}{1+b^2}\right)=2 \tan ^{-1} x$, तब $x=$
  • A
    $\frac{a-b}{1+a b}$
  • B
    $\frac{b}{1+a b}$
  • C
    $\frac{b}{1-a b}$
  • $\frac{a+b}{1-a b}$
Answer
Correct option: D.
$\frac{a+b}{1-a b}$
D
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MCQ 1851 Mark
यदि $\sin ^{-1}\left(\frac{1-x^2}{1+x^2}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)=\frac{\pi}{3}$, तब x बराबर है
  • A
    $\sqrt{3}$
  • $\frac{1}{\sqrt{3}}$
  • C
    $0$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\frac{1}{\sqrt{3}}$
B
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MCQ 1861 Mark
यदि $\cot ^{-1}\left(-\frac{1}{5}\right)=x$, तब $\sin x=?$
  • A
    $\frac{1}{\sqrt{26}}$
  • $\frac{5}{\sqrt{26}}$
  • C
    $\frac{1}{\sqrt{24}}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\frac{5}{\sqrt{26}}$
B
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MCQ 1871 Mark
यदि $\cos ^{-1} p+\cos ^{-1} q+\cos ^{-1} r=\pi$, तब $p^2+q^2+r^2+2 p q r=$
  • A
    3
  • 1
  • C
    -1
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
1
B
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MCQ 1881 Mark
यदि $\cos ^{-1} \frac{1}{x}=\theta$, तब $\tan \theta=$
  • A
    $\frac{1}{\sqrt{x^2-1}}$
  • $\sqrt{x^2-1}$
  • C
    $\sqrt{1-x^2}$
  • D
    $\sqrt{x^2+1}$
Answer
Correct option: B.
$\sqrt{x^2-1}$
B
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MCQ 1891 Mark
यदि $A=\tan ^{-1}$ तब sin 2A का मान निम्न है:
  • A
    $\frac{2 x}{1-x^2}$
  • B
    $\frac{2 x}{\sqrt{1-x^2}}$
  • $\frac{2 x}{1+x^2}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{2 x}{1+x^2}$
C
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MCQ 1901 Mark
x का वह मान जिसके लिए $\sin \left[\cot ^{-1}(x+1)\right]=\cos \left(\tan ^{-1} x\right)$ है
  • $-\frac{1}{2}$
  • B
    $0$
  • C
    $\frac{1}{2}$
  • D
    1
Answer
Correct option: A.
$-\frac{1}{2}$
A
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MCQ 1911 Mark
$\tan \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)$ का मान है
  • $\frac{17}{6}$
  • B
    34
  • C
    18
  • D
    -18
Answer
Correct option: A.
$\frac{17}{6}$
A
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MCQ 1921 Mark
$\tan \left[\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right]$ का मान निम्न है :
  • A
    $\frac{6}{17}$
  • B
    $\frac{7}{16}$
  • $\frac{17}{6}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{17}{6}$
C
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MCQ 1931 Mark
$\tan \frac{1}{2}\left(\cos ^{-1} \frac{\sqrt{5}}{3}\right)=?$
  • $\frac{3-\sqrt{5}}{2}$
  • B
    $\frac{3+\sqrt{5}}{2}$
  • C
    $\frac{5-\sqrt{3}}{2}$
  • D
    $\frac{5+\sqrt{3}}{2}$
Answer
Correct option: A.
$\frac{3-\sqrt{5}}{2}$
A
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MCQ 1941 Mark
$\tan ^{-1}(-\sqrt{3})$ का मुख्य मान है
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{4 \pi}{3}$
  • $\frac{-\pi}{3}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{-\pi}{3}$
C
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MCQ 1951 Mark
$\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ का मुख्य मान निकालें।
  • A
    $\frac{7 \pi}{6}$
  • $\frac{\pi}{6}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: B.
