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.
| 551. |
If sin2 x + sin x = 1, then what is the value of cos12 x + 3 cos10 x + 3 cos8 x + cos6 x? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 8 |
| Answer» D. 8 | |
| 552. |
A person was standing on a road near a mall. He was 1425 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 height of the tree is 10 m and it is 30 m away from him. How tall (in m) is the mall? |
| A. | 475 |
| B. | 300 |
| C. | 525 |
| D. | 425 |
| Answer» B. 300 | |
| 553. |
If Sin D = 3/5, then (sin D + cos D)2 =?A. 1B. 24/25C. 49/25D. 12/25 |
| A. | A |
| B. | B |
| C. | D |
| D. | C |
| Answer» E. | |
| 554. |
If sin θ + sin2 θ = 1, then the value of cos2 θ + cos4 θ is equal to: |
| A. | 0 |
| B. | 5 |
| C. | 1 / 2 |
| D. | 1 |
| Answer» E. | |
| 555. |
In ΔDEF measure of angle E is 90°. If cotD = 8/15, and DE = 16 cm, then what is the length (in cm) of side EF? |
| A. | 34 |
| B. | 15 |
| C. | 30 |
| D. | 14 |
| Answer» D. 14 | |
| 556. |
Cot2A – cos2A is equal to: |
| A. | cos2A – tan2 A |
| B. | cot2A |
| C. | cos2A cot2A |
| D. | cos2A sec2 A |
| Answer» D. cos2A sec2 A | |
| 557. |
If sec 4x = cosec (3x – 43°), then the value of x is: |
| A. | 19° |
| B. | 29° |
| C. | 17° |
| D. | 23° |
| Answer» B. 29° | |
| 558. |
If CosA, SinA, CotA are in geometric progression, then the value of Tan6A - Tan2A is: |
| A. | 3 |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{2}\) |
| D. | 1 |
| Answer» E. | |
| 559. |
If Sin θ = 12 / 37, then, Cot θ = ? |
| A. | 35 / 12 |
| B. | 12 / 35 |
| C. | 37 / 12 |
| D. | 35 / 37 |
| Answer» B. 12 / 35 | |
| 560. |
ΔLMN is right angled at M. If ∠N = 45°, what is the length of MN (in cm), if NL = 9√2 cm? |
| A. | 9√2 |
| B. | 9/√2 |
| C. | 18 |
| D. | 9 |
| Answer» E. | |
| 561. |
If tan A - tan B = x and cot B - cot A = y, then cot (A - B) is equal to |
| A. | \(\dfrac{1}{x}+\dfrac{1}{y}\) |
| B. | \(\dfrac{1}{x}-\dfrac{1}{y}\) |
| C. | \(-\dfrac{1}{x}+\dfrac{1}{y}\) |
| D. | \(-\dfrac{1}{x}-\dfrac{1}{y}\) |
| Answer» B. \(\dfrac{1}{x}-\dfrac{1}{y}\) | |
| 562. |
If A = sin2 θ + cos4 θ, then for all real θ, which one of the following is correct? |
| A. | 1 ≤ A ≤ 2 |
| B. | \(\frac{3}{4} \le A \le 1\) |
| C. | \(\frac{{13}}{{16}} \le A \le 1\) |
| D. | \(\frac{3}{4} \le A \le \frac{{13}}{{16}}\) |
| Answer» C. \(\frac{{13}}{{16}} \le A \le 1\) | |
| 563. |
∆UVW is right angled at V. If cosU = 8/17, then what is the value of sinW? |
| A. | 15/17 |
| B. | 17/8 |
| C. | 8/17 |
| D. | 17/15 |
| Answer» D. 17/15 | |
| 564. |
If cot A = n/(n + 1) and cot B = 1/(2n + 1), what is the value of cot (A + B)? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» B. 0 | |
| 565. |
If sin 5θ = cos (50° – 3θ), then θ is equal to |
| A. | 30° |
| B. | 20° |
| C. | 15° |
| D. | 25° |
| Answer» C. 15° | |
| 566. |
If cosecx + cotx = 2, then cosecx = ? |
| A. | 1.5 |
| B. | 1.25 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 567. |
If cos x = - 1/2 and π < x < 3π/2, then the value of 4tan2x + 3cosec2x is: |
| A. | 8 |
| B. | 10 |
| C. | 16 |
| D. | 4 |
| Answer» D. 4 | |
| 568. |
If sin A - cos A = 0, then the value of sin4 A + cos4 A is: |
| A. | 0 |
| B. | 1 |
| C. | \(\frac{1}{2}\) |
| D. | \(\frac{3}{4}\) |
| Answer» D. \(\frac{3}{4}\) | |
| 569. |
If 12cos2 θ – 2sin2θ + 3cosθ = 3, 0° < θ < 90°, then what is the value of \( \frac{{cosec\theta + sec\theta }}{{tan\theta + cot\;\theta }}?\) |
