MCQOPTIONS
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MCQOPTIONS
This section includes 1153 Mcqs, each offering curated multiple-choice questions to sharpen your UPSEE knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
If tan x = cot(45° + 2x), then what is the value of x? |
| A. | 45° |
| B. | 15° |
| C. | 45°/2 |
| D. | 20° |
| Answer» C. 45°/2 | |
| 102. |
If \(\sin \left( {{{\sin }^{ - 1}}\left( {\frac{1}{5}} \right) + {{\cos }^{ - 1}}x} \right) = 1\) then find the value of x ? |
| A. | 1 |
| B. | \(\frac{1}{5}\) |
| C. | 5 |
| D. | None of these |
| Answer» C. 5 | |
| 103. |
A spherical balloon of radius r meters subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is α, then the height of the centre of the balloon is: |
| A. | \(r\sin \frac{\alpha }{2}cosec\;\theta\) |
| B. | \(r\sin \frac{\theta }{2}cosec\;\alpha\) |
| C. | \(r\sin \theta cosec\frac{\alpha }{2}\) |
| D. | \(r\sin \alpha cosec\frac{\theta }{2}\) |
| Answer» E. | |
| 104. |
If (1 + tan2 θ) = 625/49 and θ is acute, then what is the value of √(sin θ + cos θ)? |
| A. | 1 |
| B. | (5/4) × √(31/42) |
| C. | √31/5 |
| D. | 5/7 |
| Answer» D. 5/7 | |
| 105. |
If A = (cos 12° - cos 36°) (sin 96° + sin 24°) and B = (sin 60° - sin 12°) (cos 48° - cos 72°), then what is \(\frac{{\rm{A}}}{{\rm{B}}}\) equal to? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 106. |
\(\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{x{\rm{cot}}\left( {4x} \right)}}{{{\rm{si}}{{\rm{n}}^2}x{\rm{co}}{{\rm{t}}^2}\left( {2x} \right)}}\) is equal to: |
| A. | 0 |
| B. | 2 |
| C. | 4 |
| D. | 1 |
| Answer» E. | |
| 107. |
Find the value of sin235° + sin255° |
| A. | -1 |
| B. | 1/2 |
| C. | 0 |
| D. | 1 |
| Answer» E. | |
| 108. |
If 8 sec2x – 7 tan2 x = 11 and 00 ≤ x ≤ 900, then x = ? |
| A. | 300 |
| B. | 450 |
| C. | 600 |
| D. | 900 |
| Answer» D. 900 | |
| 109. |
If Cot θ = 21/20, then what is the value of Cosec θ? |
| A. | 21/29 |
| B. | 29/21 |
| C. | 20/29 |
| D. | 29/20 |
| Answer» E. | |
| 110. |
A pole 9 m long casts a shadow of \(3\sqrt 3 \)m long on the ground. What is the Sun’s elevation at that time? |
| A. | 45° |
| B. | 30° |
| C. | 90° |
| D. | 60° |
| Answer» E. | |
| 111. |
In triangle ABC, find the value of \(ta{n^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + {\tan ^2}\frac{C}{2}\). |
| A. | ≤ 1 |
| B. | > 1 |
| C. | ≥ 1 |
| D. | < 1 |
| Answer» D. < 1 | |
| 112. |
If Cot θ = 24/7, then Sin θ = ? |
| A. | 24/25 |
| B. | 8/25 |
| C. | 7/25 |
| D. | 9/25 |
| Answer» D. 9/25 | |
| 113. |
∆ABC is right angled at B. If m∠A = 30°, then find the value of (sinC + 1/3). |
