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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.
| 751. |
If 6 tanθ - 5√3sec θ + 12 cot θ = 0, 0° < θ < 90°, then of (cosec θ + secθ) is: |
| A. | \(\frac{{2 + \sqrt 3 }}{2}\) |
| B. | \(\frac{{2\left( {3 + 2\sqrt 3 } \right)}}{3}\) |
| C. | \(\frac{{3 + 2\sqrt 3 }}{2}\) |
| D. | \(\frac{2}{3}\left( {3 + \sqrt 3 } \right)\) |
| Answer» E. | |
| 752. |
A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ΔABC, the foot of the pole is at the: |
| A. | Centroid |
| B. | Circumcentre |
| C. | Incentre |
| D. | Orthocentre |
| Answer» C. Incentre | |
| 753. |
ΔLMN is right angled at M. If ∠N = 45°. What is the length (in cm) of MN, if NL = 6√2 cm? |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 6 |
| Answer» E. | |
| 754. |
From the top of a hill 96 m high, the angles of depression of two cars parked on the same side of the hill (at the same level as the base of the hill) are 30° and 60° respectively. The distance between the cars is: (use √3 = 1.73 and round off to nearest whole number.) |
| A. | 165 m |
| B. | 111 m |
| C. | 220 m |
| D. | 243 m |
| Answer» C. 220 m | |
| 755. |
If the angles of a triangle ABC are in AP and b : c = √3 : √2, then what is the measure of angle A? |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 75° |
| Answer» E. | |
| 756. |
In ΔABC measure of angle B is 90o. If sin A = 15/17, and AB = 0.8 cm, then what is the length (in cm) of side BC? |
| A. | 1.5 |
| B. | 1.7 |
| C. | 2 |
| D. | 2.5 |
| Answer» B. 1.7 | |
| 757. |
From a tower 18 m high the angle of elevation of the top of a tall building is 45° and the angle of depression of the bottom of the same building is 60°. What is the height of the building in meters |
| A. | \(12 + 6\sqrt 3\) |
| B. | \(6\left( {3 + \sqrt 3 } \right)\) |
| C. | \(18 + \sqrt 2\) |
| D. | \(6\left( {3 + \frac{{\sqrt 3 }}{2}} \right)\) |
| Answer» C. \(18 + \sqrt 2\) | |
| 758. |
In ∆XYZ measure of angle Y is 90°. If cosec X = 13/12, and XY = 1 cm, then what is the length (in cm) of side YZ? |
| A. | 2.6 |
| B. | 1.5 |
| C. | 2.4 |
| D. | 2 |
| Answer» D. 2 | |
| 759. |
If 3 cot θ = 4 cos θ, then what is the value of cos 2θ? |
| A. | 2/16 |
| B. | -1/8 |
| C. | 7/16 |
| D. | 9/16 |
| Answer» C. 7/16 | |
| 760. |
If sec2 θ - sec θ = 1, then what is the value of (tan12 θ - 3 tan10 θ + 3 tan8 θ - tan6 θ)? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 761. |
If √3cosθ = sinθ, then the value of \(\frac{4sin^2 \theta - 5 cos \theta}{3 cos \theta + 1}\) is |
| A. | 1/4 |
| B. | 1/5 |
| C. | 5 |
| D. | 2/5 |
| Answer» C. 5 | |
| 762. |
If x, x - y and x + y are the angles of a triangle (not and equilateral triangle) such that tan (x - y), tan x and tan (x + y) are in GP, then what is x equal to? |
| A. | π/4 |
| B. | π/3 |
| C. | π/6 |
| D. | π/2 |
| Answer» C. π/6 | |
| 763. |
If 2sinθ + 15cos2θ = 7, 0° < θ < 90° then what is the value of \(\frac{{3 - tan\theta }}{{2\; + \;tan\theta }}?\) |