$\frac{\pi}{6}$
B
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MCQ 1961 Mark
$\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)$ का मान है-
  • A
    $\frac{3 \pi}{4}$
  • B
    $\frac{\pi}{4}$
  • $-\frac{\pi}{4}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$-\frac{\pi}{4}$
C
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MCQ 1971 Mark
$\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]=?$
  • A
    $\frac{\pi}{3}$
  • $\frac{\pi}{4}$
  • C
    $\frac{3 \pi}{4}$
  • D
    $\frac{2 \pi}{3}$
Answer
Correct option: B.
$\frac{\pi}{4}$
B
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MCQ 1981 Mark
$\tan ^{-1} \frac{4 \sqrt{x}}{2-2 x}=$
  • $2 \tan ^{-1} \sqrt{x}$
  • B
    $\cos ^{-1} \frac{1-x}{1+x}$
  • C
    $\sin ^{-1} \frac{2 x}{1+x^2}$
  • D
    $\sqrt{2} \tan ^{-1} x$
Answer
Correct option: A.
$2 \tan ^{-1} \sqrt{x}$
A
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MCQ 1991 Mark
$\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}$ का मान निम्न है :
  • A
    $0$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{6}$
  • $\frac{\pi}{4}$
Answer
Correct option: D.
$\frac{\pi}{4}$
D
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MCQ 2001 Mark
$\tan ^{-1}(-2)+\tan ^{-1}(-3)$ का मान बराबर है-
  • A
    $\frac{5 \pi}{4}$
  • B
    $\frac{3 \pi}{4}$
  • $-\frac{3 \pi}{4}$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: C.
$-\frac{3 \pi}{4}$
C
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MCQ 2011 Mark
$\tan ^{-1} 2+\tan ^{-1} 3$ का मान निम्न है
  • A
    $\frac{-\pi}{4}$
  • B
    $\frac{-3 \pi}{4}$
  • C
    $\frac{\pi}{4}$
  • $\frac{3 \pi}{4}$
Answer
Correct option: D.
$\frac{3 \pi}{4}$
D
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MCQ 2021 Mark
$\tan ^{-1} 1+\tan ^{-1} 2+\tan ^{-1} 3=$
  • A
    $\frac{\pi}{3}$
  • B
    $\frac{\pi}{2}$
  • $\pi$
  • D
    $\frac{\pi}{4}$
Answer
Correct option: C.
$\pi$
C
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MCQ 2031 Mark
$\tan ^{-1}(-1)+\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)=?$
  • $\frac{\pi}{2}$
  • B
    $\pi$
  • C
    $\frac{3 \pi}{2}$
  • D
    $\frac{2 \pi}{3}$
Answer
Correct option: A.
$\frac{\pi}{2}$
A
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MCQ 2041 Mark
$\sin \left[\tan ^{-1} \frac{1-x^2}{2 x}+\cos ^{-1} \frac{1-x^2}{1+x^2}\right]=$
  • A
    $0$
  • 1
  • C
    $\frac{1}{\sqrt{2}}$
  • D
    $\sqrt{2}$
Answer
Correct option: B.
1
B
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MCQ 2051 Mark
$\sin \left(\frac{1}{2} \cos ^{-1} \frac{4}{5}\right)=$
  • A
    $\frac{1}{\sqrt{5}}$
  • B
    $\frac{2}{\sqrt{5}}$
  • $\frac{1}{\sqrt{10}}$
  • D
    $\frac{2}{\sqrt{10}}$
Answer
Correct option: C.
$\frac{1}{\sqrt{10}}$
C
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MCQ 2061 Mark
$\sin \left(\cot ^{-1} x\right)$ का मान निम्न है:
  • A
    $\sqrt{1+x^2}$
  • B
    x
  • C
    $\left(1+x^2\right)^{\frac{-2}{2}}$
  • $\left(1+x^2\right)^{\frac{-1}{2}}$
Answer
Correct option: D.
$\left(1+x^2\right)^{\frac{-1}{2}}$
D
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MCQ 2071 Mark
$\sin \left(\cos ^{-1} \frac{3}{5}\right)=$
  • A
    $\frac{2}{5}$
  • $\frac{4}{5}$
  • C
    $\frac{-2}{5}$
  • D
    $\frac{3}{5}$
Answer
Correct option: B.