| A. | 4/3 |
| B. | (√3 + 1)/2 |
| C. | (√3 + 2)/√3 |
| D. | (3√3 + 2)/6 |
| Answer» E. | |
| 114. |
An aeroplane flying horizontally at a height of 3 km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is: |
| A. | 230.63 m/sec |
| B. | 230.93 m/sec |
| C. | 235.85 m/sec |
| D. | 236.25 m/sec |
| Answer» C. 235.85 m/sec | |
| 115. |
ΔABC is right angled at B. If ∠A = 60°, then what is the value of Cot C? |
| A. | √2 |
| B. | 1/√3 |
| C. | √3 |
| D. | 2/√3 |
| Answer» D. 2/√3 | |
| 116. |
If p = cosec θ – cot θ and q = (cosec θ + cot θ)-1 then which one of the following is correct? |
| A. | pq = 1 |
| B. | p = q |
| C. | p + q = 1 |
| D. | p + q = 0 |
| Answer» C. p + q = 1 | |
| 117. |
If \(\rm \frac{\tan x}{2}= \frac{\tan y}{3} = \frac{\tan z}{5}\) and x + y + z = π, then the value of tan2 x + tan2 y + tan2 z is: |
| A. | \(\frac{38}{3}\) |
| B. | \(\frac38\) |
| C. | \(\frac{11}4\) |
| D. | None of these. |
| Answer» B. \(\frac38\) | |
| 118. |
If secθ + tanθ = p, 0°< θ < 90°, then \(\frac{{{p^2} - 1}}{{{p^2} + 1}}\) is equal to: |
| A. | sin θ |
| B. | cosec θ |
| C. | cos θ |
| D. | 2 cosec θ |
| Answer» B. cosec θ | |
| 119. |
If \(\frac{sin θ + cosθ}{sin θ - cosθ}=3\) and θ is an acute angle, then the value of \(\frac{3sin \theta + 4 cos \theta }{8cos \theta - 3 sin \theta }\) is: |
| A. | 10 |
| B. | \(\frac{1}{2}\) |
| C. | 5 |
| D. | 2 |
| Answer» D. 2 | |
| 120. |
If cos θ = 1/√10, then tan θ is equal to∶ |
| A. | 1/√3 |
| B. | 1/3 |
| C. | √3 |
| D. | 3 |
| Answer» E. | |
| 121. |
If sin 7 x = cos 11x, 0° < x < 90°, then the value of tan 9x is: |
| A. | \(\frac{\sqrt{3}}{2}\) |
| B. | 1 |
| C. | \(\frac{1}{\sqrt{3}}\) |
| D. | \(\sqrt{3}\) |
| Answer» C. \(\frac{1}{\sqrt{3}}\) | |
| 122. |
If 4 (cosec265° - tan225°) – sin 90°- tan263° y tan227° = y/2, then the value of y is: |
| A. | 2 |
| B. | 1 |
| C. | \(-\frac{1}{2}\) |
| D. | -1 |
| Answer» B. 1 | |
| 123. |
If cot A = [sin B/(1 – cos B)], then what is the value of cot 2A? |
| A. | cot(B/2) |
| B. | cot 2B |
| C. | cot B |
| D. | tan B |
| Answer» D. tan B | |
| 124. |
In the second quadrant, cos θ varies from: |
| A. | 1/2 to –1 |
| B. | 0 to 1/2 |
| C. | 0 to –1 |
| D. | –1 to 1 |
| Answer» D. –1 to 1 | |
| 125. |
Nidhi looks at the base of a tree from her balcony. This formed a right-angled triangle with an angle of depression of 30°. If the base of tree is 10 m away from the base of the wall of the house, what is the distance between her eye and the base of the tree? |
| A. | 20√3 m |
| B. | 20 / √3 m |
| C. | 2 / √3 m |
| D. | √3 / 2 m |
| Answer» C. 2 / √3 m | |
| 126. |
Let θ = sin-1 (sin (-600°)), then the value of θ is: |
| A. | π/3 |
| B. | π/2 |
| C. | 2π/3 |
| D. | -2π/3 |
| Answer» B. π/2 | |
| 127. |
\(1 + \frac{{{{\tan }^2}A}}{{1 + \sec A}}\) is equal to: |
| A. | sec A |
| B. | cosec A |
| C. | cos A |
| D. | sin A |
| Answer» B. cosec A | |
| 128. |
If \(\frac{(1 +sinθ-cosθ)}{(1 +sinθ +cosθ)} + \frac{(1 + sinθ +cosθ)}{(1 + sinθ-cosθ)}\)= 4, then which of the following values will be suitable for θ ? |
| A. | 45° |
| B. | 30° |
| C. | 90° |
| D. | 60° |
| Answer» C. 90° | |
| 129. |
In ΔABC measure of angle B is 90°. If cot A = 8/15, and AB = 0.8 cm, then what is the length (in cm) of side BC? |
| A. | 1.7 |
| B. | 2 |
| C. | 1.5 |
| D. | 2.5 |
| Answer» D. 2.5 | |
| 130. |
If tan4A = cot(A – 20°), 0° |
| A. | 5° |
| B. | 80° |
| C. | 22° |
| D. | 14° |
| Answer» D. 14° | |
| 131. |
If tanα = √2 – 1, then the value of tanα – cotα = ? |
| A. | 2√2 |
| B. | -2 |
| C. | 1 |
| D. | √2 + 1 |
| Answer» C. 1 | |
| 132. |
If \(\frac{1}{{1 - sin\theta }}\; + \;\frac{1}{{1\; + \;sin\theta }}\) = 4secθ, 0° |
| A. | 5√3/3 |
| B. | 4√3 |
| C. | 5√3 |
| D. | 2√3/3 |
| Answer» B. 4√3 | |
| 133. |
From the top of a platform, the angle of elevation of a tower was 45°. The tower was 47 m high and the horizontal distance between the platform and the tower was 40 m. What was the height of the platform? |
| A. | 10 m |
| B. | 5 m |
| C. | 7 m |
| D. | 7√3 m |
| Answer» D. 7√3 m | |
| 134. |
\(\frac{{\cos\theta \cos (90^\circ \, - \,\theta )}}{{\cot (90^\circ \, - \,\theta )}}\)= ________. |
| A. | Sin2 θ |
| B. | Cos 2 θ |
| C. | Sin 2 θ |
| D. | Cos2 θ |
| Answer» E. | |
| 135. |
If sinθ = a/ [√(a2 + b2), 0° < θ < 90°, then the value of secθ + tanθ is: |
| A. | \(\frac{{\sqrt {{a^2}{\rm{\;}} + {\rm{\;}}{b^2}} {\rm{\;}} + {\rm{\;}}a}}{{2b}}\) |
| B. | \(\frac{{\sqrt {{a^2}{\rm{\;}} + {\rm{\;}}{b^2}} {\rm{\;}} + {\rm{\;}}b}}{{2a}}\) |
| C. | \(\frac{{\sqrt {{a^2}{\rm{\;}} + {\rm{\;}}{b^2}} {\rm{\;}} + {\rm{\;}}a}}{a}\) |
| D. | \(\frac{{\sqrt {{a^2}{\rm{\;}} + {\rm{\;}}{b^2}} {\rm{\;}} + {\rm{\;}}a}}{b}\) |
| Answer» E. | |
| 136. |
If sin θ + cosec θ = 2, then what is the value of sin153θ + cosec253 θ? |
| A. | 1/153 × 253 |
| B. | 253/153 |
| C. | 153/253 |
| D. | 2 |
| Answer» E. | |
| 137. |
If tan x = cot (65° + 9x), then what is the value of x? |
| A. | 2.5° |
| B. | 1.0° |
| C. | 2.0° |
| D. | 1.5° |
| Answer» B. 1.0° | |
| 138. |
In a triangle ABC if a = 2, b = 3 and sin A = 2/3, then what is angle B equal to? |
| A. | π/4 |
| B. | π/2 |
| C. | π/3 |
| D. | π/6 |
| Answer» C. π/3 | |
| 139. |
If cos 60°- sec 30°= x, then the value of x is |
| A. | 1 |
| B. | (√3 + √2)/2 |
| C. | (√3 − 4)/2√3 |
| D. | 1/√2 |
| Answer» D. 1/√2 | |
| 140. |
Fine the principal value of \(\cot^{-1}(-\sqrt{3}) ?\) |
| A. | \(\dfrac{\pi}{2}\) |
| B. | \(\dfrac{\pi}{6}\) |
| C. | \(\dfrac{7\pi}{6}\) |
| D. | \(\dfrac{5\pi}{6}\) |
| Answer» E. | |
| 141. |
If \(\frac{{{{\cot }^2}{\rm{x}}}}{{\left( {1 + \sqrt 3 } \right)}} + \frac{1}{2}\left( {3 - \sqrt 3 } \right) = \cot {\rm{x}}\), then what is the value of x? |
| A. | \(\frac{{\rm{\pi }}}{2},\frac{{\rm{\pi }}}{4}\) |
| B. | \(\frac{{\rm{\pi }}}{6},\frac{{\rm{\pi }}}{2}\) |
| C. | \(\frac{{\rm{\pi }}}{6},\frac{{\rm{\pi }}}{4}\) |
| D. | \({\rm{\pi }},\frac{{\rm{\pi }}}{4}\) |
| Answer» D. \({\rm{\pi }},\frac{{\rm{\pi }}}{4}\) | |
| 142. |
If angles M and N measures 60° and 30° respectively, (sin M) × (cot N) = ?A. 1/2B. √3/2C. 3/2D. 0 |
| A. | D |
| B. | B |
| C. | A |
| D. | C |
| Answer» E. | |
| 143. |
If tanA = 1/2 and tanB = 1/3, then what is the value of tan(2A + B)? |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 9 |
| Answer» C. 5 | |
| 144. |
Find the value of 5 sin θ - 2 cosec θ, if θ = 30°. |
| A. | 3/2 |
| B. | - 3/2 |
| C. | 2/3 |
| D. | - 2/3 |
| Answer» C. 2/3 | |
| 145. |
If 0° ≤ ∅ ≤ 90°, and cos∅ + sec∅ = 2, then ∅ is equal to: |
| A. | 90° |
| B. | 30° |
| C. | 0° |
| D. | 60° |
| Answer» D. 60° | |
| 146. |
Find the elevation angle when the height of the tree is 16√3 m and the length of the shade of the tree is 16 m. |
| A. | 60° |
| B. | 90° |
| C. | 45° |
| D. | 30° |
| Answer» B. 90° | |
| 147. |
If 5 cos2 θ + 1 = 3 sin2θ, 0°< θ < 90°, then what is the value of \(\frac{{tan{\rm{\theta \;}} + {\rm{\;sec\theta }}}}{{cot{\rm{\theta \;}} + {\rm{\;cosec\theta }}}}\)? |
| A. | \(\frac{{3\; + \;2\sqrt 3 }}{3}\) |
| B. | \(\frac{{2\; + \;3\sqrt 3 }}{3}\) |
| C. | \(\frac{{2\; + \;3\sqrt 3 }}{2}\) |
| D. | \(\frac{{3\; + \;2\sqrt 3 }}{2}\) |
| Answer» B. \(\frac{{2\; + \;3\sqrt 3 }}{3}\) | |
| 148. |
ΔDEF is right angled at E. If ∠F = 45°, then what is the value of 2 Sin F × Cot F? |
| A. | √2 |
| B. | 2 |
| C. | 1/√2 |
| D. | 1/2 |
| Answer» B. 2 | |
| 149. |
If \({\sin ^2}A{\rm{\;}} + {\sin ^2}B = \frac{1}{{16}}\), then what is the value of \(\left( {{{\cos }^2}A{{\cos }^2}B - {{\sin }^2}A{{\sin }^2}B} \right)\)? |
| A. | 11/16 |
| B. | 15/16 |
| C. | 17/16 |
| D. | 13/16 |
| Answer» C. 17/16 | |
| 150. |
If x = a cosθ + b sinθ and y = a sinθ - b cosθ, then what is (x2 + y2) equal to? |
| A. | 2ab |
| B. | a + b |
| C. | a2 + b2 |
| D. | a2 - b2 |
| Answer» D. a2 - b2 | |