| A. | 1/4 |
| B. | 3/4 |
| C. | 1/2 |
| D. | 5/8 |
| Answer» D. 5/8 | |
| 764. |
Let S = {θ ϵ [-2π, 2π] : 2 cos2 θ + 3 sin θ = 0} Then the sum of the elements of S is: |
| A. | \(\frac{{13\pi }}{6}\) |
| B. | \(\frac{{5\pi }}{3}\) |
| C. | 2π |
| D. | π |
| Answer» D. π | |
| 765. |
Find the value of \(\frac{\cos 30^\circ - \sin 30^\circ}{\sin 60^\circ + \cos 60^\circ}\) |
| A. | \(2 - \sqrt 3\) |
| B. | \(2 + \sqrt 3\) |
| C. | \(1 - \sqrt 3\) |
| D. | \(1 + \sqrt 3\) |
| Answer» B. \(2 + \sqrt 3\) | |
| 766. |
If (1 - cosA)/(1 + cosA) = x, then the value of x is? |
| A. | (cotA + cosecA)2 |
| B. | (cotA - cosecA)2 |
| C. | cotA - cosecA |
| D. | cotA + cosecA |
| Answer» C. cotA - cosecA | |
| 767. |
If sec θ + tan θ = 3, then the value of sec θ is: |
| A. | 3 / 5 |
| B. | 5 / 3 |
| C. | 3 / 4 |
| D. | 4 / 3 |
| Answer» C. 3 / 4 | |
| 768. |
If sin x = 1/2 and sin y = 2/3, then what is the value of [(6 cos2 x - 4 cos4 x)/(18 cos2 y - 27 cos4 y)]? |
| A. | 27/20 |
| B. | 15/14 |
| C. | 25/21 |
| D. | 17/14 |
| Answer» B. 15/14 | |
| 769. |
Find the value of sin 12° sin 48° sin 54°: |
| A. | \(\dfrac18\) |
| B. | \(\dfrac16\) |
| C. | \(\dfrac12\) |
| D. | \(\dfrac14\) |
| Answer» B. \(\dfrac16\) | |
| 770. |
If sin2 x tan x + cos2 x cot x - sin 2x = 1 + tan x + cot x, x ϵ (0, π), then x |
| A. | \(\frac {3\pi}{12}, \frac {5\pi}{12}\) |
| B. | \(\frac {5\pi}{12}, \frac {7\pi}{12}\) |
| C. | \(\frac {7\pi}{12}, \frac {11\pi}{12}\) |
| D. | \(\frac {7\pi}{12}, \frac {9\pi}{12}\) |
| Answer» D. \(\frac {7\pi}{12}, \frac {9\pi}{12}\) | |
| 771. |
If \(\frac{{\cos \theta }}{{1 - \sin \theta }} + \frac{{\cos \theta }}{{1 + \sin \theta }} = 4,\;0^\circ < \theta < 90^\circ,\) then what is the value of (sec θ + cosec θ + cot θ)? |
| A. | 2 + √3 |
| B. | \(\frac{{1 + 2\sqrt 3 }}{3}\) |
| C. | 1 + 2√3 |
| D. | \(\frac{{2 + \sqrt 3 }}{3}\) |
| Answer» B. \(\frac{{1 + 2\sqrt 3 }}{3}\) | |
| 772. |
Consider the following statements:1. If ABC is an equilateral triangle, then 3 tan (A + B) tan C = 12. If ABC is a triangle in which A = 78°, B = 66°, then \(\tan \left( {\frac{{\rm{A}}}{2} + {\rm{C}}} \right) < \tan {\rm{A}}\)3. If ABC is any triangle, then \(\tan \left( {\frac{{{\rm{A}} + {\rm{B}}}}{2}} \right)\sin \left( {\frac{{\rm{C}}}{2}} \right) < \cos \left( {\frac{{\rm{C}}}{2}} \right)\)Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | 1 and 2 |
| D. | 2 and 3 |
| Answer» C. 1 and 2 | |
| 773. |
If tan(θ/2)tan(2θ/5) = 1, then what is the value (in degrees) of θ ? |
| A. | 45° |
| B. | 90° |
| C. | 100° |
| D. | 120° |
| Answer» D. 120° | |
| 774. |
If D is the number of degrees and R is the number of radians in an angle θ, then which of the following is correct? |
| A. | πD = 180R |
| B. | πD = 90R |
| C. | πR = 180D |
| D. | πR = 90D |
| Answer» B. πD = 90R | |
| 775. |
A man observes the top of a pole of height 15 m with elevation angle 30°. The height of the man is 1 m. The distance between the man and the pole in meters is |
| A. | \(14\sqrt3 \) |
| B. | \(\frac{15}{\sqrt3}\) |
| C. | \(\frac{14}{\sqrt3}\) |
| D. | \(15\sqrt3\) |
| Answer» B. \(\frac{15}{\sqrt3}\) | |
| 776. |
A ladder leaning against a wall makes an angle α with the horizontal ground such that tan α = 3/4 If the foot of the ladder is 5 m away from the wall, what is the length of the ladder? |
| A. | 5.25 m |
| B. | 3.75 m |
| C. | 6.25 m |
| D. | 4.5 m |
| Answer» D. 4.5 m | |
| 777. |
For 0° ≤ θ ≤ 90°, what is θ, when √3 cos θ + sin θ = 1? |
| A. | 90° |
| B. | 0° |
| C. | 45° |
| D. | 30° |
| Answer» B. 0° | |
| 778. |
If \({\rm{\alpha }} = {\rm{co}}{{\rm{s}}^{ - 1}}\left( {\frac{3}{5}} \right),{\rm{\beta }} = {\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{1}{3}} \right)\), where \(0 < {\rm{\alpha }},{\rm{\beta }} < \frac{{\rm{\pi }}}{2},\) then α – β is equal to: |
| A. | \({\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{9}{{5\sqrt {10} }}} \right)\) |
| B. | \({\rm{co}}{{\rm{s}}^{ - 1}}\left( {\frac{9}{{5\sqrt {10} }}} \right)\) |
| C. | \({\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{9}{{14}}} \right)\) |
| D. | \({\rm{si}}{{\rm{n}}^{ - 1}}\left( {\frac{9}{{5\sqrt {10} }}} \right)\) |
| Answer» E. | |
| 779. |
If Cot \(x = \frac{5}{12},\) then Sin \(x + \frac{1}{Cot \ x} + sec \ x \ = \ ?\) |
| A. | 173 / 13 |
| B. | 77 / 13 |
| C. | 75 / 13 |
| D. | 17 / 13 |
| Answer» C. 75 / 13 | |
| 780. |
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 16 minutes for the angle of depression to change from 30° to 60°, how soon after this will the car reach the observation tower? |
| A. | 8 mins 58 secs |
| B. | 10 mins 42 secs |
| C. | 6 mins 0 secs |
| D. | 8 mins 0 secs |
| Answer» E. | |
| 781. |
Given \(\frac{{b + c}}{{11}} = \frac{{c + a}}{{12}} = \frac{{a + b}}{{13}}\) for a ΔABC with usual notion. If \(\frac{{b + c}}{{11}} = \frac{{c + a}}{{12}} = \frac{{a + b}}{{13}}\) then the ordered triad (α, β, γ) has a value: |
| A. | (7, 19, 25) |
| B. | (3, 4, 5) |
| C. | (5, 12, 13) |
| D. | (19, 7, 25) |
| Answer» B. (3, 4, 5) | |
| 782. |
If cotθ = \(\frac{3}{\sqrt 5}\), 0° |
| A. | - 20/9 |
| B. | 1/2 |
| C. | 2/3 |
| D. | 1/3 |
| E. | 1 |
| Answer» B. 1/2 | |
| 783. |
Consider the following statements:1. sin θ = x + \(\frac{1}{x}\) is possible for some real value of x.2. cos θ = x + \(\frac{1}{x}\) is possible for some real value of x.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» E. | |
| 784. |
Consider the following for triangle ABC:1. \(\sin \left( {\frac{{{\rm{B}} + {\rm{C}}}}{2}} \right) = \cos \left( {\frac{{\rm{A}}}{2}} \right)\)2. \(\tan \left( {\frac{{{\rm{B}} + {\rm{C}}}}{2}} \right) = \cot \left( {\frac{{\rm{A}}}{2}} \right)\)3. sin (B + C) = cos A4. tan (B + C) = - cot AWhich of the above are correct? |
| A. | 1 and 3 |
| B. | 1 and 2 |
| C. | 1 and 4 |
| D. | 2 and 3 |
| Answer» C. 1 and 4 | |
| 785. |
If sin θ1 + sin θ2 + sin θ3 + sin θ4 = 4, then what is the value of cos θ1 + cos θ2 + cos θ3 + cos θ4? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» B. 1 | |
