NCERT Exemplar Problems – Class 10 Mathematics
Chapter 8: Introduction to Trigonometry and its Applications
Multiple Choice Questions (Exercise 8.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. If \(\cos A = \dfrac{4}{5}\), then the value of \(\tan A\) is
(A) \(\dfrac{3}{5}\) (B) \(\dfrac{3}{4}\) (C) \(\dfrac{4}{3}\) (D) \(\dfrac{5}{3}\)
Correct Answer: (B)
2. If \(\sin A = \dfrac{1}{2}\), then the value of \(\cot A\) is
(A) \(\sqrt{3}\) (B) \(\dfrac{1}{\sqrt{3}}\) (C) \(\dfrac{\sqrt{3}}{2}\) (D) 1
Correct Answer: (A)
3. The value of the expression \([\operatorname{cosec}(75^\circ + \theta) - \sec(15^\circ - \theta) - \tan(55^\circ + \theta) + \cot(35^\circ - \theta)]\) is
(A) –1 (B) 0 (C) 1 (D) \(\dfrac{3}{2}\)
Correct Answer: (B)
4. Given that \(\sin \theta = \dfrac{a}{b}\), then \(\cos \theta\) is equal to
(A) \(\dfrac{b}{\sqrt{b^{2}-a^{2}}}\) (B) \(\dfrac{b}{a}\) (C) \(\dfrac{\sqrt{b^{2}-a^{2}}}{b}\) (D) \(\dfrac{a}{\sqrt{b^{2}-a^{2}}}\)
Correct Answer: (C)
5. If \(\cos(\alpha + \beta) = 0\), then \(\sin(\alpha - \beta)\) can be reduced to
(A) \(\cos \beta\) (B) \(\cos 2\beta\) (C) \(\sin \alpha\) (D) \(\sin 2\alpha\)
Correct Answer: (B)
6. The value of \((\tan 1^\circ \tan 2^\circ \tan 3^\circ \ldots \tan 89^\circ)\) is
(A) 0 (B) 1 (C) 2 (D) \(\dfrac{1}{2}\)
Correct Answer: (B)
7. If \(\cos 9\alpha = \sin \alpha\) and \(9\alpha < 90^\circ\), then the value of \(\tan 5\alpha\) is
(A) \(\dfrac{1}{\sqrt{3}}\) (B) \(\sqrt{3}\) (C) 1 (D) 0
Correct Answer: (C)
8. If \(\triangle ABC\) is right angled at C, then the value of \(\cos(A + B)\) is
(A) 0 (B) 1 (C) \(\dfrac{1}{2}\) (D) \(\dfrac{\sqrt{3}}{2}\)
Correct Answer: (A)
9. If \(\sin A + \sin^{2} A = 1\), then the value of the expression \((\cos^{2} A + \cos^{4} A)\) is
(A) 1 (B) \(\dfrac{1}{2}\) (C) 2 (D) 3
Correct Answer: (A)
10. Given that \(\sin \alpha = \dfrac{1}{2}\) and \(\cos \beta = \dfrac{1}{2}\), then the value of \((\alpha + \beta)\) is
(A) \(0^\circ\) (B) \(30^\circ\) (C) \(60^\circ\) (D) \(90^\circ\)
Correct Answer: (D)
11. The value of the expression \(\left[ \dfrac{\sin^{2} 22^\circ + \sin^{2} 68^\circ}{\cos^{2} 22^\circ + \cos^{2} 68^\circ} + \sin^{2} 63^\circ + \cos 63^\circ \sin 27^\circ \right]\) is
(A) 3 (B) 2 (C) 1 (D) 0
Correct Answer: (B)
12. If \(4 \tan \theta = 3\), then \(\left( \dfrac{4\sin \theta - \cos \theta}{4\sin \theta + \cos \theta} \right)\) is equal to
(A) \(\dfrac{2}{3}\) (B) \(\dfrac{1}{3}\) (C) \(\dfrac{1}{2}\) (D) \(\dfrac{3}{4}\)
Correct Answer: (C)
13. If \(\sin \theta - \cos \theta = 0\), then the value of \((\sin^{4} \theta + \cos^{4} \theta)\) is
(A) 1 (B) \(\dfrac{3}{4}\) (C) \(\dfrac{1}{2}\) (D) \(\dfrac{1}{4}\)
Correct Answer: (C)
14. \(\sin(45^\circ + \theta) - \cos(45^\circ - \theta)\) is equal to
(A) \(2\cos \theta\) (B) 0 (C) \(2\sin \theta\) (D) 1
Correct Answer: (B)
15. A pole 6 m high casts a shadow \(2\sqrt{3}\) m long on the ground, then the Sun’s elevation is
(A) \(60^\circ\) (B) \(45^\circ\) (C) \(30^\circ\) (D) \(90^\circ\)
Correct Answer: (A)
Answers taken from the official NCERT Exemplar answer key.