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.
| 451. |
If α cos θ – b sin θ = c, then α sin θ + b cos θ is equal to |
| A. | \(\pm \sqrt{b^2 + c^2 - a^2}\) |
| B. | \(\pm \sqrt{a^2 + b^2 - c^2}\) |
| C. | \(\pm \sqrt{c^2 + a^2 - b^2}\) |
| D. | \(\pm \sqrt{a^2 + b^2 + c^2}\) |
| Answer» C. \(\pm \sqrt{c^2 + a^2 - b^2}\) | |
| 452. |
If cos (A/2) = X, then the value of X is |
| A. | \(\sqrt {\left[ {\frac{{1 - cosA}}{2}} \right]}\) |
| B. | \(\sqrt {\left[ {\frac{{1\; + \;sinA}}{2}} \right]} \) |
| C. | \(\sqrt {\left[ {\frac{{1 - sinA}}{2}} \right]}\) |
| D. | \(\sqrt {\left[ {\frac{{1\; + \;cosA}}{2}} \right]}\) |
| Answer» E. | |
| 453. |
In ΔABC, ∠B = 90°. If points D and E are on side BC such that BD = DE = EC, then which of the following is true? |
| A. | 8 AE2 = 5 AC2 + 3 AD2 |
| B. | 5 AE2 = 2 AC2 + 3 AD2 |
| C. | 8 AE2 = 3 AC2 + 5 AD2 |
| D. | 5 AE2 = 3 AC2 + 2AD2 |
| Answer» D. 5 AE2 = 3 AC2 + 2AD2 | |
| 454. |
If \(\cos \theta = \frac{{{x^2} - {y^2}}}{{{x^2}\; + \;{y^2}}}\) then the value of cot θ is equal to [If 0° ≤ θ ≤ 90°] |
| A. | \(\frac{{2xy}}{{{x^2} - {y^2}}}\) |
| B. | \(\frac{{2xy}}{{{x^2}{\rm{\;}} + {\rm{\;}}{y^2}}}\) |
| C. | \(\frac{{{x^2}{\rm{\;}} + {\rm{\;}}{y^2}}}{{2xy}}\) |
| D. | \(\frac{{{x^2} - {y^2}}}{{2xy}}\) |
| Answer» E. | |
| 455. |
If secθ + tanθ = 4, then sec θ – tan θ = ? |
| A. | 1 |
| B. | 0.75 |
| C. | 0.25 |
| D. | 0.5 |
| Answer» D. 0.5 | |
| 456. |
If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ? |
| A. | (P + 1)/(P – 1) |
| B. | (P2 + 1)/2P |
| C. | 2(P2 + 1)/P |
| D. | 2P/(P2 + 1) |
| Answer» E. | |
| 457. |
If Sec A = 5/3, then what is the value of Cot A ? |
| A. | 4/5 |
| B. | 4/3 |
| C. | 3/5 |
| D. | 3/4 |
| Answer» E. | |
| 458. |
If 2sec2x – tan2x = 5 and 0° ≤ x ≤ 90°, then x = ? |
| A. | 45° |
| B. | 60° |
| C. | 30° |
| D. | 90° |
| Answer» C. 30° | |
| 459. |
If 7sin2x + 3cos2x = 4, 0 < x < 90°, then what is the value of tanx? |
| A. | √2 |
| B. | 1 |
| C. | √3/2 |
| D. | 1/√3 |
| Answer» E. | |
| 460. |
A Person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall ? |
| A. | 405 |
| B. | 375 |
| C. | 300 |
| D. | 250 |
| Answer» B. 375 | |
| 461. |
If the length of the shadow of a vertical pole on the horizontal ground is √3 times its height, then the angle of elevation A. 40° B. 50° C. 30° D. 45° |
| A. | C |
| B. | D |
| C. | A |
| D. | B |
| Answer» B. D | |
| 462. |
In the right triangle shown in the figure, what is the value of cosecθ? |
| A. | 12/13 |
| B. | 5/11 |
| C. | 13/5 |
| D. | 5/13 |
| Answer» D. 5/13 | |
| 463. |
If tanα = √15 + 4, then the value of tanα - cotα is ______. |
| A. | 4 - √15 |
| B. | √15 - 4 |
| C. | 2√15 |
| D. | 8 |
