Trigonometric Function MCQ Quiz in తెలుగు - Objective Question with Answer for Trigonometric Function - ముఫ్త్ [PDF] డౌన్లోడ్ కరెన్
Last updated on Apr 29, 2025
Latest Trigonometric Function MCQ Objective Questions
Trigonometric Function Question 1:
\(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)
Answer (Detailed Solution Below)
Trigonometric Function Question 1 Detailed Solution
Trigonometric Function Question 2:
\(\displaystyle\lim _{\theta \rightarrow \frac{\pi}{2}^{-}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4}=\)
Answer (Detailed Solution Below)
Trigonometric Function Question 2 Detailed Solution
Trigonometric Function Question 3:
\(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \cdot \sin 5 x}{x^2 \sin 3 x}\) విలువ
Answer (Detailed Solution Below)
Trigonometric Function Question 3 Detailed Solution
గణన:
ఇచ్చినది, \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^2 \sin 3 x}\)
= \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x \cdot x}{x^3 \cdot \sin 3 x}\)
= \(\lim _{x \rightarrow 0} \frac{2 \sin ^2 x}{x^2} \cdot \frac{\sin 5 x}{x} \cdot \frac{x}{\sin 3 x}\)
= \(2\left(\lim _{x \rightarrow 0} \frac{\sin x}{x}\right)^2 \cdot 5\left(\lim _{x \rightarrow 0} \frac{\sin 5 x}{5 x}\right) \cdot \frac{1}{3}\left(\frac{1}{\lim _{x \rightarrow 0} \frac{\sin 3 x}{3 x}}\right)\)
= 2 x 1 x 5 x 1 x \(\frac{1}{3}\) x 1
= \(\frac{10}{3}\)
కాబట్టి, పరిమితి విలువ \(\frac{10}{3}\).
సరైన సమాధానం ఎంపిక 1.
Top Trigonometric Function MCQ Objective Questions
Trigonometric Function Question 4:
\(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \cdot \sin 5 x}{x^2 \sin 3 x}\) విలువ
Answer (Detailed Solution Below)
Trigonometric Function Question 4 Detailed Solution
గణన:
ఇచ్చినది, \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^2 \sin 3 x}\)
= \(\lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x \cdot x}{x^3 \cdot \sin 3 x}\)
= \(\lim _{x \rightarrow 0} \frac{2 \sin ^2 x}{x^2} \cdot \frac{\sin 5 x}{x} \cdot \frac{x}{\sin 3 x}\)
= \(2\left(\lim _{x \rightarrow 0} \frac{\sin x}{x}\right)^2 \cdot 5\left(\lim _{x \rightarrow 0} \frac{\sin 5 x}{5 x}\right) \cdot \frac{1}{3}\left(\frac{1}{\lim _{x \rightarrow 0} \frac{\sin 3 x}{3 x}}\right)\)
= 2 x 1 x 5 x 1 x \(\frac{1}{3}\) x 1
= \(\frac{10}{3}\)
కాబట్టి, పరిమితి విలువ \(\frac{10}{3}\).
సరైన సమాధానం ఎంపిక 1.
Trigonometric Function Question 5:
\(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)
Answer (Detailed Solution Below)
Trigonometric Function Question 5 Detailed Solution
Trigonometric Function Question 6:
\(\displaystyle\lim _{\theta \rightarrow \frac{\pi}{2}^{-}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4}=\)