Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 71-80 of 96 questions.
What is \(\tan^{-1}x+\cot^{-1}x\), where (x>0)?
B. \(\frac{\pi}{2}\)
धनात्मक (x) के लिए \(\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}\) होता है। चिह्न बदलने पर सावधानी रखें। / For positive (x), \(\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}\). Be careful when the sign changes.
Login to save your score, XP, coins and progress.
What is the principal value of (\csc^{-1}(-2))?
A. \(-\frac{\pi}{6}\)
\(\csc y=-2\) से \(\sin y=-\frac{1}{2}\), इसलिए मुख्य मान \(y=-\frac{\pi}{6}\) है। \(\csc^{-1}\) का परिसर याद रखें। / From \(\csc y=-2\), \(\sin y=-\frac{1}{2}\), so the principal value is \(y=-\frac{\pi}{6}\). Remember the range of \(\csc^{-1}\).
Login to save your score, XP, coins and progress.
What is (\sin^{-1}(-x)) equal to?
A. \(-\sin^{-1}x\)
\(\sin^{-1}x\) विषम फलन है, इसलिए (\sin^{-1}(-x)=-\sin^{-1}x)। विषम और सम गुणों को अलग रखें। / The function \(\sin^{-1}x\) is odd, so (\sin^{-1}(-x)=-\sin^{-1}x). Keep odd and even properties separate.
Login to save your score, XP, coins and progress.
What is (\cos^{-1}(-x)) equal to, where \(x\in\left[-1,1\right]\)?
C. \(\pi-\cos^{-1}x\)
मानक संबंध (\cos^{-1}(-x)=\pi-\cos^{-1}x) है। इसे (\sin^{-1}(-x)) की तरह विषम न मानें। / The standard relation is (\cos^{-1}(-x)=\pi-\cos^{-1}x). Do not treat it as odd like (\sin^{-1}(-x)).
Login to save your score, XP, coins and progress.
What is the value of (\tan^{-1}\(\sqrt{3}\))?
B. \(\frac{\pi}{3}\)
\(\tan\frac{\pi}{3}=\sqrt{3}\) और \(\frac{\pi}{3}\) मुख्य परिसर में है। विशेष कोण याद रखना जरूरी है। / Since \(\tan\frac{\pi}{3}=\sqrt{3}\) and \(\frac{\pi}{3}\) lies in the principal range. Remember special angles well.
Login to save your score, XP, coins and progress.
What is the domain of the function \(\sec^{-1}x\)?
B. (\mathbb{R}\setminus\left\(-1,1\right\))
\(\sec y\) के मान (\left\(-1,1\right\)) में नहीं आते, इसलिए \(\sec^{-1}x\) का प्रांत (\mathbb{R}\setminus\left\(-1,1\right\)) है। शून्य भी प्रांत में नहीं है। / Values of \(\sec y\) do not lie in (\left\(-1,1\right\)), so the domain of \(\sec^{-1}x\) is (\mathbb{R}\setminus\left\(-1,1\right\)). Zero is also not in the domain.
Login to save your score, XP, coins and progress.
Which expression is defined as a real number?
C. \(\tan^{-1}5\)
\(\tan^{-1}x\) सभी वास्तविक (x) के लिए परिभाषित है। बाकी विकल्पों में प्रांत की शर्त टूटती है। / The function \(\tan^{-1}x\) is defined for every real (x). In the other options the domain condition fails.
Login to save your score, XP, coins and progress.
Which pair gives the correct domain and range of \(\tan^{-1}x\)?
A. (\mathbb{R},\left\(-\frac{\pi}{2},\frac{\pi}{2}\right\))
\(\tan^{-1}x\) का प्रांत \(\mathbb{R}\) और परिसर (\left\(-\frac{\pi}{2},\frac{\pi}{2}\right\)) है। खुले अंतराल के अंत बिंदु शामिल नहीं हैं। / The domain of \(\tan^{-1}x\) is \(\mathbb{R}\) and its range is (\left\(-\frac{\pi}{2},\frac{\pi}{2}\right\)). The endpoints of the open interval are not included.
Login to save your score, XP, coins and progress.
On which interval is \(\cos^{-1}x\) a decreasing function?
A. \(\left[-1,1\right]\)
\(\cos x\) को \(\left[0,\pi\right]\) पर एक-एक बनाने से \(\cos^{-1}x\) \(\left[-1,1\right]\) पर घटता है। ग्राफ की दिशा से भी पुष्टि करें। / By making \(\cos x\) one-one on \(\left[0,\pi\right]\), \(\cos^{-1}x\) becomes decreasing on \(\left[-1,1\right]\). The graph direction also confirms this.
Login to save your score, XP, coins and progress.
On which interval is \(\sin^{-1}x\) an increasing function?
A. \(\left[-1,1\right]\)
\(\sin^{-1}x\) अपने पूरे प्रांत \(\left[-1,1\right]\) पर बढ़ता है। यह \(\sin x\) की चुनी गई शाखा से मिलता है। / The function \(\sin^{-1}x\) is increasing on its whole domain \(\left[-1,1\right]\). This matches the chosen branch of \(\sin x\).
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.