| Answer» D. 8 | |
| 464. |
If sec 2x = cosec(3x - 45°), then x is equal to∶ |
| A. | 35° |
| B. | 27° |
| C. | 40° |
| D. | 45° |
| Answer» C. 40° | |
| 465. |
A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 metres from point P observes that angle of elevation of the balloon is 60°. Assume that the point of observation and point P are on the same level. What is the speed (in m/s) of the balloon? |
| A. | 4.25 |
| B. | 3.75 |
| C. | 4.5 |
| D. | 3.45 |
| Answer» C. 4.5 | |
| 466. |
If cos2 x + sin x = 5/4, then find the value of 'sin x'. |
| A. | 3/2 |
| B. | -1/2 |
| C. | 3/4 |
| D. | 1/2 |
| Answer» E. | |
| 467. |
If p = cotθ + tanθ and q = secθ – cosθ, then (p2q)2/3 – (q2p)2/3 is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 468. |
∆XYZ is right angled at Y. If m∠Z = 60°, then find the value of (cot X – 1/3). |
| A. | (3√3 – 1)/3 |
| B. | (2√3 – √6)/2√2 |
| C. | -5/3 |
| D. | (2 – √3)/2√3 |
| Answer» B. (2√3 – √6)/2√2 | |
| 469. |
If 12sin θ = 5 cos θ, then sin θ + cos θ – cot θ is equal to: |
| A. | 139/156 |
| B. | -71/65 |
| C. | 116/156 |
| D. | -16/65 |
| Answer» C. 116/156 | |
| 470. |
If sin x + sin y = cos y - cos x, where 0 < y < x |
| A. | 0 |
| B. | 1 / 2 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 471. |
If \(\sin \left( {A - B} \right) = \frac{1}{2}\) and \(\cos \left( {A + B} \right) = \frac{1}{2}\), where A > B > 0° and A + B is an acute angle, then the value of A is: |
| A. | 30° |
| B. | 60° |
| C. | 45° |
| D. | 15° |
| Answer» D. 15° | |
| 472. |
If (2 sin A + cosec A) = 2√2, 0° < A < 90°, then the value of 2(sin4 A + cos4 A) is: |
| A. | 0 |
| B. | 2 |
| C. | 1 |
| D. | 4 |
| Answer» D. 4 | |
| 473. |
If Sec θ = 13/12, then Cot θ = ? |
| A. | 12/5 |
| B. | 13/5 |
| C. | 5/13 |
| D. | 5/12 |
| Answer» B. 13/5 | |
| 474. |
Find the value of [(cot A – cosec A + 1)(tan A + sec A + 1)]/((cos A cosec A)? |
| A. | 2 cos A |
| B. | 2 sin A |
| C. | 2 cot A |
| D. | 2 tan A |
| Answer» E. | |
| 475. |
ΔDEF is right angled at E. If cosec D = 25/24, then what is the value of cos F? |
| A. | 25/7 |
| B. | 24/7 |
| C. | 24/25 |
| D. | 7/24 |
| Answer» D. 7/24 | |
| 476. |
If triangle ABC is right angled at C, then the value of cos(A+B) is |
| A. | 0 |
| B. | 1 |
| C. | 1/2 |
| D. | √ 3/2 |
| Answer» B. 1 | |
| 477. |
If x = cos-1 (cos 4) and y = sin-1 (sin 3), then which of the following conditions is true? |
| A. | tan (x – y ) = \(\tan \frac{1}{2}\) |
| B. | x + 2y = 2 |
| C. | tan (x + y) = - tan7 |
| D. | x + y + 1 = 0 |
| Answer» D. x + y + 1 = 0 | |
| 478. |
Form the top of a platform, the angle of elevation of a tower was 30°. The tower was 45 m high and the horizontal distance between the platform and the tower was 40√3 m. What is the height of the platform? |
