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.
| 351. |
If \(.\frac{{\cos \theta }}{{1 + sin\theta }} + \frac{{cos\theta }}{{1 - sin\theta }} = 4\;and\;\theta \) is acute, then what is the value (in degrees) of θ |
| A. | 30 |
| B. | 45 |
| C. | 60 |
| D. | 90 |
| Answer» D. 90 | |
| 352. |
A flag of height 4 metres is standing on the top of a building. The angle of elevation of the top of the flag from a point X is 45° and the angle of elevation of the top of building from X is 30°. Point X is on the ground level. What is the height (in metres) of the building? |
| A. | √3 + 2 |
| B. | 2(√3 + 1) |
| C. | 4(√3 + 1) |
| D. | (√3 + 1) |
| Answer» C. 4(√3 + 1) | |
| 353. |
If Δ = a2 - (b - c)2, where Δ is the area of the ΔABC, then tan A equals |
| A. | \(\frac {15}{16}\) |
| B. | \(\frac {8}{15}\) |
| C. | \(\frac {8}{17}\) |
| D. | \(\frac {1}{2}\) |
| Answer» C. \(\frac {8}{17}\) | |
| 354. |
If \(\dfrac{\sin θ + \cos θ }{\sin θ - \cos θ}=3\) then the value of sin4 θ is |
| A. | \(\dfrac{16}{25}\) |
| B. | \(\dfrac{2}{3}\) |
| C. | \(\dfrac{1}{9}\) |
| D. | \(\dfrac{2}{9}\) |
| Answer» B. \(\dfrac{2}{3}\) | |
| 355. |
If the sides of an acute angle triangle ABC are 7cm, 8cm and 9cm, find the value of sec C? |
| A. | 3/2 |
| B. | 2/3 |
| C. | 1/3 |
| D. | 2 |
| Answer» B. 2/3 | |
| 356. |
If (A + B + C) = 90°, then what is the value of sin (A / 2) sin [(180 - B - C) / 2] + cos (A / 2) sin (B + C) / 2? |
| A. | 1 / 2 |
| B. | 1 |
| C. | 1 / √2 |
| D. | √3 / 2 |
| Answer» D. √3 / 2 | |
| 357. |
If cos x = tan y, cot y = tan z and cot z = tan x, then sin x = ? |
| A. | \(\dfrac{\sqrt{5}-1}{2}\) |
| B. | \(\dfrac{\sqrt{5}+1}{2}\) |
| C. | \(\dfrac{\sqrt{5}+1}{4}\) |
| D. | \(\dfrac{\sqrt{5}-1}{4}\) |
| Answer» B. \(\dfrac{\sqrt{5}+1}{2}\) | |
| 358. |
If 0 < A, B < 45°, cos (A + B) = 24/25 and sin (A – B) = 15/17, then tan2A is: |
| A. | 0 |
| B. | 1 |
| C. | 213/4 |
| D. | 416/87 |
| Answer» E. | |
| 359. |
If cos x = -√3/2 and π < x < 3π/2, then the value of 4 cot2 x – 3 cosec2 x is: |
| A. | 0 |
| B. | 2 |
| C. | 8 |
| D. | 1 |
| Answer» B. 2 | |
| 360. |
If sin x + sin2 x = 1, then cos4 x + cos2 x is equal to: |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» C. -1 | |
| 361. |
Find the value of sin (180° – θ) cos (90° – θ) – cos (180° – θ) sin (90° – θ). |
| A. | cos θ |
| B. | 1 |
| C. | tan θ |
| D. | 0 |
| Answer» C. tan θ | |
| 362. |
If 7 cos2θ + 3sin2θ = 6, 0° < θ < 90°, then the value of \(\frac{{{\rm{co}}{{\rm{t}}^2}2{\rm{\theta }} + {\rm{se}}{{\rm{c}}^2}2{\rm{\theta }}}}{{{\rm{ta}}{{\rm{n}}^2}2{\rm{\theta }} - {\rm{si}}{{\rm{n}}^2}2{\rm{\theta }}}}\) is: |
| A. | 49/45 |
| B. | 28/27 |
| C. | 52/27 |
| D. | 26/15 |
| Answer» D. 26/15 | |
| 363. |
If θ measured in radians is the angle between the hour hand and the minute hand of a clock when the time is 4:36 pm, then which one of the following is correct? |
| A. | 3π/5 < θ < 4π/5 |
| B. | 2π/5 < θ < 3π/5 |
| C. | π/5 ≤ θ ≤ 2π/5 |
| D. | 7π/15 ≤ θ ≤ 8π/15 |
| Answer» C. π/5 ≤ θ ≤ 2π/5 | |
| 364. |
If √[(1 - cosA)/2] = x, then the value of x is |
| A. | cos(A/2) |
| B. | tan(A/2) |
| C. | sin(A/2) |
| D. | cot(A/2) |
| Answer» D. cot(A/2) | |
| 365. |
A vertical pole, 30 m long, casts a shadow 20 m long on the ground. At the same time, a vertical building casts a shadow 60 m long on the ground. What is the height of the building? |
| A. | 60 m |
| B. | 120 m |
| C. | 150 m |
| D. | 90 m |
| Answer» E. | |
| 366. |
If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60 m. The height of the pillar is: |
| A. | 60(√3 + 1) m |
| B. | 30(√3 - 1) m |
| C. | 30(√3 + 1) m |
| D. | 60(√3 - 1) m |
| Answer» D. 60(√3 - 1) m | |
| 367. |
In ΔABC measure of angle B is 90°, if sin A = 24/25, and AB = 1.4 cm, then what is the length (in cm) of side BC? |
| A. | 4.8 |
| B. | 5 |
| C. | 3 |
| D. | 5.6 |
| Answer» B. 5 | |
| 368. |
If \({\rm{tan}}\theta = \frac{2}{3},\) then what is the value of \(\frac{{15si{n^2}\theta - 3co{s^2}\theta }}{{5{{\sin }^2}\theta + 3co{s^2}\theta }}?\) |
| A. | 33/32 |
| B. | 11/29 |
| C. | 33/47 |
| D. | 11/32 |
| Answer» D. 11/32 | |
| 369. |
If tan θ = a/b such that \(\frac{asin~\theta ~-b\cos \theta }{a\sin \theta ~+~b\cos \theta }~=~{{\left[ \frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}} \right]}^{k}}\) , then k is: |
| A. | 6 |
| B. | 2 |
| C. | 1 |
| D. | 8 |
| Answer» D. 8 | |
| 370. |
If \(\text{co}{{\text{s}}^{-1}}\left( \frac{2}{3\text{x}} \right)+\text{co}{{\text{s}}^{-1}}\left( \frac{3}{4\text{x}} \right)=\frac{\text{ }\!\!\pi\!\!\text{ }}{2}\left( \text{x}>\frac{3}{4} \right),\) then x is equal to: |
| A. | \(\frac{\sqrt{145}}{12}\) |
| B. | \(\frac{\sqrt{145}}{10}\) |
| C. | \(\frac{\sqrt{146}}{12}\) |
| D. | \(\frac{\sqrt{145}}{11}\) |
| Answer» B. \(\frac{\sqrt{145}}{10}\) | |
| 371. |
If Cosec θ = 25/7, then Tan θ = ? |
| A. | 24/7 |
| B. | 7/25 |
| C. | 27/25 |
| D. | 7/24 |
| Answer» E. | |
| 372. |
If \(\frac{{\sin \left( {x\; + \;y} \right)}}{{\sin \left( {x\; - \;y} \right)}} = \;\frac{{a\; + \;b}}{{a\; - \;b}}\) then what is \(\frac{{\tan x}}{{\tan y}}\) equal to? |
| A. | \(\frac{a}{b}\) |
| B. | \(\frac{b}{a}\) |
| C. | \(\frac{{a + b}}{{a - b}}\) |
| D. | \(\frac{{a - b}}{{a + b}}\) |
| Answer» B. \(\frac{b}{a}\) | |
| 373. |
If cot θ (1 + sin θ) = 4m and cot θ (1 – sin θ) = 4n, then which one of the following is correct? |
| A. | (m2 + n2)2 = mn |
| B. | (m2 – n2)2 = mn |
| C. | (m2 – n2)2 = m2n2 |
| D. | (m2 + n2)2 = m2n2 |
| Answer» C. (m2 – n2)2 = m2n2 | |
| 374. |
If cosec2 |
| A. | √3/2 |
| B. | 5/2√3 |
| C. | 12/√3 |
| D. | 2√3/3 |
| Answer» C. 12/√3 | |
| 375. |
In a triangle the length of the sides AB and BC are both 1.5 m. What is the length of AC, if the angle formed at B is 60o? |
| A. | 1.25 m |
| B. | 1.5 m |
| C. | 2.25 m |
| D. | 1 m |
| Answer» C. 2.25 m | |
| 376. |
80 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. What is the height (in metres) of the tower? |
| A. | 40 |
| B. | 60√3 |
| C. | 80√3 |
| D. | 40/√3 |
| Answer» D. 40/√3 | |
| 377. |
If tanθ - cotθ = cosecθ, 0° < θ < 90°, then what is the value of \(\frac{{2tan\theta - cos\theta }}{{\sqrt 3 cot\theta+ sec\theta }}\)? |
| A. | \(\frac{{2\sqrt 3 - 1}}{3}\) |
| B. | \(\frac{{23\left( {2\sqrt 3 - 1} \right)}}{3}\) |
| C. | \(\frac{{4\sqrt 3 - 1}}{6}\) |
| D. | \(\frac{{3\sqrt 3 - 1}}{6}\) |
| Answer» D. \(\frac{{3\sqrt 3 - 1}}{6}\) | |
| 378. |
If the length of the shadow is \(\sqrt{3}\) times the height of the tower, then the angle of elevation of the sun is: |
| A. | 30° |
| B. | 45 |
| C. | 90° |
| D. | 60° |
| Answer» B. 45 | |
| 379. |
A man observes the angle of elevation of the top of mountain to be 30°. He walks 1000 feet nearer and finds the angle of elevation to be 45°. What is the distance of the first point of observation from the foot of the mountain? |
| A. | \(\rm 500\sqrt{3}(\sqrt{3}+1)ft\) |
| B. | \(\rm 500(\sqrt{3}+1)ft\) |
| C. | \(\rm 500(\sqrt{3}-1)ft\) |
| D. | \(\rm 500\sqrt{3}(\sqrt{3}-1)ft\) |
| Answer» B. \(\rm 500(\sqrt{3}+1)ft\) | |
| 380. |
In Sin3θ = cos(θ - 26°), where 3θ and (θ - 26°) are acute angles, then value of θ |
| A. | 30° |
| B. | 27° |
| C. | 26° |
| D. | 29° |
| Answer» E. | |
| 381. |
A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30°. After some time angle of depression becomes 60°. What is the distance travelled by car during this time? |
| A. | 100√3 m |
| B. | 200√3/3 m |
| C. | 100√3/3 m |
| D. | 200√3 m |
| Answer» C. 100√3/3 m | |
| 382. |
If 3sin θ + 5cos θ = 4, then what is the value of (3cos θ – 5sin θ)2? |
| A. | 9 |
| B. | 12 |
| C. | 16 |
| D. | 18 |
| Answer» E. | |
| 383. |
If tanA + cotA = 2, then tan3A + cot3A = ?A. –(2)B. 1C. 0D. 3 |
| A. | A |
| B. | B |
| C. | C |
| D. | D |
| Answer» B. B | |
| 384. |
If A > 0, B > 0 and A + B > \(\frac \pi 6\), then the minimum value of tan A + tan B is |
| A. | √3 - √2 |
| B. | 4 - 2√3 |
| C. | \(\frac 2 {\sqrt 3}\) |
| D. | 2 - √3 |
| Answer» C. \(\frac 2 {\sqrt 3}\) | |
| 385. |
If \(\rm \sin^{-1} \dfrac{2a}{1+a^2} + \sin^{-1} \dfrac{2b}{1+b^2}=2 \tan^{-1} n\) then? |
| A. | \(n=\dfrac{a-b}{1+ab}\) |
| B. | \(n=\dfrac{(ab)}{(a-a)}\) |
| C. | \(n=\dfrac{(a+b)}{(1-ab)}\) |
| D. | \(n=\dfrac{(1-ab)}{(1+ab)}\) |
| Answer» D. \(n=\dfrac{(1-ab)}{(1+ab)}\) | |
| 386. |
If cosecθ = 3x and cotθ = 3/x, (x ≠ 0) then the value of 6(x2 - 1/x2) is: |
| A. | 12 |
| B. | 1 |
| C. | 14 |
| D. | 2/3 |
| Answer» E. | |
| 387. |
Consider the following statements :1. If \(\;\frac{{cos\theta }}{{1 - sin\theta }} + \frac{{\cos \theta }}{{1 + sin\theta }} = 4,\) where 0 < θ < 90°, then θ = 60°2. If 3 tan θ + cot θ = 5 cosec θ, where 0 < θ < 90°, then θ = 60°.Which of the statements given above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 388. |
If x cos θ + y sin θ = z, then what is the value of (x sin θ – y cos θ)2? |
| A. | x2 + y2 – z2 |
| B. | x2 – y2 – z2 |
| C. | x2 – y2 + z2 |
| D. | x2 + y2 + z2 |
| Answer» B. x2 – y2 – z2 | |
| 389. |
If \(cos x = \frac{3}{5}\), then find the value of sin x - sin3 x. |
| A. | 0.476 |
| B. | 0.288 |
| C. | 0.358 |
| D. | 0.389 |
| Answer» C. 0.358 | |
| 390. |
30 degree is equal to _________ radians. |
| A. | π/3 |
| B. | π/6 |
| C. | π/2 |
| D. | π/4 |
| Answer» C. π/2 | |
| 391. |
If tan245° – cos2 60° = x sin 45° cos 45° cot 30°, then find the value of ‘x’. |
| A. | 1/√2 |
| B. | 3/2 |
| C. | √3/2 |
| D. | 2/√3 |
| Answer» D. 2/√3 | |
| 392. |
If 4θ is an acute angle, and cot 4θ = tan (θ -5°) , then what is the value of θ? |
| A. | 24° |
| B. | 45° |
| C. | 21° |
| D. | 19° |
| Answer» E. | |
| 393. |
If sin A = 1/2, then sin2 2A = ____________ |
| A. | 1/2 |
| B. | 1/4 |
| C. | 3/4 |
| D. | \(\sqrt{3}/2\) |
| Answer» D. \(\sqrt{3}/2\) | |
| 394. |
If sin (θ + 23°) = cos 58°, then what is the value of cos 5θ? |
| A. | 1/2 |
| B. | 1/√2 |
| C. | √3/2 |
| D. | 0 |
| Answer» C. √3/2 | |
| 395. |
If 11 sin2 θ – cos2 θ + 4 sin θ – 4 = 0, 0° < θ < 90°, then what is the value of \(\frac{{\cos 2\;\theta \; + \;\cot 2\theta }}{{\sec 2\theta - \tan 2\;\theta }}?\) |
| A. | \(\frac{{12\; + \;5\sqrt 3 }}{3}\) |
| B. | \(\frac{{10\; + \;5\sqrt 3 }}{3}\) |
| C. | \(\frac{{12\; + \;7\sqrt 3 }}{6}\) |
| D. | \(\frac{{10\; + \;7\sqrt 3 }}{6}\) |
| Answer» D. \(\frac{{10\; + \;7\sqrt 3 }}{6}\) | |
| 396. |
If sin x + sin y = a and cos x + cos y = b, then \({\tan ^2}\left( {\frac{{{\rm{x}} + {\rm{y}}}}{2}} \right) + {\tan ^2}\left( {\frac{{{\rm{x}} - {\rm{y}}}}{2}} \right)\) is equal to |
| A. | \(\frac{{{{\rm{a}}^4} + {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\) |
| B. | \(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{b}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{b}}^4}}}\) |
| C. | \(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}\) |
| D. | None of the above |
| Answer» C. \(\frac{{{{\rm{a}}^4} - {{\rm{b}}^4} + 4{{\rm{a}}^2}}}{{{{\rm{a}}^2}{{\rm{b}}^2} + {{\rm{a}}^4}}}\) | |
| 397. |
If A is in the fourth quadrant and cos \(A = \frac{5}{{13}},\) then find the value of \(\frac{{13\;sinA\; + \;5\sec A}}{{5\tan A\; + \;6cosec\;A}}\) |
| A. | \(\frac{{ - 4}}{{37}}\) |
| B. | \(\frac{2}{{37}}\) |
| C. | \(\frac{{ - 3}}{{37}}\) |
| D. | \(\frac{{ - 2}}{{37}}\) |
| Answer» E. | |
| 398. |
For α and β both being acute angles, it is given thatSin(α + β) = 1, cos(α - β) = 1/2. The values of α and β are: |
| A. | 45°, 15° |
| B. | 60°, 30° |
| C. | 75°, 45° |
| D. | 75°, 15° |
| Answer» E. | |
| 399. |
\(\frac{sin^2 \ \theta}{cos\theta(1 + cos\theta)} +\frac{1 + cos \theta}{cos\theta} = \ ?\) |
| A. | cosecθ |
| B. | 2secθ |
| C. | 2cosθ |
| D. | secθ |
| Answer» C. 2cosθ | |
| 400. |
If θ is an acute angle, and its is given that 5 sinθ + 12 cosθ = 13, then what is the value of tanθ? |
| A. | 5/13 |
| B. | 12/13 |
| C. | 13/12 |
| D. | 5/12 |
| Answer» E. | |