$\frac{4}{5}$
B
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MCQ 2081 Mark
$\sin \left[2 \tan ^{-1} \frac{5}{8}\right]$
  • A
    $\frac{25}{64}$
  • $\frac{80}{89}$
  • C
    $\frac{75}{128}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\frac{80}{89}$
B
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MCQ 2091 Mark
$\sin \left[2 \sin ^{-1} \frac{4}{5}\right]=$
  • A
    $\frac{12}{25}$
  • B
    $\frac{16}{25}$
  • $\frac{24}{25}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$\frac{24}{25}$
C
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MCQ 2101 Mark
$\sin ^{-1} \tan \left(-\frac{5 \pi}{4}\right)$ का मुख्य मान है-
  • A
    $\frac{\pi}{4}$
  • B
    $-\frac{\pi}{4}$
  • C
    $\frac{\pi}{2}$
  • $-\frac{\pi}{2}$
Answer
Correct option: D.
$-\frac{\pi}{2}$
D
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MCQ 2111 Mark
$\sin ^{-1}\left(\sin \frac{7 \pi}{6}\right)=$
  • A
    $\frac{7 \pi}{6}$
  • B
    $\frac{\pi}{6}$
  • $-\frac{\pi}{6}$
  • D
    $\frac{5 \pi}{6}$
Answer
Correct option: C.
$-\frac{\pi}{6}$
C
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MCQ 2121 Mark
$\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$ का मुख्य मान निम्न है:
  • A
    $\frac{-2 \pi}{3}$
  • $\frac{-\pi}{3}$
  • C
    $\frac{4 \pi}{3}$
  • D
    $\frac{5 \pi}{3}$
Answer
Correct option: B.
$\frac{-\pi}{3}$
B
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MCQ 2131 Mark
$\sin ^{-1}\left(\frac{-1}{2}\right)$ का मुख्य मान है
  • $\frac{-\pi}{6}$
  • B
    $\frac{5 \pi}{6}$
  • C
    $\frac{7 \pi}{6}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{-\pi}{6}$
A
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MCQ 2141 Mark
$\sin ^{-1}\left(-\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{-\sqrt{3}}{2}\right)=?$
  • A
    $\frac{\pi}{2}$
  • B
    $\pi$
  • $\frac{3 \pi}{2}$
  • D
    $2 \pi$
Answer
Correct option: C.
$\frac{3 \pi}{2}$
C
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MCQ 2151 Mark
$\sec ^{-1}\left(\sec \frac{8 \pi}{5}\right)$ का मान है-
  • $\frac{2 \pi}{5}$
  • B
    $\frac{3 \pi}{5}$
  • C
    $\frac{8 \pi}{5}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{2 \pi}{5}$
A
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MCQ 2161 Mark
$\sec ^{-1}\left(\frac{-2}{\sqrt{3}}\right)$ का मुख्य मान है-
  • A
    $\frac{\pi}{6}$
  • B
    $-\frac{\pi}{6}$
  • $\frac{5 \pi}{6}$
  • D
    $\frac{7 \pi}{5}$
Answer
Correct option: C.
$\frac{5 \pi}{6}$
C
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MCQ 2171 Mark
$\operatorname{cosec}^{-1}(-\sqrt{2})$ का मुख्य मान है
  • $\frac{-\pi}{4}$
  • B
    $\frac{3 \pi}{4}$
  • C
    $\frac{5 \pi}{4}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{-\pi}{4}$
A
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MCQ 2181 Mark
$\operatorname{cosec}^{-1}(-2)$ का मुख्य मान है
  • A
    $-\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{2 \pi}{3}$
  • $-\frac{\pi}{6}$
Answer
Correct option: D.
$-\frac{\pi}{6}$
D
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MCQ 2191 Mark
$\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)=?$
  • A
    $0$
  • B
    $\frac{2 \pi}{3}$
  • $\frac{\pi}{2}$
  • D
    $\pi$
Answer
Correct option: C.