| A. | \(\frac{{2 + \sqrt 3 }}{4}\) |
| B. | \(\frac{{4 + \sqrt 3 }}{4}\) |
| C. | \(\frac{{1 + 2\sqrt 2 }}{2}\) |
| D. | \(\frac{{1 + \sqrt 3 }}{2}\) |
| Answer» E. | |
| 570. |
\(\frac{d}{dx}(tan(cos^{-1}x))^2\) is equal to |
| A. | -2/x3 |
| B. | 2/x3 |
| C. | \(\frac{\sqrt{1-x^2}}{x}\) |
| D. | \(-\frac{x}{\sqrt{1-x^2}}\) |
| Answer» B. 2/x3 | |
| 571. |
In ΔDEF measure of angle E is 90o. If cot D = 5/12, and DE = 1 cm, then what is the length (in cm) of side EF? |
| A. | 2.4 |
| B. | 2.6 |
| C. | 1.5 |
| D. | 2 |
| Answer» B. 2.6 | |
| 572. |
If \(\frac{{x - x{{\tan }^2}15^\circ }}{{1 + {{\tan }^2}15^\circ }} = \sin 60^\circ + \cos 30^\circ ,\) then what is then what is the value of x? |
| A. | 2 |
| B. | -1 |
| C. | -2 |
| D. | 1 |
| Answer» B. -1 | |
| 573. |
In ΔDEF measure of angle E is 90°. If cos D = 8/17, and DE = 16 cm, then what is the length (in cm) of side DF? |
| A. | 30 |
| B. | 20 |
| C. | 26 |
| D. | 34 |
| Answer» E. | |
| 574. |
In ΔPQR measure of angle Q is 90°. If sin P = 12/13, and PQ = 1 cm, then what is the length (in cm) of side QR? |
| A. | 2.6 |
| B. | 3 |
| C. | 2.4 |
| D. | 4 |
| Answer» D. 4 | |
| 575. |
A is an angle in the fourth quadrant. If satisfies the trigonometric equation 3 (3 – tan2 A - cot A)2 = 1. Which one of the following is a value of A? |
| A. | 300° |
| B. | 315° |
| C. | 330° |
| D. | 345° |
| Answer» B. 315° | |
| 576. |
In ΔPQR measure of angle Q is 90°. If cotP = 8/15, and PQ = 4 cm, then what is the length (in cm) of side PR? |
| A. | 8.5 |
| B. | 7.5 |
| C. | 5 |
| D. | 4 |
| Answer» B. 7.5 | |
| 577. |
If Tan θ = 7/24, then what is the value of Sec θ? |
| A. | 24/25 |
| B. | 24/7 |
| C. | 25/7 |
| D. | 25/24 |
| Answer» E. | |
| 578. |
If cotθ = \(80 \over 39\), Find the value of cosecθ |
| A. | \(89 \over 39\) |
| B. | \(39 \over 89\) |
| C. | \(89 \over 80\) |
| D. | \(39 \over 80\) |
| Answer» B. \(39 \over 89\) | |
| 579. |
If \(\tan \theta = \dfrac{4}{3} \ \rm then \ \left(\dfrac{2 \sin \theta - 3 \cos \theta}{2 \sin \theta + 3 \cos \theta }\right)=?\) |
| A. | 0 |
| B. | -1 |
| C. | \(-\dfrac{1}{7}\) |
| D. | \(-\dfrac{1}{17}\) |
| Answer» E. | |
| 580. |
If \(\cos x = \dfrac{24}{25}, 0 \le x \le 90^\circ\), then the value of cot x + cosec x is: |
| A. | 0 |
| B. | \(\dfrac{7}{2}\) |
| C. | 1 |
| D. | 7 |
| Answer» E. | |
| 581. |
A triangle is NOT said to be right - angled triangle if its sides measure: |
| A. | 5 cm, 12 cm and 13 cm |
| B. | 3 cm, 4 cm and 5 cm |
| C. | 6 cm, 8 cm and 10 cm |
| D. | 5 cm, 7 cm and 9 cm |
| Answer» E. | |
| 582. |
If \(\sin {\rm{A}} = \frac{3}{5},\) where 450° < A < 540°, then \(\cos \frac{{\rm{A}}}{2}\) is equal to |
| A. | \(\frac{1}{{\sqrt {10} }}\) |
| B. | \(- \sqrt {\frac{3}{{10}}}\) |
| C. | \(\frac{{\sqrt 3 }}{{\sqrt {10} }}\) |
| D. | None of the above |
| Answer» B. \(- \sqrt {\frac{3}{{10}}}\) | |
| 583. |
If tan A \(= \frac{{15}}{8}\) and tan B \(= \frac{{7}}{24}\) then tan (A + B) = ?A. 416/87B. 87/416C. 304/297D. 297/304 |
| A. | C |
| B. | A |
| C. | B |
| D. | D |
| Answer» C. B | |
| 584. |
Evaluate: (sin 72° + cos 18°) (sin 72° – cos 18°) |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | -1 |
| Answer» C. 2 | |
| 585. |
If \(2x = \sin \theta \) and \(\frac{2}{x} =\cos \theta \), then the value of \(4\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\) is: |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | 4 |
| Answer» B. 0 | |
| 586. |
