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.
| 251. |
If 3cosθ = 4sinθ, then what is the value of tan (45° + θ)? |
| A. | 10 |
| B. | 7 |
| C. | \(\dfrac{7}{2}\) |
| D. | \(\dfrac{7}{4}\) |
| Answer» C. \(\dfrac{7}{2}\) | |
| 252. |
if cot4θ + cot2θ = 4, then cosec4θ – cosec2θ = ? |
| A. | 4 |
| B. | 0 |
| C. | 3 |
| D. | 2 |
| Answer» B. 0 | |
| 253. |
If sinθ cosθ = 1/2, then the value of sin6θ + cos6θ is |
| A. | 1/2 |
| B. | 3/2 |
| C. | 1 |
| D. | 1/4 |
| Answer» E. | |
| 254. |
In ΔXYZ measure of angle Y is 90o. If tan X = 15/8, and XY = 16cm, then what is the length (in cm) of side YZ? |
| A. | 34 |
| B. | 30 |
| C. | 15 |
| D. | 14 |
| Answer» C. 15 | |
| 255. |
If cosec θ = 1.25, then \(\frac{{4tan\theta - 5\cos \theta \; + \;1}}{{\sec \theta \; + \;4\cot \theta - 1}} = ?\) |
| A. | 9/11 |
| B. | 2 |
| C. | 10/11 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 256. |
If a straight line makes angles α, β and γ with the co-ordinate axes, then sin2α + sin2β + sin2γ is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» D. None of these | |
| 257. |
An observer 1.5 m tall is 20.5 m away from a tower 22 m high. The angle of elevation of the top of the tower from the eye of the observer is - |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 75° |
| Answer» C. 60° | |
| 258. |
If cosec 3θ = sec (20° + 2θ), then θ is equal to∶ |
| A. | 30° |
| B. | 14° |
| C. | 15° |
| D. | 20° |
| Answer» C. 15° | |
| 259. |
If 2sinθ + 15cos2θ = 7, 0° < θ < 90°, then tanθ + cosθ + secθ = ? |
| A. | \(3\frac{4}{5}\) |
| B. | 4 |
| C. | 3 |
| D. | \(3\frac{3}{5}\) |
| Answer» E. | |
| 260. |
(1 + cot2θ)(1 – cos2θ) = ? |
| A. | 0 |
| B. | 1/2 |
| C. | 1 |
| D. | Not defined |
| Answer» D. Not defined | |
| 261. |
If 21 tan θ = 20, then (1 + sin θ + cos θ) : (1 – sin θ + cos θ) = ? |
| A. | 3 : 1 |
| B. | 2 : 1 |
| C. | 5 : 2 |
| D. | 7 : 3 |
| Answer» E. | |
| 262. |
If sin(3θ)sec(2θ) = 1, then what is the value of [3tan2(5θ/2) – 1]? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 263. |
If tan4θ + tan2θ = 1 then the value of cos4θ + cos2θ is: |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | -1 |
| Answer» D. -1 | |
| 264. |
If 2 sin2θ = 3 cos θ, and 0 ≤ θ < 90°, then θ = ? |
| A. | 45° |
| B. | 30° |
| C. | 60° |
| D. | 90° |
| Answer» D. 90° | |
| 265. |
If Cos θ = 35/37, then what is the value of Cosec θ? |
| A. | 37/12 |
| B. | 33/12 |
| C. | 35/12 |
| D. | 12/35 |
| Answer» B. 33/12 | |
| 266. |
ΔPQR is right angled at Q. If cos P = 5/13, then what is the value of cosec R? |
| A. | 13/5 |
| B. | 5/12 |
| C. | 5/13 |
| D. | 13/12 |
| Answer» B. 5/12 | |
| 267. |
If \(0 \le x < \frac{\pi }{2},\) then the number of values of x for which sin x – sin 2x + sin 3x = 0, is: |
| A. | 3 |
| B. | 1 |
| C. | 4 |
| D. | 2 |
| Answer» E. | |
| 268. |
If Cosec θ = 17/8, then Cot θ = ? |
| A. | 17/8 |
| B. | 15/8 |
| C. | 8/15 |
| D. | 17/15 |
| Answer» C. 8/15 | |
| 269. |
∆XYZ is right angled at Y. If cosec X = 17/15, then what is the value of cot Z? |
| A. | 17/15 |
| B. | 8/17 |
| C. | 17/8 |
| D. | 15/8 |
| Answer» E. | |
| 270. |
If \(\frac{1}{{{\rm{cosec\theta \;}} + {\rm{\;}}1}}{\rm{\;}} + {\rm{\;}}\frac{1}{{{\rm{cosec\theta }} - 1}}{\rm{\;}} = {\rm{\;}}2{\rm{sec\theta }},0^\circ < {\rm{\theta }} < 90^\circ ,\) then the value of \(\frac{{{\rm{tan\theta \;}} + {\rm{\;}}2\sec {\rm{\theta }}}}{{{\rm{cosec\theta }}}}\) is: |
| A. | \(\frac{{2{\rm{\;}} + {\rm{\;}}\sqrt 3 }}{2}\) |
| B. | \(\frac{{4{\rm{\;}} + {\rm{\;}}\sqrt 3 }}{2}\) |
| C. | \(\frac{{2{\rm{\;}} + {\rm{\;}}\sqrt 2 }}{2}\) |
| D. | \(\frac{{4{\rm{\;}} + {\rm{\;}}\sqrt 2 }}{2}\) |
| Answer» E. | |
| 271. |
If (cotA – tan A)/2 = x, then the value of x is |
| A. | tan2A |
| B. | cot2A |
| C. | tan3A |
| D. | cotA |
| Answer» C. tan3A | |
| 272. |
A girl 1.2 m tall can just see the sum over a 3.62 m tall wall which is 2.42 m away from her. The angle of elevation of the sun is∶ |
| A. | 60° |
| B. | 30° |
| C. | 90° |
| D. | 45° |
| E. | 75° |
| Answer» E. 75° | |
| 273. |
3sin230° + 2cos245° - 5tan230° = ______ |
| A. | 1/2 |
| B. | 1/6 |
| C. | 1/12 |
| D. | 1/3 |
| Answer» D. 1/3 | |
| 274. |
If A lies in the third quadrant, and 20 tanA = 21, then the value of \(\frac{{5sinA - 2cosA}}{{4cosA - \frac{5}{7}sinA}}\) is: |
| A. | 1 |
| B. | 13/12 |
| C. | 5/29 |
| D. | -65/29 |
| Answer» B. 13/12 | |
| 275. |
A and B are positive acute angles such that cos 2B = 3 sin2 A and 3 sin 2A = 2 sin 2B. What is the value of (A + 2B)? |
| A. | π / 6 |
| B. | π / 4 |
| C. | π / 3 |
| D. | π / 2 |
| Answer» E. | |
| 276. |
If sin θ = 3 sin (θ + 2α), then the value of tan (θ + α) + 2 tan α is |
| A. | 3 |
| B. | 2 |
| C. | -1 |
| D. | 0 |
| Answer» E. | |
| 277. |
From a height of h units, a man observes the angle of elevation as α and angle of depression as β of the top and bottom respectively of a tower of height H (> 4h). To what further height should be climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower? |
| A. | H - h units |
| B. | H - 2h units |
| C. | H - 3h units |
| D. | H - 4h units |
| Answer» C. H - 3h units | |
| 278. |
If \(2\cot \theta = 3\), then \(\frac{{\sqrt {13} \cos \theta - 3\tan \theta }}{{3\tan \theta + \sqrt {13} \sin \theta }}\) is: |
| A. | 3/4 |
| B. | 1/4 |
| C. | 2/3 |
| D. | 1/5 |
| Answer» C. 2/3 | |
| 279. |
3 sin2 30° + 2 cos2 45° - 5 tan2 30° = _______ |
| A. | 1/2 |
| B. | 1/6 |
| C. | 1/12 |
| D. | 1/3 |
| Answer» D. 1/3 | |
| 280. |
If \(sin\theta =\frac{4}{5}\), then \(\frac{1 - cos\theta}{1 + cos\theta} =\) |
| A. | 1/2 |
| B. | 1/8 |
| C. | 1/16 |
| D. | 1/4 |
| Answer» E. | |
| 281. |
If tan a = √3 + 2, then the value of tan a - cot a is |
| A. | 2 |
| B. | 2√3 |
| C. | √3 - 2 |
| D. | 4 |
| Answer» C. √3 - 2 | |
| 282. |
Consider the following statements:1. The equation 2 sin2 θ - cos θ + 4 = 0 is possible for all θ2. tan θ + cot θ cannot be less than 2, where 0 |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 283. |
If sin P + cosec P = 2, then the value of sin7P + cosec7P is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» C. 3 | |
| 284. |
If sin θ + sin2θ = 1, then find cos2θ + cos4θ. |
| A. | -2 |
| B. | 2 |
| C. | -1 |
| D. | 1 |
| Answer» E. | |
| 285. |
If cot θ = a/b, then find \(\frac{{\cos \theta \; - {\rm{\;sin}}\theta }}{{\cos \theta \; + \;{\rm{\;sin}}\theta }}\) |
| A. | b/a |
| B. | a/b |
| C. | a2/b2 |
| D. | (a – b)/(a + b) |
| Answer» E. | |
| 286. |
An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground? |
| A. | 100√3 m |
| B. | 100/√3 m |
| C. | 50√3 m |
| D. | 150(√3 + 1) m |
| Answer» B. 100/√3 m | |
| 287. |
2cos(π/2 – θ) + 3sin(π/2 + θ) – (3sinθ + 2cosθ) = ?A. cosθ – sin θB. sinθ – cosθC. sinθ + cosθD. cotθ – tanθ |
| A. | B |
| B. | D |
| C. | C |
| D. | A |
| Answer» E. | |
| 288. |
If cos θ = 2p/(p2 + 1), then sin θ is equal to: |
| A. | (p2 - 1)/(p2 + 1) |
| B. | 2p/(p2 - 1) |
| C. | (p2 + 1)/(p2 - 1) |
| D. | p2/(p2 + 1) |
| Answer» B. 2p/(p2 - 1) | |
| 289. |
A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15°. What is the length (in metres) of the ladder? |
| A. | 5√6 - 5√3 |
| B. | 5√6 - 5√2 |
| C. | 5√2 - 1 |
| D. | 5√3 + 5√2 |
| Answer» C. 5√2 - 1 | |
| 290. |
If cosec θ - cot θ = m, then what is cosec θ equal to? |
| A. | \(m + \frac{1}{m}\) |
| B. | \(m - \frac{1}{m}\) |
| C. | \(\frac{m}{2} + \frac{2}{m}\) |
| D. | \(\frac{m}{2} + \frac{1}{2m}\) |
| Answer» E. | |
| 291. |
If \(\frac{\cos \theta }{1-sin\theta }-\frac{cos\theta }{1+sin\theta }=2\) find the value of ‘θ’. |
| A. | 60° |
| B. | 90° |
| C. | 45° |
| D. | 30° |
| Answer» D. 30° | |
| 292. |
If 4(cosec2 66° - tan2 24°) + \(\frac{1}{2}\)sin 90° - 4 tan266°.y.tan2 24° = \(\frac{y}{2}\), then the value of y is: |
| A. | -12 |
| B. | 1 |
| C. | 12 |
| D. | -1 |
| Answer» C. 12 | |
| 293. |
If 3 sec2x – 2 tan2 x = 6 and 0° ≤ x ≤ 90° then x = ? |
| A. | 60° |
| B. | 30° |
| C. | 45° |
| D. | 90° |
| Answer» B. 30° | |
| 294. |
If (tanA – tanB)/(1 + tanAtanB) = x, then the value of x is |
| A. | tan(A – B) |
| B. | tan(A + B) |
| C. | cot(A – B) |
| D. | cot(A + B) |
| Answer» B. tan(A + B) | |
| 295. |
∆ABC is right angled at B. If cosA = 8/17, then what is the value of cotC ? |
| A. | 15/8 |
| B. | 15/17 |
| C. | 8/17 |
| D. | 17/15 |
| Answer» B. 15/17 | |
| 296. |
In ΔXYZ measure of angle Y is 900. If cot X = 5/12, and XY = 2.5cm, then what is the length (in cm) of side XZ? |
| A. | 6 |
| B. | 4 |
| C. | 5.6 |
| D. | 6.5 |
| Answer» E. | |
| 297. |
If \({\rm{K}} = \sin \left( {\frac{{\rm{\pi }}}{{18}}} \right)\sin \left( {\frac{{5{\rm{\pi }}}}{{18}}} \right)\sin \left( {\frac{{7{\rm{\pi }}}}{{18}}} \right)\), then what is the value of K? |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{8}\) |
| D. | \(\frac{1}{{16}}\) |
| Answer» D. \(\frac{1}{{16}}\) | |
| 298. |
If p = sinθ + cosθ and q = secθ + cosecθ, then \(q\left( {{p^2} - 1} \right)\)is - |
| A. | p |
| B. | 2p |
| C. | 3p |
| D. | 4p |
| Answer» C. 3p | |
| 299. |
For θ being an acute angle, if cosec θ = 1.25, then the value of (4tanθ – 5cosθ)/(secθ + 4cotθ) is equal to: |
| A. | 1/2 |
| B. | 4/7 |
| C. | 1/4 |
| D. | 3/7 |
| Answer» B. 4/7 | |
| 300. |
If tanθ = 4/3, what is the value of sin θ + cos θ? |
| A. | 4/3 |
| B. | 1 |
| C. | 7/3 |
| D. | 7/5 |
| Answer» E. | |