$\frac{\pi}{2}$
C
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MCQ 2201 Mark
$\cot ^{-1}(-\sqrt{3})$ का मुख्य गान है-
  • A
    $-\frac{\pi}{6}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{7 \pi}{6}$
  • $\frac{5 \pi}{6}$
Answer
Correct option: D.
$\frac{5 \pi}{6}$
D
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MCQ 2211 Mark
$\cot ^{-1} \frac{a b+1}{a-b}+\cot ^{-1} \frac{b c+1}{b-c}+\cot ^{-1} \frac{c a+1}{c-a}=$
  • A
    $-\pi$
  • B
    $\pi$
  • $0$
  • D
    इनमें से कोई नहीं
Answer
Correct option: C.
$0$
C
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MCQ 2221 Mark
$\cot ^{-1}(-1)$ का मुख्य मान है
  • A
    $\frac{-\pi}{4}$
  • B
    $\frac{\pi}{4}$
  • C
    $\frac{5 \pi}{4}$
  • $\frac{3 \pi}{4}$
Answer
Correct option: D.
$\frac{3 \pi}{4}$
D
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MCQ 2231 Mark
$\cos \left(\tan ^{-1} \frac{3}{4}\right)=?$
  • A
    $\frac{3}{5}$
  • $\frac{4}{5}$
  • C
    $\frac{4}{9}$
  • D
    $\frac{3}{7}$
Answer
Correct option: B.
$\frac{4}{5}$
B
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MCQ 2241 Mark
$\cos \left(2 \tan ^{-1} \frac{1}{2}\right)=$
  • $\frac{3}{5}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{7}{8}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{3}{5}$
A
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MCQ 2251 Mark
$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ का मुख्य मान है
  • $\frac{\pi}{6}$
  • B
    $\frac{5 \pi}{6}$
  • C
    $\frac{7 \pi}{6}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: A.
$\frac{\pi}{6}$
A
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MCQ 2261 Mark
$\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$ का मुख्य मान है
  • A
    $\frac{-\pi}{4}$
  • B
    $\frac{\pi}{4}$
  • $\frac{3 \pi}{4}$
  • D
    $\frac{5 \pi}{4}$
Answer
Correct option: C.
$\frac{3 \pi}{4}$
C
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MCQ 2271 Mark
$\cos ^{-1}\left(\cos \frac{5 \pi}{4}\right)=$
  • A
    $\frac{5 \pi}{4}$
  • $\frac{3 \pi}{4}$
  • C
    $\frac{-\pi}{4}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\frac{3 \pi}{4}$
B
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MCQ 2281 Mark
$\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)+\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=?$
  • A
    $\frac{4 \pi}{3}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{3 \pi}{4}$
  • $\pi$
Answer
Correct option: D.
$\pi$
D
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MCQ 2291 Mark
$\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)$ का मान है-
  • A
    $\frac{13 \pi}{6}$
  • B
    $\frac{7 \pi}{6}$
  • C
    $\frac{5 \pi}{6}$
  • $\frac{\pi}{6}$
Answer
Correct option: D.
$\frac{\pi}{6}$
D
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MCQ 2301 Mark
$\cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2}=$
  • A
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{6}$
  • C
    $\frac{\pi}{3}$
  • $\frac{2 \pi}{3}$
Answer
Correct option: D.
$\frac{2 \pi}{3}$
D
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MCQ 2311 Mark
$2 \tan ^{-1} \frac{1}{3}=$
  • A
    $\tan ^{-1} \frac{3}{2}$
  • $\tan ^{-1} \frac{3}{4}$
  • C
    $\tan ^{-1} \frac{4}{3}$
  • D
    इनमें से कोई नहीं
Answer
Correct option: B.
$\tan ^{-1} \frac{3}{4}$
B
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MCQ 2321 Mark
$2\left[\sin ^{-1} \cos \left(\sin ^{-1} x\right)+\cos ^{-1} \sin \left(\cos ^{-1} x\right)\right]=$
  • A
    $\frac{\pi}{2}$
  • B
    $0$
  • C
    $2 \pi$
  • $\pi$
Answer
Correct option: D.
$\pi$
D
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