| A. | 45√3 m |
| B. | 5 m |
| C. | 40 m |
| D. | 20√3 m |
| Answer» C. 40 m | |
| 479. |
A kite is flying at a height of 123 m. The thread attached to it is assumed to be stretched straight and makes an angle of 60° with the level ground. The length of the string is (nearest to a whole number): |
| A. | 138 m |
| B. | 142 m |
| C. | 139 m |
| D. | 140 m |
| Answer» C. 139 m | |
| 480. |
An aeroplane fl ying at a height of 300 m above the ground passes vertically above a plane at an instant when the angle of elevation of two planes from the same point on the ground are 60° and 45° respectively. What is the height of lower plane from ground ? |
| A. | 500 m |
| B. | 100 √3 m |
| C. | 500 √3 m |
| D. | 15 \((\sqrt 3 +1)\)m |
| Answer» C. 500 √3 m | |
| 481. |
A ladder is leaning against a vertical wall. The ladder is 9 meter high. When the foot of the ladder is taken 3 meter awaythen the top of the ladder reach equal to the bottom of the wall. What is the height of wall? |
| A. | √46 meters |
| B. | √45 meters |
| C. | √20 meters |
| D. | √30 meters |
| Answer» C. √20 meters | |
| 482. |
A tower is broken at a point P above the ground. The top of the tower makes an angle 60° with the ground at Q. From another point R on the opposite side of Q angle of elevation of point P is 30°. If QR = 180 m, then what is the total height (in metres) of the tower? |
| A. | 90 |
| B. | 45√3 |
| C. | 45(√3 + 1) |
| D. | 45(√3 + 2) |
| Answer» E. | |
| 483. |
If \(\rm f(x)=\tan^{-1} \left[\dfrac{\sin x}{1 + \cos x}\right]\), then what is the first derivative of f(x)? |
| A. | 1/2 |
| B. | -1/2 |
| C. | 2 |
| D. | -2 |
| Answer» B. -1/2 | |
| 484. |
In a right-angled triangle, right-angled at A, what is the value of sec B, if BC is 5.2 cm and AB is 3 cm. |
| A. | 1.6 |
| B. | 1.07 |
| C. | 1.5 |
| D. | 1.7 |
| Answer» E. | |
| 485. |
If \(\frac{{tan\theta }}{{1 - cot\theta }}{\rm{}} + {\rm{}}\frac{{\cot \theta }}{{1 - \tan \theta }}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k\), then k = _________. |
| A. | cosec θ.sec θ |
| B. | cot θ + sec θ |
| C. | tan θ + sec θ |
| D. | tan θ cosec θ |
| Answer» B. cot θ + sec θ | |
| 486. |
Find x if 2sin2x - 1 = 0 |
| A. | \(\pi \over 4\) |
| B. | \(\pi \over 2\) |
| C. | 0 |
| D. | π |
| Answer» B. \(\pi \over 2\) | |
| 487. |
If cot θ = √6, then the value of \(\frac{{cose{c^2}\theta \; + \;se{c^2}\theta }}{{cose{c^2}\theta \; - \;se{c^2}\theta }}\) |
| A. | 48/35 |
| B. | 7/5 |
| C. | 43/36 |
| D. | 49/36 |
| Answer» C. 43/36 | |
| 488. |
Find the value of \(\frac{{{{\cos }^2}30^\circ - {{\sin }^2}30^\circ }}{{{{\sin }^2}15^\circ \; + \;{{\cos }^2}15^\circ \;}}\) |
