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.
| 151. |
Find the value of \(\frac{{tan31^\circ \; + \;\tan 29^\circ }}{{cot45^\circ - cot59^\circ cot61^\circ }}\) |
| A. | \(\sqrt 3 \) |
| B. | \(- \sqrt 3\) |
| C. | \(\frac{1}{{\sqrt 3 }}\) |
| D. | \(- \frac{1}{{\sqrt 3 }}\) |
| Answer» B. \(- \sqrt 3\) | |
| 152. |
In a Δ ABC, the value of (b + c) cos A + (c + a) cos B + (a + b) cos C is equal to |
| A. | 0 |
| B. | rR |
| C. | Rr2 |
| D. | a + b + c |
| Answer» E. | |
| 153. |
If 1/(cosθ + secθ) = ½; then what is the value of cos100θ+ sec100θ? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 154. |
If cot α and cot β are the roots of the equation x2 - 5x + 4 = 0, then what is cot (α + β) equal to ? |
| A. | 1/3 |
| B. | 1/4 |
| C. | 3/5 |
| D. | 2/5 |
| Answer» D. 2/5 | |
| 155. |
At a certain time of a day a tree 5.4 m height casts a shadow of 9 m. If a pole casts a shadow of 13.5 m at the same time, then the height of the pole is∶ |
| A. | 6.3 m |
| B. | 9.9 m |
| C. | 7.2 m |
| D. | 8.1 m |
| Answer» E. | |
| 156. |
If sinθ = \(\frac{1}{2}\) (where |
| A. | 0 |
| B. | 1 |
| C. | \(\frac{1}{2}\) |
| D. | None of these |
| Answer» B. 1 | |
| 157. |
If x = sin 70° ⋅ sin 50° and y = cos 60° ⋅ cos 80°, then what is xy equal to? |
| A. | 1/16 |
| B. | 1/8 |
| C. | 1/4 |
| D. | 1/2 |
| Answer» B. 1/8 | |
| 158. |
As observed from the top of a lighthouse, 45 m high above the sea-level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. The distance travelled by ship during the period of observation is: (Your answer should be correct to one decimal place). |
| A. | 36.9 m |
| B. | 32.9 m |
| C. | 33.4 m |
| D. | 24.8 m |
| Answer» C. 33.4 m | |
| 159. |
If the equation x2 + y2 - 2xy sin2 θ = 0 contains real solution for x and y, then |
| A. | x = y |
| B. | x = -y |
| C. | x = 2y |
| D. | 2x = y |
| Answer» B. x = -y | |
| 160. |
A 18 m long ladder (whose foot is on the ground) leans against a wall making an angle of 30° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground? |
| A. | 9√3 |
| B. | 9√2 |
| C. | (9√3)/2 |
| D. | 18 |
| Answer» B. 9√2 | |
| 161. |
If sin θ + cosec θ = 2, then the value of sin8 θ + cosec8 θ will be: |
| A. | 1 |
| B. | 2 |
| C. | 24 |
| D. | 28 |
| Answer» C. 24 | |
| 162. |
If tan 3x = cot (30° + 2x), then what is the value of x? |
| A. | 12° |
| B. | 18° |
| C. | 10° |
| D. | 15° |
| Answer» B. 18° | |
| 163. |
If 10 sin4α + 15 cos4α = 6, then find the value of 27 cosec6α + 8 sec6α. |
| A. | 75 |
| B. | 125 |
| C. | 250 |
| D. | 50 |
| Answer» D. 50 | |
| 164. |
