Class 11 Mathematics Trigonometric Ratios MCQs Set 01

Question. \( -13\pi / 6 \) radians =
(a) \( -390^\circ \)
(b) \( -490^\circ \)
(c) \( -410^\circ \)
(d) \( -30^\circ \)
Answer: (a) \( -390^\circ \)

Question. \( \cot(1358^\circ) + \tan(3608^\circ) = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (b) 0

Question. \( \frac{\sin(-660^\circ) \tan(1050^\circ) \sec(-420^\circ)}{\cos(225^\circ) \operatorname{cosec}(315^\circ) \cos(510^\circ)} = \)
(a) \( \frac{\sqrt{3}}{4} \)
(b) \( \frac{\sqrt{3}}{2} \)
(c) \( \frac{2}{\sqrt{3}} \)
(d) \( \frac{4}{\sqrt{3}} \)
Answer: (c) \( \frac{2}{\sqrt{3}} \)

Question. \( \sin 48^\circ \sec 42^\circ + \cos 48^\circ \operatorname{cosec} 42^\circ = \)
(a) 0
(b) 2
(c) 1
(d) -1
Answer: (b) 2

Question. \( \log \tan 17^\circ + \log \tan 37^\circ + \log \tan 53^\circ + \log \tan 73^\circ = \)
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a) 0

Question. \( \cos 24^\circ + \cos 55^\circ + \cos 125^\circ + \cos 204^\circ = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (b) 0

Question. \( \sec A + \tan A = 3 \)
\( \implies \sec A = \)
(a) \( \frac{10}{3} \)
(b) \( \frac{5}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{4}{3} \)
Answer: (b) \( \frac{5}{3} \)

Question. \( \sec \theta - \tan \theta = 3 \)
\( \implies \theta \) lies in the quadrant
(a) I
(b) II
(c) III
(d) IV
Answer: (d) IV

Question. \( \sin 10^\circ + \sin 20^\circ + \sin 30^\circ + \dots + \sin 360^\circ = \)
(a) 0
(b) 1
(c) -1
(d) 2
Answer: (a) 0

Question. \( 3[\sin x - \cos x]^4 + 6[\sin x + \cos x]^2 + 4[\sin^6 x + \cos^6 x] = \)
(a) 3
(b) 6
(c) 4
(d) 13
Answer: (d) 13

Question. \( \frac{\sin^2 \alpha}{1 + \cot^2 \alpha} + \frac{\tan^2 \alpha}{(1 + \tan^2 \alpha)^2} + \cos^2 \alpha = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (c) 1

Question. \( 1 - \frac{\sin^2 x}{1 + \cos x} + \frac{1 + \cos x}{\sin x} - \frac{\sin x}{1 - \cos x} = \)
(a) \( \sin x \)
(b) \( \cos x \)
(c) \( \operatorname{cosec} x \)
(d) \( \sec x \)
Answer: (b) \( \cos x \)

Question. If A, B, C are the angles of a triangle ABC then \( \cos\left(\frac{3A + 2B + C}{2}\right) + \cos\left(\frac{A - C}{2}\right) = \)
(a) 0
(b) 1
(c) \( \cos A \)
(d) \( \cos C \)
Answer: (a) 0

Question. \( \frac{\cot \theta + \operatorname{cosec} \theta - 1}{\cot \theta - \operatorname{cosec} \theta + 1} = \)
(a) \( \frac{\sin \theta}{1 + \cos \theta} \)
(b) \( \frac{\sin \theta}{1 - \cos \theta} \)
(c) \( \frac{1 - \cos \theta}{\sin \theta} \)
(d) \( \frac{\cos \theta}{1 - \sin \theta} \)
Answer: (b) \( \frac{\sin \theta}{1 - \cos \theta} \)

Question. \( \sin^2(51^\circ - x) + \sin^2(39^\circ + x) = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (c) 1

Question. \( \frac{\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9}}{\cos^2 \frac{\pi}{18} + \cos^2 \frac{\pi}{9} + \cos^2 \frac{7\pi}{18} + \cos^2 \frac{4\pi}{9}} = \)
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1

Question. If ABCD is a cyclic quadrilateral, then \( \cos(180^\circ + A) + \cos(180^\circ - B) + \cos(180^\circ - C) - \sin(90^\circ - D) = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (b) 0

Question. \( \left[\sin\left(\frac{\pi}{2} - x\right) + \sin(\pi - x)\right]^2 + \left[\cos\left(\frac{3\pi}{2} - x\right) + \cos(2\pi - x)\right]^2 = \)
(a) 0
(b) 2
(c) 4
(d) 8
Answer: (b) 2

Question. \( \sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3 \)
\( \implies \cos \theta_1 + \cos \theta_2 + \cos \theta_3 = \)
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a) 0

Question. \( 8\sin^2 x + 3\cos^2 x = 5 \)
\( \implies \cot x = \)
(a) \( \pm \frac{1}{\sqrt{2}} \)
(b) \( \pm \frac{1}{\sqrt{3}} \)
(c) \( \pm \sqrt{\frac{3}{2}} \)
(d) \( \pm \sqrt{\frac{2}{3}} \)
Answer: (c) \( \pm \sqrt{\frac{3}{2}} \)

Question. \( \sin x + \sin^2 x = 1 \)
\( \implies \cos^2 x + \cos^4 x = \)
(a) 0
(b) 1
(c) 2
(d) -1
Answer: (b) 1