| 786. |
If \(\frac{{{{\cos }^2}{\rm{\theta }}}}{{{{\cot }^2}{\rm{\theta }} - {{\cos }^2}{\rm{\theta }}}} = 3,{\rm{}}\)0° < θ < 90°, then the value of cot θ + cosec θ is: |
| A. | √3/2 |
| B. | √3 |
| C. | 2√3 |
| D. | (3√3)/4 |
| Answer» C. 2√3 | |
| 787. |
In the given figure, cosθ is equal to: |
| A. | 12/5 |
| B. | 12/13 |
| C. | 5/12 |
| D. | 5/13 |
| Answer» E. | |
| 788. |
Find the value of tan(210°).A. 1/√3B. -1/√3C. -1D. 1 |
| A. | D |
| B. | A |
| C. | C |
| D. | B |
| Answer» C. C | |
| 789. |
A man finds the angle of elevation of a cliff to be 45°. When he goes 2 km towards the cliff on an inclined path making an angle of 30° with horizontal, the angle of elevation of the cliff becomes 60°. The height of the cliff is: |
| A. | 1000(√3 + 1)m |
| B. | 1000(√3 – 1)m |
| C. | 1000(√3 + 2)m |
| D. | 1000√3 m |
| Answer» B. 1000(√3 – 1)m | |
| 790. |
Find the value of \(sin {7\pi\over 4}sin {3\pi\over 4}sin {\pi\over 4}sin {5\pi\over 4}\) |
| A. | 1/16 |
| B. | 1/8 |
| C. | 3/18 |
| D. | 1/4 |
| Answer» E. | |
| 791. |
if \(\tan \theta = \frac{1}{{\sqrt 5 }},\;cose{c^2}\theta = \) ? |
| A. | 5 |
| B. | √5 |
| C. | √3 |
| D. | 6 |
| Answer» E. | |
| 792. |
If sin8 θ + cos8 θ - 1 = 0, then what is the value of cos2 θ sin2 θ (If θ ≠ 0 or π/2)? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 793. |
A house of height of a 20 m long tree is broken by the wind and the top struck the ground at an angle 30°. The height of the point where the tree is broken, is |
| A. | 10 m |
| B. | (2√3 - 3) 20 m |
| C. | \(\frac{20}{3} \ m\) |
| D. | None of this |
| Answer» D. None of this | |
| 794. |
If sin α + sin β = 0 = cos α + cos β, where 0 < β < α < 2π, then which one of the following is correct? |
| A. | α = π - β |
| B. | α = π + β |
| C. | α = 2π β |
| D. | 2 α = π + 2β |
| Answer» C. α = 2π β | |
| 795. |
In a triangle ABC, Let \(C = \frac {\pi} 2\), If r is the inradius and R is circumradius of the triangle ABC, then 2(r + R) equals |
| A. | a + b |
| B. | a + b + c |
| C. | a + c |
| D. | b + c |
| Answer» B. a + b + c | |
| 796. |
If tan 4° tan 43° tan 47° tan 86° |
| A. | 1 |
| B. | 1/2 |
| C. | 2 |
| D. | 2/3 |
| Answer» B. 1/2 | |
| 797. |
A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 meters from the bank he finds the angle to be 30°. Then, the breadth of the river is |
| A. | 40 m |
| B. | 60 m |
| C. | 20 m |
| D. | 30 m |
| Answer» D. 30 m | |
| 798. |
If sinx = 2/3, then find the value of cos3x. |
| A. | -0.5797 |
| B. | 0.5678 |
| C. | 0.6735 |
| D. | -0.8765 |
| Answer» B. 0.5678 | |
| 799. |
A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 5 m high, then the width of the street is: |
| A. | 17 m |
| B. | 16 m |
| C. | 14 m |
| D. | 15 m |
| Answer» B. 16 m | |
| 800. |
If cosec2 θ + cot2 θ = 7, then what is the value (in degrees) of θ if θ belongs to first quadrant? |
| A. | 15° |
| B. | 30° |
| C. | 45° |
| D. | 60° |
| Answer» C. 45° | |