If sin x = 5 / 13 then cot x will be |
| A. | 5 / 12 |
| B. | 7 / 13 |
| C. | 12 / 5 |
| D. | 13 / 5 |
| Answer» D. 13 / 5 | |
| 165. |
If 117 Cos2 A + 129 Sin2 A = 120 and 170 Cos2 B + 158 Sin2 B = 161, then the value of Cosec2 A Sec2 B is: |
| A. | 16 |
| B. | 9 |
| C. | 1 |
| D. | 4 |
| Answer» B. 9 | |
| 166. |
Find the value of sin 60° cos 45° – cos 60° sin 45° |
| A. | \(\frac{{\sqrt 3 + 1}}{2}\) |
| B. | \(\frac{{\sqrt 3 + 1}}{2\sqrt 2}\) |
| C. | \(\frac{{\sqrt 3 - 1}}{\sqrt 2}\) |
| D. | \(\frac{{\sqrt 3 - 1}}{2\sqrt 2}\) |
| Answer» E. | |
| 167. |
Let 0° < θ < 90° and 100θ = 90°. If \(\alpha = {\rm{\Pi }}_{n = 1}^{99}\cot n\theta \), then which one of the following is correct? |
| A. | α = 1 |
| B. | α = 0 |
| C. | α > 1 |
| D. | 0 < α < 1 |
| Answer» B. α = 0 | |
| 168. |
If \(\cos \theta \; = \;\frac{8}{{17}},\) find cosec θ. |
| A. | \(\frac{{15}}{{17}}\) |
| B. | \(\frac{{17}}{{15}}\) |
| C. | \(\frac{{15}}{8}\) |
| D. | \(\frac{{17}}{8}\) |
| Answer» C. \(\frac{{15}}{8}\) | |
| 169. |
If the length of the shadow of a tower is equal to its height, then what is the sun’s altitude at that time? |
| A. | 15° |
| B. | 30° |
| C. | 45° |
| D. | 60° |
| Answer» D. 60° | |
| 170. |
If 2 cos2 θ = 3 sin θ, 0° < θ < 90°, then the value of \(\left(\dfrac{1}{2} \rm cosec^2 \ \theta - \cot^2 \theta \right)\) is: |
| A. | \(\dfrac{1}{4}\) |
| B. | \(\dfrac{1}{2}\) |
| C. | 0 |
| D. | -1 |
| Answer» E. | |
| 171. |
A tree of height 15 m is broken by wind in such a way that its top touches the ground and makes an angle 30° with the ground. What is the height from the ground to the point where tree is broken? |
| A. | 10 m |
| B. | 7 m |
| C. | 5 m |
| D. | 3 m |
| Answer» D. 3 m | |
| 172. |
If α + β = 90° and α = 2β, then the value of 3 cos2 α - 2 sin2 β is equal to: |
| A. | 3 / 4 |
| B. | 1 / 4 |
| C. | 4 / 3 |
| D. | 3 / 2 |
| Answer» C. 4 / 3 | |
| 173. |
θ is being an acute angle, it is given that sec2θ + 4tan2θ = 6. What is the value of θ? |
| A. | 45° |
| B. | 0° |
| C. | 60° |
| D. | 30° |
| Answer» B. 0° | |
| 174. |
Find x if Cosx = \(-\frac{1}{2}\) |
| A. | \(\frac{3\pi}{2}\) |
| B. | \(\frac{2\pi}{3}\) |
| C. | \(\frac{5\pi}{3}\) |
| D. | \(\frac{5\pi}{2}\) |
| Answer» C. \(\frac{5\pi}{3}\) | |
| 175. |
If cos2 θ – sin2 θ – 3cosθ + 2 = 0, 0° < θ < 90°, then what is the value of 4 cosecθ + cotθ? |
| A. | \(3\sqrt 3\) |
| B. | 3 |
| C. | 4 |
| D. | \(4\sqrt 3\) |
| Answer» B. 3 | |
| 176. |
If sin x + a cos x = b, then |a sin x - cos x| is: |
| A. | \(\rm \sqrt{a^2 + b^2 +1}\) |
| B. | \(\rm \sqrt{a^2 - b^2 +1}\) |
| C. | \(\rm \sqrt{a^2 + b^2 -1}\) |
| D. | None of the above. |
| Answer» C. \(\rm \sqrt{a^2 + b^2 -1}\) | |
| 177. |
If 7 sin2 θ – cos2 θ + 2 sin θ = 2, 0° < θ < 90°, then the value of \(\frac{{\sec 2\theta + \cot 2\theta }}{{cosec\;2\;\theta + \tan 2\theta }}\) is: |
| A. | \(\frac{2}{5}\left( {1 + \sqrt 3 } \right)\) |
| B. | \(\frac{1}{5}\left( {1 + 2\sqrt 3 } \right)\) |
| C. | \(\frac{{2\sqrt 3 + 1}}{3}\) |
| D. | 1 |
| Answer» C. \(\frac{{2\sqrt 3 + 1}}{3}\) | |
| 178. |
In ΔPQR measure of angle Q is 90o. If tan P = 24/7, and PQ = 14 cm, then what is the length (in cm) of side QR? |
| A. | 50 |
| B. | 20 |
| C. | 26 |
| D. | 48 |
| Answer» E. | |
| 179. |
If cos θ + sec θ = 2, then (cos117 θ + sec117 θ) is equal to: |
| A. | 117 |
| B. | 2117 |
| C. | 234 |
| D. | 2 |
| Answer» E. | |
| 180. |
If tan A = 5/9, then what the value of [5 sin A + 9 cos A]/[5 sin A - 9 cos A]? |
| A. | 17/12 |
| B. | -53/28 |
| C. | -27/25 |
| D. | 31/23 |
| Answer» C. -27/25 | |
| 181. |
A vertical tower standing at the corner of a rectangular field subtends angles of 60° and 45° at the two nearer corners. If θ is the angle that the tower subtends at the farthest corner, then what is cot θ equal to? |
| A. | \(\frac{1}{2}\) |
| B. | 2 |
| C. | \(\frac{2}{{\sqrt 3 }}\) |
| D. | \(\frac{4}{{\sqrt 3 }}\) |
| Answer» D. \(\frac{4}{{\sqrt 3 }}\) | |
| 182. |
In ΔABC measure of angle B is 90°. If cosec A = 13/12, and AB = 10 cm, then what is the length (in cm) of side AC? |
| A. | 24 |
| B. | 12 |
| C. | 14 |
| D. | 26 |
| Answer» E. | |
| 183. |
If the height of a pole and the distance between the pole and a man standing nearby are equal, what would be the angle of elevation to the top of the pole? |
| A. | 60° |
| B. | 90° |
| C. | 30° |
| D. | 45° |
| Answer» E. | |
| 184. |
If \(\sec θ + \cos θ = \frac{5}{2}\), where 0 ≤ θ ≤ 90°, then what is the value of sin2 θ |
| A. | \(\frac{1}{4}\) |
| B. | \(\frac{1}{2}\) |
| C. | \(\frac{3}{4}\) |
| D. | 1 |
| Answer» D. 1 | |
| 185. |
645 - Δ LMN is right angled at M. If m∠N = 30°, thenTan L × (1 / 2) Cosec L = ? |
| A. | 2 |
| B. | 1 / √2 |
| C. | 1 |
| D. | 1 / 2 |
| Answer» D. 1 / 2 | |
| 186. |
If 7 × \(\left( cose{{c}^{2}}55{}^\circ -{{\tan }^{2}}35{}^\circ \right)+2\sin 90{}^\circ -y{{\tan }^{2}}52{}^\circ {{\tan }^{2}}38{}^\circ =\frac{y}{2},\) then the value of y is: |
| A. | 6 |
| B. | 2 |
| C. | 1 |
| D. | 3 |
| Answer» B. 2 | |
| 187. |
If \(\sec \theta = \frac{{13}}{5}\), then the value of \(\frac{{10\tan \theta + 24\cos ec\theta }}{{39\sin \theta - 10\sec \theta }}\) is: |
| A. | 3 |
| B. | 5 |
| C. | 2 |
| D. | \(\frac{{1 }}{{5}}\) |
| Answer» C. 2 | |
| 188. |
Δ ABC is right angled at B. If ∠A = 60°, then what is the value of sec C.sin A? |
| A. | 2/√3 |
| B. | √3/2 |
| C. | 2/3 |
| D. | 1 |
| Answer» E. | |
| 189. |
If 3 cos2 A + 7 sin2 A = 4, then what is the value of cot A, given that A is an acute angle? |
| A. | 1 |
| B. | √3 |
| C. | √3/2 |
| D. | 1/√3 |
| Answer» C. √3/2 | |
| 190. |
If \(\sinθ - \cosθ= \dfrac{7}{13}\) and 0° |
| A. | \(\dfrac{17}{13}\) |
| B. | \(\dfrac{13}{17}\) |
| C. | \(\dfrac{1}{13}\) |
| D. | \(\dfrac{1}{17}\) |
| Answer» B. \(\dfrac{13}{17}\) | |
| 191. |
Cos2θ + 1/Cosec2θ + 17 = x. What is the value of x2? |
| A. | 18 |
| B. | 324 |
| C. | 256 |
| D. | 16 |
| Answer» C. 256 | |
| 192. |
If tan4 x - tan2 x = 1, then the value of sin4 x + sin2 x is: |
| A. | 1 |
| B. | 3 / 2 |
| C. | 1 / 2 |
| D. | 3 / 4 |
| Answer» B. 3 / 2 | |
| 193. |
In ΔABC if sin2 A + sin2 B = sin2 C and l(AB) = 10 then the maximum value of the area of ΔABC is |
| A. | 50 |
| B. | \(10\sqrt{2}\) |
| C. | 25 |
| D. | \(25\sqrt{2}\) |
| Answer» D. \(25\sqrt{2}\) | |
| 194. |
If cosec2θ = sec (3θ – 15°), then θ is equal to: |
| A. | 21° |
| B. | 20° |
| C. | 25° |
| D. | 22° |
| Answer» B. 20° | |
| 195. |
If 2cos2θ – 5cos θ + 2 = 0, 0° < θ < 90°, then the value of (cosec θ + cot θ) is: |
| A. | 17 |
| B. | 23 |
| C. | 13 |
| D. | √3 |
| Answer» E. | |
| 196. |
A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 10 m away from the wall, what is the length of the ladder? |
| A. | 34.6 m |
| B. | 17.3 m |
| C. | 20 m |
| D. | 40 m |
| Answer» D. 40 m | |
| 197. |
(1 – sin A + cos A) 2 is equal to |
| A. | 2(1 – cos A)(1 + sin A) |
| B. | 2(1 – sin A)(1 + cos A) |
| C. | 2(1 – cos A)(1 – sin A) |
| D. | None of the above |
| Answer» C. 2(1 – cos A)(1 – sin A) | |
| 198. |
If x and y are positive acute angles such that sin (2x + 3y) = √3/2 and cos (4x - 3y) = √3/2, then what is the value of tan (6x - 3y)? |
| A. | 0 |
| B. | 1 |
| C. | 1/√3 |
| D. | √3 |
| Answer» E. | |
| 199. |
If cos (θ + 31°) = sin 47°, then what is the value of sin 5θ? |
| A. | ½ |
| B. | 1/√2 |
| C. | √3/2 |
| D. | 0 |
| Answer» D. 0 | |
| 200. |
Mishra observes the top of a tower of height \(25\sqrt 3 \;m\) from a point on the ground at an angle α. After walking 50 m towards the tower along the line joining the foot of the tower and the first point of observation. He observes that the angle of elevation of the top of the tower is 2α. Find α. |
| A. | 60° |
| B. | 90° |
| C. | 45° |
| D. | 30° |
| Answer» E. | |