| A. | 1 |
| B. | 1/2 |
| C. | 1 - √3 |
| D. | 0 |
| Answer» C. 1 - √3 | |
| 489. |
If cos α - cos β = 2 (sin β - sin α), then the value of sin 3α + sin 3β is equal to |
| A. | 0 |
| B. | sin 6α |
| C. | 2⋅sin 3α |
| D. | None of the above |
| Answer» D. None of the above | |
| 490. |
If √2 sin (60° – α) = 1, 0° < α < 90°, then α is equal to: |
| A. | 45° |
| B. | 30° |
| C. | 15° |
| D. | 60° |
| Answer» D. 60° | |
| 491. |
If tanθ = 3/4 then \(\frac{{4\sin {\rm{\theta }} - \cos {\rm{\theta }}}}{{4\sin {\rm{\theta \;}} + {\rm{\;}}\cos {\rm{\theta }}}}\) is equal to ∶ |
| A. | 3/5 |
| B. | 1/4 |
| C. | 1/2 |
| D. | 2/5 |
| Answer» D. 2/5 | |
| 492. |
\(\frac{{1 - \tan A}}{{1 + \tan A}} = \frac{{\tan 3^\circ \tan 15^\circ \tan 30^\circ \tan 75^\circ \tan 87^\circ }}{{\tan 27^\circ \tan 39^\circ \tan 51^\circ \tan 60^\circ \tan 63^\circ }}\), then the value of cot A is: |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 493. |
If sinθ = (m2 – n2)/(m2 + n2) and 0 < θ < π/2, then what is the value of cosθ? |
| A. | 2mn/(m2 + n2) |
| B. | 2mn/(m2 - n2) |
| C. | (m2 + n2)/2mn |
| D. | (m2 - n2)/2mn |
| Answer» B. 2mn/(m2 - n2) | |
| 494. |
If cos x = −√3/2 and π< x < 3π/2, then the value of 2cot2x – 3sec2 x is: |
| A. | 4 |
| B. | 2 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 495. |
If \(\frac{{\tan \theta + \sin \theta }}{{\tan \theta - \sin \theta }} = \frac{{k + 1}}{{k - 1}},\) then k = ? |
| A. | cos θ |
| B. | sec θ |
| C. | sin θ |
| D. | cosec θ |
| Answer» C. sin θ | |
| 496. |
If Cos 3θ = √3/2 and 0 |
| A. | 15° |
| B. | 0° |
| C. | 12° |
| D. | 10° |
| Answer» E. | |
| 497. |
ABC is a triangle inscribed in a circle with centre O. Let α = ∠BAC, where 45° < α < 90°. Let β = ∠BOC. Which one of the following is correct? |
| A. | \(\cos {\rm{\beta }} = \frac{{1 - {{\tan }^2}{\rm{\alpha }}}}{{1 + {{\tan }^2}{\rm{\alpha }}}}\) |
| B. | \(\cos {\rm{\beta }} = \frac{{1 + {{\tan }^2}{\rm{\alpha }}}}{{1 - {{\tan }^2}{\rm{\alpha }}}}\) |
| C. | \(\cos {\rm{\beta }} = \frac{{2\tan {\rm{\alpha }}}}{{1 + {{\tan }^2}{\rm{\alpha }}}}\) |
| D. | sin β = 2 sin2 α |
| Answer» B. \(\cos {\rm{\beta }} = \frac{{1 + {{\tan }^2}{\rm{\alpha }}}}{{1 - {{\tan }^2}{\rm{\alpha }}}}\) | |
| 498. |
If sin θ sec2 θ = 2/3, 0° |
| A. | 7/12 |
| B. | 13/12 |
| C. | 11/12 |
| D. | 5/4 |
| Answer» B. 13/12 | |
| 499. |
If √3 tanθ = 3 sinθ, then the value of (sin2θ – cos2θ) is: |
| A. | 1 |
| B. | 3 |
| C. | 1/3 |
| D. | None of these |
| Answer» D. None of these | |
| 500. |
If 2cosec2 30° + xsin2 60° - \(\frac{3}{4}\) tan2 30° = 10 then value of x is _____. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |