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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.
| 401. |
If \(\rm cosec\;\theta = \frac {13}{12}\), then the value of \( \frac{{2\sin\theta - 3\cos\theta }}{{4\sin\theta - 9\cos\theta }}\) is: |
| A. | 3 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» B. 4 | |
| 402. |
A man standing in a point C of a ground. He observes a flying an aero-plane in the east at an angle of elevation of 30° and after 30 seconds, he observes the same aero-plane in the west at an angle of elevation of 60°. If the aero-plane flies all along in a straight line at a height of 480√3 m, then its speed in km/h is: |
| A. | 249.8 |
| B. | 230.4 |
| C. | 247.8 |
| D. | 257.5 |
| Answer» C. 247.8 | |
| 403. |
4/7 part of a pillar is buried in mud, if one-third of it is pulled out then 250 cm of the pillar is buried in the mud, find the length of the pole? |
| A. | 10.5 meter |
| B. | 11.5 meter |
| C. | 13.5 meter |
| D. | 9.5 meter |
| Answer» B. 11.5 meter | |
| 404. |
Given that A = cot30° and \(B = \frac{{\cot 60^\circ \cot 30^\circ + 1}}{{\cot 30^\circ - \cot 60^\circ }},\) which of the relations stated below is true? |
| A. | A < B |
| B. | A > B |
| C. | A = B |
| D. | A + B = 1 |
| Answer» D. A + B = 1 | |
| 405. |
From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 270 m high, the distance of point P from the foot of the tower is∶ |
| A. | 467.65 m |
| B. | 476.65 m |
| C. | 376.65 m |
| D. | 367.65 m |
| Answer» B. 476.65 m | |
| 406. |
If \(sec\theta = \frac{a}{b},b \ne 0,then\frac{{1 - {{\tan }^2}\theta }}{{2 - {{\sin }^2}\theta }}\)=? |
| A. | \(\frac{{{b^2}\left( {2{b^2} - {a^2}} \right)}}{{{a^2}\left( {{a^2} + {b^2}} \right)}}\) |
| B. | \(\frac{{{b^2}\left( {2{b^2} + {a^2}} \right)}}{{{a^2}\left( {{a^2} + {b^2}} \right)}}\) |
| C. | \(\frac{{{a^2}\left( {2{b^2} - {a^2}} \right)}}{{{b^2}\left( {{a^2} + {b^2}} \right)}}\) |
| D. | \(\frac{{{a^2}\left( {2{b^2} - {a^2}} \right)}}{{{a^2}\left( {{a^2} - {b^2}} \right)}}\) |
| Answer» D. \(\frac{{{a^2}\left( {2{b^2} - {a^2}} \right)}}{{{a^2}\left( {{a^2} - {b^2}} \right)}}\) | |
| 407. |
If 3 + cos2θ = 3(cot2θ + sin2θ), 0° < θ < 90°, then what is the value of (cos θ + 2sinθ)? |
| A. | \(\frac{{3\sqrt 3 + 1}}{2}\) |
| B. | \(\frac{{2\sqrt {3\;} + 1}}{2}\) |
| C. | \(\frac{{\sqrt {3\;} + 2}}{2}\) |
| D. | 3√2 |
| Answer» C. \(\frac{{\sqrt {3\;} + 2}}{2}\) | |
| 408. |
If 3 sec2 x - 4 = 0, then the value of x (0 < x < 90°) |
| A. | 45° |
| B. | 15° |
| C. | 30° |
| D. | 60° |
| Answer» D. 60° | |
| 409. |
If cos θ = 5/13, then cosec θ = ? |
| A. | 5/12 |
| B. | 12/5 |
| C. | 13/5 |
| D. | 13/12 |
| Answer» E. | |
| 410. |
If \(sin\;x = \frac{4}{5}\) then sec2 x – 1 = ?A. \(\frac{{16}}{{25}}\)B. \(\frac{{25}}{{9}}\)C.\(\frac{{9}}{{16}}\)D. \(\frac{{16}}{{9}}\) |
| A. | A |
| B. | D |
| C. | B |
| D. | C |
| Answer» C. B | |
| 411. |
If Secθ - Tanθ = 1/3, the value of (Secθ + tanθ) is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 412. |
ΔDEF is right angled at E. If ∠D = 60°, then find the value of (cot F + 1/√3). |
| A. | 3√3/2 |
| B. | 4/√3 |
| C. | (2 + 2√3)/√3 |
| D. | 7/2√3 |
| Answer» C. (2 + 2√3)/√3 | |
| 413. |
If 0° |
| A. | √3 + 2 |
| B. | 2(2 – √3) |
| C. | √3 + 1 |
| D. | 2(√3 – 1) |
| Answer» C. √3 + 1 | |
| 414. |
If \(\frac {\cos^2 θ }{\cot^2 θ - \cos^2 θ} = 3,\) where 0° |
| A. | 60° |
| B. | 50° |
| C. | 45° |
| D. | 30° |
| Answer» B. 50° | |
| 415. |
ΔABC is right angled at B. If cot A = 8/15, then what is the value of cos C? |
| A. | 15/8 |
| B. | 8/17 |
| C. | 17/15 |
| D. | 15/17 |
| Answer» E. | |
| 416. |
In ΔPQR measure of angle Q is 90°. If tan P = 4/3, and PQ = 1.5 cm, then what is the length (in cm) of side PR? |
| A. | 2 |
| B. | 2.5 |
| C. | 3 |
| D. | 4.8 |
| Answer» C. 3 | |
| 417. |
For 0° < θ < 90°, if 2 cos2θ = 3 sin θ, then the value of (cosec2θ – cot2θ + cos2θ) is equal to: |
| A. | \(1\frac{1}{2}\) |
| B. | \(2\frac{3}{4}\) |
| C. | \(1\frac{3}{4}\) |
| D. | \(2\frac{1}{4}\) |
| Answer» D. \(2\frac{1}{4}\) | |
| 418. |
If 4(cosec2 57° - tan2 33°) - cos 90° - y tan2 66° tan2 24° \(=\dfrac{y}{2}\), the value of y is: |
| A. | \(\dfrac{1}{3}\) |
| B. | \(\dfrac{8}{3}\) |
| C. | \(8\) |
| D. | \(\dfrac{3}{8}\) |
| Answer» C. \(8\) | |
| 419. |
If cosec θ = 13/12, then sin θ + cos θ - tan θ is equal to: |
| A. | -71/65 |
| B. | 91/65 |
| C. | 71/65 |
| D. | 139/65 |
| Answer» B. 91/65 | |
| 420. |
If sin θ = √3cosθ, 0° < θ < 90°, then the value of 2sin2θ + sec2θ + sinθsec θ + cosec θ is ∶ |
| A. | \(\frac{{33\; + \;10\sqrt 3 }}{6}\) |
| B. | \(\frac{{19\; + \;10\sqrt 3 }}{6}\) |
| C. | \(\frac{{33\; + \;10\sqrt 3 }}{3}\) |
| D. | \(\frac{{19\; + \;10\sqrt 3 }}{3}\) |
| Answer» B. \(\frac{{19\; + \;10\sqrt 3 }}{6}\) | |
| 421. |
If cosec2x - 2 = 0, then the value of x(0 < x < 90°) is: |
| A. | 15° |
| B. | 60° |
| C. | 30° |
| D. | 45° |
| Answer» E. | |
| 422. |
If 4 – 2sin2 θ – 5cos θ = 0, 0° < θ < 90°, then the value of sin θ + tan θ is: |
| A. | (3√2)/2 |
| B. | (3√3)/2 |
| C. | 3√2 |
| D. | 2√3 |
| Answer» C. 3√2 | |
| 423. |
If sinθ + sin5θ = sin3θ and 0 < θ < (π/2), then what is the value of θ (in degrees)? |
| A. | 30 |
| B. | 45 |
| C. | 50 |
| D. | 75 |
| Answer» B. 45 | |
| 424. |
A balloon is connected to a meteorological station by a cable of length 130 m, inclined at 60° to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the cable.A. 110.32 mB. 173 mC. 163.28 mD. 112.58 m |
| A. | C |
| B. | A |
| C. | B |
| D. | D |
| Answer» E. | |
| 425. |
If 3cos2 A + 7sin2 A = 3, 0° ≤ A ≤ 90°, then the value of A is: |
| A. | 90° |
| B. | 45° |
| C. | 0° |
| D. | 30° |
| Answer» D. 30° | |
| 426. |
If tan x = 1, 0 < x < 90°, then what is the value of 2 sin x cos x? |
| A. | \(\frac{1}{2}\) |
| B. | 1 |
| C. | \(\frac{{\sqrt 3 }}{2}\) |
| D. | √3 |
| Answer» C. \(\frac{{\sqrt 3 }}{2}\) | |
| 427. |
If \(a^2 \sec^2 x - b^2 \tan^2 x = c^2\) then the value of \(\sec^2 x + \tan^2 x\) is equal to (assume b2 ≠ a2) |
| A. | \(\dfrac{b^2- a^2 + 2c^2}{b^2 + a^2}\) |
| B. | \(\dfrac{b^2+ a^2 - 2c^2}{b^2 - a^2}\) |
| C. | \(\dfrac{b^2 - a^2 - 2c^2}{b^2 + a^2}\) |
| D. | \(\dfrac{b^2 - a^2}{b^2 + a^2 + 2c^2}\) |
| Answer» C. \(\dfrac{b^2 - a^2 - 2c^2}{b^2 + a^2}\) | |
| 428. |
If 3 sin x + 4 cos x = 2, then the value of 3 cos x - 4 sin x is equal to: |
| A. | 21 |
| B. | \(\sqrt {21}\) |
| C. | \(\sqrt {23}\) |
| D. | \(\sqrt {29}\) |
| Answer» C. \(\sqrt {23}\) | |
| 429. |
If cos θ = 35/37, then what is the value of cot θ? |
| A. | 12/35 |
| B. | 35/12 |
| C. | 37/12 |
| D. | 12/37 |
| Answer» C. 37/12 | |
| 430. |
If sec (3x – 20)° = cosec (3y + 20)°, what is the value of tan (x + y)? |
| A. | 1 |
| B. | √3 |
| C. | 1/√3 |
| D. | 2√3 |
| Answer» D. 2√3 | |
| 431. |
Find the value of sin (2190°) |
| A. | 0 |
| B. | \(\frac 12\) |
| C. | \(\frac {1}{\sqrt2}\) |
| D. | \(\frac {\sqrt3}{2}\) |
| Answer» C. \(\frac {1}{\sqrt2}\) | |
| 432. |
If x = (sec2 θ – tan θ) / (sec2 θ + tan θ), then which one of the following is correct? |
| A. | 1/3 < x < 3 |
| B. | x ∈ [1/3, 3] |
| C. | -3 < x < -1/3 |
| D. | 1/3 ≤ x ≤ 3 |
| Answer» E. | |
| 433. |
If 0 < θ ≤ 90°, solve for 'θ' where cos2 θ – 3 cos θ + 2 = 2 sin2θ. |
| A. | 30° |
| B. | 45° |
| C. | 90° |
| D. | 60° |
| Answer» D. 60° | |
| 434. |
If 7 sinθ + 24 cosθ = 25, then what is the value of (sin θ + cos θ)? |
| A. | 1 |
| B. | \(\dfrac{26}{25}\) |
| C. | \(\dfrac{6}{5}\) |
| D. | \(\dfrac{31}{25}\) |
| Answer» E. | |
| 435. |
If tanh z = 1, then find the value of z |
| A. | 0 |
| B. | 1 |
| C. | 0.693 |
| D. | Can not be determined |
| Answer» E. | |
| 436. |
If sec x cosec x = 2, then what is the tannx + cotnx equal to? |
| A. | 2 |
| B. | 2n + 1 |
| C. | 2n |
| D. | 2n - 1 |
| Answer» B. 2n + 1 | |
| 437. |
Five line segments of equal lengths PQ, RS, QS, QT and RT are used to form a star as shown in the figure above.The value of θ, in degrees, is ______. |
| A. | 360 |
| B. | 720 |
| C. | 1080 |
| D. | 450 |
| Answer» B. 720 | |
| 438. |
A 6 feet tall man finds that the angle of elevation of the top of a 24 feet height pillar and the angle of depression of its base are complementary angles. The distance of the man from the piller is: |
| A. | 2√3 feet |
| B. | 6√3 feet |
| C. | 8√3 feet |
| D. | None of these |
| Answer» C. 8√3 feet | |
| 439. |
If sin x = 1/3 and cos y = 1/3, then what is the value of sin (x + y)? |
| A. | 2/3 |
| B. | 4/9 |
| C. | 5/9 |
| D. | 1 |
| Answer» E. | |
| 440. |
If tan |
| A. | 2/3 |
| B. | 3/4 |
| C. | 5/6 |
| D. | 6/7 |
| Answer» E. | |
| 441. |
If a, b, c are the sides of a triangle ABC, then \({a^{\frac{1}{p}}} + {b^{\frac{1}{p}}} - {c^{\frac{1}{p}}}\) where p > 1, is |
| A. | always negative |
| B. | always positive |
| C. | always zero |
| D. | positive if 1 < p < 2 and negative if p > 2 |
| Answer» C. always zero | |
| 442. |
If the function \(f\) defined on \(\left( {\frac{\pi }{6},\frac{\pi }{3}} \right)\) by\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\sqrt 2 {\rm{cos}}x - 1}}{{{\rm{cot}}x - 1}},}&{x \ne \frac{\pi }{4}}\\ {{\rm{k}},}&{x = \frac{\pi }{4}} \end{array}} \right.\) is continuous, then k is equal to: |
| A. | 2 |
| B. | \(\frac{1}{2}\) |
| C. | 1 |
| D. | \(\frac{1}{{\sqrt 2 }}\) |
| Answer» C. 1 | |
| 443. |
If cot A = k, then sin A is equal to:(presume that A is an acute angle) |
| A. | \(\frac{k^2}{\sqrt {1+k^2}}\) |
| B. | \(\frac{1}{k}\) |
| C. | \(-\frac{1}{k}\) |
| D. | \(\frac{1}{\sqrt {1+k^2}}\) |
| Answer» E. | |
| 444. |
A 7 m 20 cm pole casts a shadow of length 8 m 30 cm. Find the height of a tree that casts a shadow of length 6 m 64 cm, under similar conditions. |
| A. | 5 m 86 cm |
| B. | 5 m 76 cm |
| C. | 5 m 80 cm |
| D. | 6 m 90 cm |
| Answer» C. 5 m 80 cm | |
| 445. |
In ΔDEF measure of angle E is 90°. If sin D = 15/17, and DE = 4 cm, then what is the length (in cm) of side EF? |
| A. | 8.5 |
| B. | 7.5 |
| C. | 5 |
| D. | 6 |
| Answer» C. 5 | |
| 446. |
A ladder is resting against a wall, The angle between the foot of the ladder and the wall is 45° and the foot of the ladder is 6.6 m away from the wall. The length of the ladder (in m) is: |
| A. | \(6.6 \times \sqrt 2 \) |
| B. | \(3.3 \times \sqrt 2\) |
| C. | \(2.2\times \sqrt 2\) |
| D. | \(3.6 \times \sqrt 2\) |
| Answer» B. \(3.3 \times \sqrt 2\) | |
| 447. |
If 5cosθ – 12sinθ = 0, then value of \(\frac{{2sin\theta \; + \;cos\theta }}{{cos\theta \; - \;sin\theta }}\;\)is∶ |
| A. | \(1\frac{{75}}{{119}}\) |
| B. | \(3\frac{1}{7}\) |
| C. | \(2\frac{{34}}{{35}}\) |
| D. | \(3\frac{2}{3}\) |
| Answer» C. \(2\frac{{34}}{{35}}\) | |
| 448. |
If tan \(A = \frac{1}{3}\) and tan \(B = \frac{2}{5}\), then what is the value of tan (2A + B)? |
| A. | 8/15 |
| B. | 6/13 |
| C. | 37/115 |
| D. | 23/14 |
| Answer» E. | |
| 449. |
Δ DEF is right angled at E. If ∠D = 30°, what is the length of DE (in cm), if EF = 6√3 cm? |
| A. | 18 |
| B. | 12√3 |
| C. | 18√3 |
| D. | 12 |
| Answer» B. 12√3 | |
| 450. |
If \(tanA\; = \;\frac{1}{2}.\), then the value of sin 2A + cos 2A = ?. |
| A. | \(\frac{7}{6}\) |
| B. | \(\frac{8}{7}\) |
| C. | \(\frac{6}{7}\) |
| D. | \(\frac{7}{5}\) |
| Answer» E. | |