Question. If \( \cos(x - y) = -1 \), then \( \cos x + \cos y = \)
(a) 0
(b) 1
(c) 2
(d) -1
Answer: (a) 0

Question. If \( \sin x + \operatorname{cosec} x = 2 \) then \( \sin^8 x + \operatorname{cosec}^8 x = \)
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2

Question. If \( \sin x + \cos x = a \) then \( |\sin x - \cos x| = \)
(a) \( \sqrt{1 - a^2} \)
(b) \( \sqrt{a^2 - 1} \)
(c) \( \sqrt{2 - a^2} \)
(d) \( \sqrt{a^2 - 2} \)
Answer: (c) \( \sqrt{2 - a^2} \)

Question. \( (1 + \sin A)(1 + \sin B)(1 + \sin C) = (1 - \sin A)(1 - \sin B)(1 - \sin C) = k \)
\( \implies k = \)
(a) \( +\sin A \sin B \sin C \)
(b) \( \pm \cos A \cos B \cos C \)
(c) \( \pm \sec A \sec B \sec C \)
(d) \( \pm \operatorname{cosec} A \operatorname{cosec} B \operatorname{cosec} C \)
Answer: (b) \( \pm \cos A \cos B \cos C \)

Question. \( \operatorname{cosec}^2 A \cot^2 A - \sec^2 A \tan^2 A - (\cot^2 A - \tan^2 A)(\sec^2 A \operatorname{cosec}^2 A - 1) = \)
(a) 0
(b) 1
(c) -1
(d) 2
Answer: (a) 0

Question. \( \tan^2 \theta + \sec \theta = 5 \)
\( \implies \sec \theta = \)
(a) 3
(b) 2
(c) 1
(d) -1
Answer: (b) 2

Question. \( \log \sin 1^\circ \cdot \log \sin 2^\circ \cdots \log \sin 179^\circ \)
(a) 1
(b) 0
(c) -1
(d) 2
Answer: (b) 0

Question. If \( \tan(\alpha + \beta) = \sqrt{3}, \tan(\alpha - \beta) = 1 \) then \( \tan 6\beta = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (c) 1

Question. If \( x = r \cos \theta \cos \phi, y = r \cos \theta \sin \phi, z = r \sin \theta \) then \( x^2 + y^2 + z^2 = \)
(a) \( r^2 \)
(b) \( y^2 \)
(c) \( x^2 \)
(d) \( z^2 \)
Answer: (a) \( r^2 \)

Question. \( \sin^2 A \cos^2 B + \cos^2 A \sin^2 B + \sin^2 A \sin^2 B + \cos^2 A \cos^2 B = \)
(a) -1
(b) 0
(c) 1
(d) 2
Answer: (c) 1

Question. If \( 2 \sin^2 A - \cot^2 B = 1 \) then \( \sin A \sin B = \)
(a) \( -\frac{1}{\sqrt{2}} \)
(b) \( \pm \frac{1}{\sqrt{2}} \)
(c) \( \frac{1}{\sqrt{2}} \)
(d) \( \frac{-1}{2\sqrt{2}} \)
Answer: (b) \( \pm \frac{1}{\sqrt{2}} \)

Question. The value of \( \sin^6 \theta + \cos^6 \theta + 3 \sin^2 \theta \cos^2 \theta \) is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1

Question. If \( x \tan^2 120^\circ + 4 \cos^2 150^\circ = 9 \) then \( x = \)
(a) 3
(b) 1
(c) 2
(d) 4
Answer: (c) 2

Question. In \( \Delta ABC \), right angled at C, then \( \tan A + \tan B = \)
(a) \( \frac{a^2}{bc} \)
(b) \( \frac{b^2}{ac} \)
(c) \( \frac{c^2}{ab} \)
(d) \( \frac{ab}{c} \)
Answer: (c) \( \frac{c^2}{ab} \)

Question. If \( a = \sin 170^\circ + \cos 170^\circ \) then
(a) \( a > 0 \)
(b) \( a < 0 \)
(c) \( a = 0 \)
(d) \( a = 1 \)
Answer: (b) \( a < 0 \)

Question. \( \tan \frac{\pi}{24} \tan \frac{3\pi}{24} \tan \frac{5\pi}{24} \tan \frac{7\pi}{24} \tan \frac{9\pi}{24} \tan \frac{11\pi}{24} \tan \frac{16\pi}{24} = \)
(a) 1
(b) -1
(c) \( \sqrt{3} \)
(d) \( -\sqrt{3} \)
Answer: (d) \( -\sqrt{3} \)

Question. \( x = a \sec^3 \theta \tan \theta, y = b \tan^3 \theta \sec \theta \) then \( \sin^2 \theta = \)
(a) \( \frac{x}{a} - \frac{y}{b} \)
(b) \( \frac{x}{a} + \frac{y}{b} \)
(c) \( \frac{xy}{ab} \)
(d) \( \frac{ay}{bx} \)
Answer: (d) \( \frac{ay}{bx} \)

Question. If \( \frac{x}{a} \cos \theta + \frac{y}{b} \sin \theta = 1, \frac{x}{a} \sin \theta - \frac{y}{b} \cos \theta = 1 \) then \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = \)
(a) 1
(b) -1
(c) 2
(d) 3
Answer: (c) 2

Question. In a \( \Delta ABC \), if \( \cot A \cot B \cot C > 0 \) then the triangle is
(a) acute angled
(b) right angled
(c) obtuse angled
(d) can't be decided
Answer: (a) acute angled