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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.
| 801. |
From the top of a 120 m high tower, the angle of depression of the top of a pole 45° and the angle of depression of the foot of the pole is θ, such that tan θ = 3/2, what is the height of the pole? |
| A. | 80 m |
| B. | 75 m |
| C. | 60 m |
| D. | 40 m |
| Answer» E. | |
| 802. |
As the value of ‘θ’ increases from 0 to 90°, the value of Sinθ ______. |
| A. | Decreases |
| B. | Remains constant |
| C. | Increases |
| D. | Tends to zero |
| Answer» D. Tends to zero | |
| 803. |
If cos θ = 2p/(1 + p2), then tan θ is equal to: |
| A. | \(\frac{{2{\rm{p}}}}{{1 - {{\rm{p}}^2}}}\) |
| B. | \(\frac{{{{\rm{p}}^2}}}{{1{\rm{\;}} + {\rm{\;}}{{\rm{p}}^2}}}\) |
| C. | \(\frac{{1 - {{\rm{p}}^2}}}{{2{\rm{p}}}}\) |
| D. | \(\frac{{1 - {{\rm{p}}^2}}}{{1{\rm{\;}} + {\rm{\;}}{{\rm{p}}^2}}}\) |
| Answer» D. \(\frac{{1 - {{\rm{p}}^2}}}{{1{\rm{\;}} + {\rm{\;}}{{\rm{p}}^2}}}\) | |
| 804. |
Evaluate: (sin 30°/cos 45°) × (sin 45°/cos 30°) |
| A. | \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeWaaOaaa8aabaWdbiaaikdaaSqabaaak8aabaWd % bmaakaaapaqaa8qacaaIZaaaleqaaaaaaaa!3859! \frac{{\sqrt 2 }}{{\sqrt 3 }}\)1 |
| B. | \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeWaaOaaa8aabaWdbiaaikdaaSqabaaak8aabaWd % bmaakaaapaqaa8qacaaIZaaaleqaaaaaaaa!3859! \frac{{2 }}{{\sqrt 3 }}\)1/2 |
| C. | \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWcaaWdaeaapeWaaOaaa8aabaWdbiaaikdaaSqabaaak8aabaWd % bmaakaaapaqaa8qacaaIZaaaleqaaaaaaaa!3859! \frac{{1 }}{{√ 3 }}\)1/√2 |
| D. | 1/√3 |
| Answer» E. | |
| 805. |
Let ‘S’ be the set of all α ∈ R such that the equation cos 2x + α sin x = 2α – 7 has a solution. Then S is equal to: |
| A. | R |
| B. | [1, 4] |
| C. | [3, 7] |
| D. | [2, 6] |
| Answer» E. | |
| 806. |
Find the value of sin230cos245 + 4tan230 + (1/2)sin290 – 2cos290 + 1/24 |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 807. |
If 5 tan α = 4 then \(\rm \dfrac{5\ sin\ \alpha-3\ cos \ \alpha}{5\ sin\ \alpha+2\ cos \ \alpha}\) is equal to |
| A. | \(\dfrac{1}{6}\) |
| B. | \(\dfrac{5}{3}\) |
| C. | 2 |
| D. | 0 |
| Answer» B. \(\dfrac{5}{3}\) | |
| 808. |
\(\frac{{\cos x}}{{1 + \sin x}} + \frac{{1 + \sin x}}{{\cos x}}\;\) is equal to: |
| A. | 2cos x |
| B. | 2sin x |
| C. | 2sec x |
| D. | 2cosec x |
| Answer» D. 2cosec x | |
| 809. |
If tan x = cot (45° + 2x), then what is the value of x? |
| A. | 45° |
| B. | 20° |
| C. | 22.5° |
| D. | 15° |
| Answer» E. | |
| 810. |
If 4sinθ – 3cosθ = 0, then secθ.cosecθ is:A) 5/12B) 25/12C) 13/12D) 12/5 |
| A. | B |
| B. | A |
| C. | C |
| D. | D |
| Answer» B. A | |
| 811. |
If in a triangle ABC, \(\frac{{2\cos A}}{a} + \frac{{\cos B}}{b} + \frac{{2\cos C}}{c} = \frac{a}{{bc}} + \frac{b}{{ca}}\) then the value of the angle A is |
| A. | \(\frac{\pi }{3}\) |
| B. | \(\frac{\pi }{4}\) |
| C. | \(\frac{\pi }{2}\) |
| D. | \(\frac{\pi }{6}\) |
| Answer» D. \(\frac{\pi }{6}\) | |
| 812. |
Let ABC be a triangle right angled at C, then what is tan A + tan B equal to? |
| A. | \(\frac{a}{{bc}}\) |
| B. | \(\frac{{{a^2}}}{{bc}}\) |
| C. | \(\frac{{{b^2}}}{{ca}}\) |
| D. | \(\frac{{{c^2}}}{{ab}}\) |
| Answer» E. | |
| 813. |
If 3 sin θ = 2 cos2θ, 0° < θ < 90°, then the value of (tan θ + cos θ + sin θ) is: |
| A. | √3 + 7 |
| B. | √3 + 5 |
| C. | (7 + 2√3)/3√3 |
| D. | (5 + √3)/2√3 |
| Answer» E. | |
| 814. |
If Sin θ = 20/29, then what is the value of Cos θ? |
| A. | 29/21 |
| B. | 21/29 |
| C. | 21/20 |
| D. | 20/29 |
| Answer» C. 21/20 | |
| 815. |
For any \({\rm{\theta }} \in \left( {\frac{{\rm{\pi }}}{4},{\rm{\;}}\frac{{\rm{\pi }}}{2}} \right),\) the expression 3(sin θ – cos θ)4 + 6(sin θ + cos θ)2 + 4sin6 θ equals |
