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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.
| 601. |
If sec θ = 13/12 and θ is acute, then what is the value of √(cot θ + tan θ)? |
| A. | 13/2√15 |
| B. | 12/2√13 |
| C. | 13/2√5 |
| D. | 2/13 |
| Answer» B. 12/2√13 | |
| 602. |
If (sinA + cosA)/(sinA – cosA) = 5/4, the value of (tan2A + 1)/(tan2A – 1) = ? |
| A. | 41/40 |
| B. | 12/13 |
| C. | 40/41 |
| D. | None of the above |
| Answer» E. | |
| 603. |
If a right triangle is right-angled at A and AC = 6, BC = 10, find the value of tan B × tan C. |
| A. | 1 |
| B. | 4/5 |
| C. | 3/5 |
| D. | 1/2 |
| Answer» B. 4/5 | |
| 604. |
A kite is flying at an inclination of 60° with the horizontal plane. If the length of the thread is 120 m, then the height of the kite from the horizontal plane is: |
| A. | 60√3 m |
| B. | 60 m |
| C. | \(\frac {60}{\sqrt 3}\) m |
| D. | 120 m |
| Answer» B. 60 m | |
| 605. |
If cos x = p/q and 0° < x < 90°, then the value of tan x is: |
| A. | \(\frac{{\sqrt {{q^2} - {p^2}} }}{p}\) |
| B. | \(\frac{p}{{\sqrt {{p^2} - {q^2}} }}\) |
| C. | \(\frac{q}{{\sqrt {{q^2} - {p^2}} }}\) |
| D. | \(\frac{{\sqrt {{q^2} - {p^2}} }}{q}\) |
| Answer» B. \(\frac{p}{{\sqrt {{p^2} - {q^2}} }}\) | |
| 606. |
From the top of a platform 17 m high, the angle of elevation of the top of a tower was 30°. If the platform was positioned 50√3 m away from the tower, how tall was the tower? |
| A. | 67 m |
| B. | 50 m |
| C. | (25√3 + 17)m |
| D. | 25√3m |
| Answer» B. 50 m | |
| 607. |
An aeroplane is moving at a constant altitude 'h'. At 10:00 AM, it is seen at an elevation of 30°. 1 minute later, it is observed at an elevation of 60°. If the speed of the plane is 960 km/h, then find 'h'. |
| A. | 13.86 km |
| B. | 15 km |
| C. | 12.46 km |
| D. | 20 km |
| Answer» B. 15 km | |
| 608. |
Find the smallest positive angle which satisfies the given trigonometric equation. 2sin2x+\(\sqrt{3}\)cosx + 1 = 0 |
| A. | \(\frac{5 \pi }{6}\) |
| B. | \(\frac{ \pi }{6}\) |
| C. | \(\frac{2 \pi }{3}\) |
| D. | \(\frac{ \pi }{3}\) |
| Answer» B. \(\frac{ \pi }{6}\) | |
| 609. |
∆DEF is right angled at E. If ∠F = 45°, then find the value of (tanD - √3/2). |
| A. | -√3/2 |
| B. | -1/2√3 |
| C. | (2 - √3)/2 |
| D. | (3√3 - 1)/3 |
| Answer» D. (3√3 - 1)/3 | |
| 610. |
In the triangle given above ∠ADB = 90o, ∠ABC = 45o, AD = 10 cm, AC = 20 cm. The length of BC is∶ |
| A. | 10 cm |
| B. | 27.32 cm |
| C. | 18.42 cm |
| D. | 14.14 cm |
| Answer» C. 18.42 cm | |
| 611. |
As observed from the of a lighthouse, 120√3 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 60°. The distance travelled by ship during the period of observation is: |
| A. | 180√3 m |
| B. | 180 m |
| C. | 240 m |
| D. | 240√3 m |
| Answer» D. 240√3 m | |
| 612. |
Consider the following statements:1. The value of cos 61° + sin 29° cannot exceed 1.2. The value of tan 23° - cot 67° is less than 0.Which of the above statements is / are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 613. |
If \(\rm \tan θ = \frac {\cos 17^\circ - \sin 17^\circ}{\cos 17^\circ + \sin 17^\circ},\) then what is the value of θ? |
| A. | 0° |
| B. | 28° |
| C. | 38° |
| D. | 52° |
| Answer» C. 38° | |
| 614. |
cosec 31°/sec 59° is equal to: |
| A. | 1 |
| B. | 3 |
| C. | 0 |
| D. | 2 |
| Answer» B. 3 | |
| 615. |
In a triangle ABC, a – 2b + c = 0. The value of \(\cot \left( {\frac{A}{2}} \right)\cot \left( {\frac{C}{2}} \right)\) is |
| A. | \(\frac{9}{2}\) |
| B. | 3 |
| C. | \(\frac{3}{2}\) |
| D. | 1 |
| Answer» C. \(\frac{3}{2}\) | |
| 616. |
If sinθ - cosθ = 0, then what is the value of the expression (sin6θ + cos6θ)?A. 1B. 3/4C. 1/2D. 1/4 |
| A. | C |
| B. | B |
| C. | D |
| D. | A |
| Answer» D. A | |
| 617. |
If tanθ = 7/24, then find the value of p such that (tanθ - secθ)/sinθ = -p/28. |
| A. | 25 |
| B. | 75 |
| C. | 50 |
| D. | 100 |
| Answer» C. 50 | |
| 618. |
If \(\frac{{\cos θ + \sin θ }}{{\cos θ - \sin θ }} = 8\), then the value of cot θ is equal to: |
| A. | 7/6 |
| B. | 9/7 |
| C. | 6/5 |
| D. | 8/5 |
| Answer» C. 6/5 | |
| 619. |
If 0 < x |
| A. | \(\frac {-4 - \sqrt 7} 3\) |
| B. | \(\frac {4 + \sqrt 7} 3\) |
| C. | \(\frac {1 + \sqrt 7} 4\) |
| D. | \(\frac {1 - \sqrt 7} 4\) |
| Answer» B. \(\frac {4 + \sqrt 7} 3\) | |
| 620. |
In a right-angled triangle ABC, the angle A is 90o, What the value of sec B, if BC is 5 cm and AB is 3 cm. |
| A. | 1.5 |
| B. | 1.07 |
| C. | 1.67 |
| D. | 1.73 |
| Answer» D. 1.73 | |
| 621. |
If tan \(A\; = \;\frac{3}{4},\) then (1 + cos A) (1 – cos A) / (1 + sin A) (1 – sin A) = ? |
| A. | \(\frac{{16}}{{25}}\) |
| B. | \(\frac{9}{{\;25}}\) |
| C. | \(\frac{{16}}{9}\) |
| D. | \(\frac{{\;9}}{{16}}\) |
| Answer» E. | |
| 622. |
If cos2x + cosx = 1, then what is the value of sin12x + 3sin10x + 3sin8x + sin6x? |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 8 |
| Answer» B. 2 | |
| 623. |
If 12 cot2θ – 31 cosec θ + 32 = 0, 0° < θ < 90°, then the values of sin θ will be: |
| A. | 1/3, 3/2 |
| B. | 4/5, 3/4 |
| C. | 5/4, 4/3 |
| D. | 2/3, 1/4 |
| Answer» C. 5/4, 4/3 | |
| 624. |
From the top of a platform 7 m high, the angle of elevation of a tower was 30°. If the platform was positioned 50√3 m away from the tower, how tall was the tower? |
| A. | 57 m |
| B. | 50 m |
| C. | 25√3 + 7 m |
| D. | 25√3 m |
| Answer» B. 50 m | |
| 625. |
If cos θ = 2p/(p2 + 1), (p≠±1) then cosec θ is equal to: |
| A. | 2p/(p2 - 1) |
| B. | 2p/(p2 + 1) |
| C. | (p2 + 1)/(p2 - 1) |
| D. | (p2 - 1)/2p |
| Answer» D. (p2 - 1)/2p | |
| 626. |
If x = sec 57°, then cot2 33° + sin2 57° + sin2 33° + cosec2 57° cos2 33° + sec2 33° sin2 57° is equal to |
| A. | 2x2 + 1 |
| B. | x2 + 1 |
| C. | \(\frac{1}{x^2 + 1}\) |
| D. | x2 + 2 |
| Answer» E. | |
| 627. |
If 5sin2θ + 14 cosθ = 13, 0° < θ < 90°, then what is the value of \(\frac{{sec{\rm{\theta }} + {\rm{cot\theta }}}}{{cosec{\rm{\theta }} + {\rm{tan\theta }}}}\)? |
| A. | 9/8 |
| B. | 32/27 |
| C. | 21/28 |
| D. | 31/29 |
| Answer» E. | |
| 628. |
If cos 47° + sin 47° = k, then what is the value of cos2 47° - sin2 47°? |
| A. | \(k\sqrt {2 - {k^2}}\) |
| B. | \(-k\sqrt {2 - {k^2}}\) |
| C. | \(k\sqrt {1 - {k^2}}\) |
| D. | \(-k\sqrt {1 - {k^2}}\) |
| Answer» B. \(-k\sqrt {2 - {k^2}}\) | |
| 629. |
If A + B = 90° and A : B = 2 : 1, Then tan A : tan B = ? |
| A. | 4 : 5 |
| B. | 2 : 3 |
| C. | 3 : 1 |
| D. | 1 : 3 |
| Answer» D. 1 : 3 | |
| 630. |
If tan2 θ + cot2 θ = 2, then what is the value of 2sec θ cosec θ? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» E. | |
| 631. |
If tan 2A = cot(A - 18°) and 2A is an acute angle, then find 'A'. |
| A. | 24° |
| B. | 36° |
| C. | 28° |
| D. | 18° |
| Answer» C. 28° | |
| 632. |
If tan A + tan B = a and cot A + cot B = b, then 1/a - 1/b is equal to ____. |
| A. | tan(A + B) |
| B. | cos(A + B) |
| C. | sin(A + B) |
| D. | cot(A + B) |
| Answer» E. | |
| 633. |
If \(\frac{{\sin \theta }}{{1 + cos\theta }} + \frac{{1 + \cos \theta }}{{sin\theta }} = \frac{4}{{\sqrt 3 }},0^\circ < \theta < 90^\circ ,\) then the value of (secθ + tanθ)-1 is: |
| A. | 3 + √2 |
| B. | 2 + √3 |
| C. | 2 – √3 |
| D. | 3 – √2 |
| Answer» D. 3 – √2 | |
| 634. |
If Sin θ = 12/13, then what is the value of Cot θ? |
| A. | 13/12 |
| B. | 5/13 |
| C. | 5/12 |
| D. | 13/5 |
| Answer» D. 13/5 | |
| 635. |
If 2 sin2 θ + 5 cos θ – 4 = 0, 0° < θ < 90°, then the value of tan θ + sin θ is: |
| A. | 2/√3 |
| B. | √3/2 |
| C. | √3 |
| D. | 3√3/2 |
| Answer» E. | |
| 636. |
If \({\rm{cos}}\left( {{\rm{\alpha }} + {\rm{\beta }}} \right) = \frac{3}{5},\;{\rm{sin}}\left( {{\rm{\alpha }} - {\rm{\beta }}} \right) = \frac{5}{{13}}\;\)and \(0 < \alpha ,{\rm{\;}}\beta < \frac{\pi }{4}\), then tan 2α is equal to: |
| A. | \(\frac{{63}}{{52}}\) |
| B. | \(\frac{{63}}{{16}}\) |
| C. | \(\frac{{21}}{{16}}\) |
| D. | \({\rm{\;}}\frac{{33}}{{52}}\) |
| Answer» C. \(\frac{{21}}{{16}}\) | |
| 637. |
if the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these angles is |
| A. | \(\sqrt{2} : 2 : \sqrt{3} + 1\) |
| B. | \(2 : \sqrt{2} : \sqrt{3} + 1\) |
| C. | \(2 : \sqrt{2} : \dfrac{\sqrt{2}}{\sqrt{3}-1}\) |
| D. | \(\dfrac{1}{\sqrt{2}} : 2 : \dfrac{\sqrt{3}+1}{2}\) |
| Answer» B. \(2 : \sqrt{2} : \sqrt{3} + 1\) | |
| 638. |
Find the value of (sin 150° × cos 300°) + (sin 210° × cos 240°) |
| A. | 2 |
| B. | \(\frac{{1}}{2}\) |
| C. | - 2 |
| D. | \(-~\frac{{1}}{2}\) |
| Answer» C. - 2 | |
| 639. |
If 0 ≤ α, β ≤ 90° such that cos (α - β) = 1, then what is sin α - sin β + cos α - cos β equal to? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 640. |
If 3sin θ + 5cos θ = 5, then the value of 5sin θ - 3cos θ is equal to: |
| A. | 3 |
| B. | 4 |
| C. | None of these |
| D. | 5 |
| Answer» B. 4 | |
| 641. |
If [6(sec259° - cot231°)] – [(2/3)sin 90°] – [3tan256°ytan234°] = y/3, then the value of y is: |
| A. | 8/5 |
| B. | -2/3 |
| C. | -8/5 |
| D. | 2/3 |
| Answer» B. -2/3 | |
| 642. |
If sin θ + cos θ = √2 cos θ, then what is (cos θ – sin θ) equal to? |
| A. | -√2 cos θ |
| B. | -√2 sin θ |
| C. | √2 sin θ |
| D. | 2 sin θ |
| Answer» D. 2 sin θ | |
| 643. |
If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is: |
| A. | 6/7 |
| B. | 7/6 |
| C. | 5/6 |
| D. | 6/5 |
| Answer» C. 5/6 | |
| 644. |
If the equation possesses solution, then what is the minimum value of k? |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» C. 4 | |
| 645. |
If the equation possesses solution, then what is the maximum value of k? |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 646. |
If 3(cot2 ϕ – cos2 ϕ) = cos2 ϕ, 0° < ϕ < 90°, then the value of (tan2 ϕ + cosec2 ϕ + sin2 ϕ) is∶ |
| A. | 13/3 |
| B. | 25/12 |
| C. | 61/12 |
| D. | 15/4 |
| Answer» D. 15/4 | |
| 647. |
In an isosceles triangle DEF, ∠D = 110°. If I is the in center of the triangle, then what is the value (in degrees) of ∠EIF? |
| A. | 110 |
| B. | 130 |
| C. | 145 |
| D. | 155 |
| Answer» D. 155 | |
| 648. |
A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower? |
| A. | 3.90 m |
| B. | 4.00 m |
| C. | 4.10 m |
| D. | 4.25 m |
| Answer» D. 4.25 m | |
| 649. |
If cotθ + tanθ = 2secθ, 0°< θ < 90°, then the value of \(\frac{{{\rm{tan}}2{\rm{\theta }} - {\rm{sec\theta }}}}{{{\rm{cot}}2{\rm{\theta \;}} + {\rm{\;cosec\theta }}}}\) is: |
| A. | \(\frac{{2\sqrt 3 - 1}}{{11}}\) |
| B. | \(\frac{{3 - \sqrt 2 }}{{11}}\) |
| C. | \(\frac{{2\sqrt 3 - 2}}{{11}}\) |
| D. | \(\frac{{3 - \sqrt 2 }}{5}\) |
| Answer» B. \(\frac{{3 - \sqrt 2 }}{{11}}\) | |
| 650. |
If cot θ = √11, then what is the value of \(\frac{{cose{c^2}\theta \; + \;{{\sec }^2}\theta }}{{cose{c^2}\theta - {{\sec }^2}\theta }}\) |
| A. | 2/3 |
| B. | 6/5 |
| C. | 3/4 |
| D. | 7/6 |
| Answer» C. 3/4 | |