Find the value of cos 120° cos 240° cos 180° cos 60°. |
| A. | –1/8 |
| B. | 1/2 |
| C. | 1/4 |
| D. | 1/16 |
| Answer» B. 1/2 | |
| 587. |
If Sinθ = 20/29, then what is the value of SecθSinθ? |
| A. | 20/21 |
| B. | 29/20 |
| C. | 21/20 |
| D. | 21/29 |
| Answer» B. 29/20 | |
| 588. |
Consider the following:1. sin 1° > sin 1c2. cos 1° < cos 1c3. tan 1° > tan 1cWhich of the above is not correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 589. |
A 165 cm tall man standing 500 cm away from the wall looks at a hooks on the wall with an angle of elevation of 450 what is the height at which the hooks is in the wall? |
| A. | 600 cm |
| B. | 750 cm |
| C. | 700 cm |
| D. | 665 cm |
| Answer» E. | |
| 590. |
If \(\cot \theta = \frac{1}{{\sqrt 3 }},\) then the value of \(\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }} + \left( {cose{c^2}\theta + \sec \theta } \right)\) is: |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» C. 6 | |
| 591. |
If cosec 31° = x, sec 59° cosec 31° − (sec2 θ – tan2 θ) is equal to: |
| A. | x + 1 |
| B. | x2 + 1 |
| C. | x2 - 1 |
| D. | x - 1 |
| Answer» D. x - 1 | |
| 592. |
If 4cotθ = 3, then the value of \(\frac{{3sin\theta - 4cos\theta }}{{3sin\theta \; + \;4cos\theta }}\) is: |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{5}{7}\) |
| C. | \(\frac{5}{3}\) |
| D. | 0 |
| Answer» E. | |
| 593. |
If \(\sin A = \frac{1}{{\sqrt 2 }}\) and \({\mathop{\rm Cos}\nolimits} B = \frac{{\sqrt 3 }}{2}\), then, find the value of (A + B)º.A. 60º B. 75º C. 105º D. 90º |
| A. | C |
| B. | A |
| C. | D |
| D. | B |
| Answer» E. | |
| 594. |
∆DEF is right angled at E. If tan D = 4/3, then what is the value of tan F? |
| A. | 3/4 |
| B. | 5/3 |
| C. | 4/5 |
| D. | 4/3 |
| Answer» B. 5/3 | |
| 595. |
If cos 27° = x, then the value of tan 63° is: |
| A. | \(\frac{\sqrt{1+x^2}}{x}\) |
| B. | \(\frac{x}{\sqrt{1+x^2}}\) |
| C. | \(\frac{\sqrt{1-x^2}}{x}\) |
| D. | \(\frac{x}{\sqrt{1-x^2}}\) |
| Answer» E. | |
| 596. |
If \(\tan x = \dfrac{3}{2}\), then the value of \(\dfrac{3 \sin x + 2 \cos x}{3 \sin x - 2 \cos x}\) is: |
| A. | 5 |
| B. | \(\dfrac{5}{13}\) |
| C. | \(\dfrac{13}{5}\) |
| D. | \(\dfrac{1}{5}\) |
| Answer» D. \(\dfrac{1}{5}\) | |
| 597. |
A ladder of length 13 metres is placed against the wall and the foot of the ladder is 6.5 metres from the wall. What is the angle of elevation of the ladder leaning against a wall? |
| A. | 105° |
| B. | 30° |
| C. | 45° |
| D. | 60° |
| Answer» E. | |
| 598. |
\(\frac{(1 + tan\theta + sec\theta)(1 + cot\theta - cosec\theta)}{(sec\theta + tan\theta)(1 - sin\theta)}\) is equal to: |
| A. | 2cosecθ |
| B. | cosecθ |
| C. | secθ |
| D. | 2secθ |
| Answer» E. | |
| 599. |
On the top of a hemispherical dome of radius r, there stands a flag of height h. From a point on the ground, the elevation of the top of the flag is 30°. After moving a distance d towards the dome, when the flag is just visible, the elevation is 45°. The ratio of h to r is equal to |
| A. | √2 – 1 |
| B. | \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\) |
| C. | \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}d\) |
| D. | \(\frac{{\left( {\sqrt 3 + 1} \right)\left( {\sqrt 2 - 1} \right)}}{{2\sqrt 2 }}d\) |
| Answer» B. \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\) | |
| 600. |
ΔDEF is right angled at E. If ∠F = 45°, then what is the value of 2 Sin F x Cot F? |
| A. | √2 |
| B. | 2 |
| C. | 1/√2 |
| D. | 1/2 |
| Answer» B. 2 | |