| A. | 13 – 4 cos2 θ + 6 sin2 θ cos2 θ |
| B. | 13 – 4 cos6 θ |
| C. | 13 – 4 cos2 θ + 6 cos4 θ |
| D. | 13 – 4 cos4 θ + 2 sin2 θ cos2 θ |
| Answer» C. 13 – 4 cos2 θ + 6 cos4 θ | |
| 816. |
If 3tanθ = 2, find the value of (2sinθ – cosθ)/(2cosθ – sinθ). |
| A. | 0 |
| B. | 1/3 |
| C. | 1/4 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 817. |
If tan2x + 1/tan2x = 2 and 0° < x < 90°, then what is the value of x? |
| A. | 15° |
| B. | 30° |
| C. | 45° |
| D. | 60° |
| Answer» D. 60° | |
| 818. |
If sin x – cos x = 0, 0° < x < 90° then the value of (sec x + cosec x)2 is: |
| A. | 8 |
| B. | 4 |
| C. | 10 |
| D. | 6 |
| Answer» B. 4 | |
| 819. |
If \(6\left( {sec^259^\circ - cot^231^\circ} \right) + \frac{2}{3}sin90^\circ - 3tan^256^\circ \;ytan^234^\circ = \frac{y}{3},\) then the value of y is: |
| A. | 2 |
| B. | -23 |
| C. | -2 |
| D. | 23 |
| Answer» B. -23 | |
| 820. |
A pole on the ground leans at 60° with the vertical. At a point x metre away from the base of the pole on the ground, two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, then what is the length of the pole? |
| A. | \(\sqrt 2 x\) metre |
| B. | \(\sqrt 3 x\) metre |
| C. | 2x metre |
| D. | \(2\sqrt 2 x\) metre |
| Answer» C. 2x metre | |
| 821. |
If sin θ.sec2θ = 2/3, 0° ∠θ ∠90°, then the value of (tan2θ + cos2θ) is: |
| A. | 11/12 |
| B. | 7/6 |
| C. | 13/12 |
| D. | 5/4 |
| Answer» D. 5/4 | |
| 822. |
If \(\frac{{\sin A + \cos A}}{{\cos A}} = \frac{{17}}{{12}},\) then the value of \(\frac{{1 - \cos A}}{{\sin A}}\) is: |
| A. | 5/12 |
| B. | 1/5 |
| C. | -5 |
| D. | 1 |
| Answer» C. -5 | |
| 823. |
If tan θ tan 5θ = 1, then what is the value of sin 2θ? |
| A. | 0 |
| B. | 1/2 |
| C. | 1√2 |
| D. | √3/2 |
| Answer» C. 1√2 | |
| 824. |
\(\frac{{\sin 30^\circ }}{{1 + \;cos30^\circ }} + \frac{{1 + {\rm{\;cos}}30^\circ }}{{sin30^\circ }} = \;?\) |
| A. | 3 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» E. | |
| 825. |
If P + Q + R = 60°, then what is the value of cosQ.cosR.(cosP - sinP) + sinQ.sinR.(sinP - cosP)? [where Q = - R] |
| A. | (1 - √3) /2 |
| B. | (1 + √3) /2 |
| C. | (√3 - 1) /2 |
| D. | (√3 + 1) /2 |
| Answer» B. (1 + √3) /2 | |
| 826. |
If \(\frac{{si{n^2}\theta }}{{1 + co{s^2}\theta }} + \frac{{si{n^2}\theta }}{{1 - co{s^2}\theta }} = \frac{8}{5}\) and |
| A. | 0 |
| B. | 30 |
| C. | 45 |
| D. | 60 |
| Answer» E. | |
| 827. |
If \(\sec\theta=\dfrac{4}{\sqrt7}\), then the value of \(\sqrt{\dfrac{2 tan^2 \theta-cosec^2 \theta}{2cos^2\theta-cot^2 \theta}}\) is |
| A. | \(\dfrac{20}{7}\) |
| B. | 0 |
| C. | 4 |
| D. | None of these |
| Answer» B. 0 | |
| 828. |
Let S be the set {a ϵ Z+ : a ≤ 100}. If the equation [tan2 x] - tan x - a = 0 has real roots (where [.] is the greatest integer function), then the number of elements is S is |
| A. | 10 |
| B. | 8 |
| C. | 9 |
| D. | 0 |
| Answer» D. 0 | |
| 829. |
If tan(α – β).cot(α + β) = 1/n, then what will be the value of (n – 1)/(n + 1). |
| A. | cosec2α/cosec2β |
| B. | sin2α/sin2β |
| C. | - cosec2α /cosec2β |
| D. | - sin2α/sin2β |
| Answer» B. sin2α/sin2β | |
| 830. |
cosA(secA - cosA) (cotA + tanA)=? |
| A. | tan A |
| B. | sec A |
| C. | sin A |
| D. | cot A |
| Answer» B. sec A | |
| 831. |
If tanθ = 3/5, (0°< θ < 90°) then sinθ.cosθ is equal to: |
| A. | 14/34 |
| B. | 17 |
| C. | 15/34 |
| D. | 16/34 |
| Answer» D. 16/34 | |
| 832. |
It is given that, \(\sqrt {\frac{{\left( {1 - {\rm{sinx}}} \right)}}{{\left( {1{\rm{\;}} + {\rm{\;sinx}}} \right)}}} \) = a - tanx then α is equal to: |
| A. | cosecx |
| B. | cosx |
| C. | secx |
| D. | sinx |
| Answer» D. sinx | |
| 833. |
Cosine of angle A of the triangle ABC with vertices A(1, -1, 2), B(6, 11, 2) and C(1, 2, 6) is |
| A. | 30/65 |
| B. | 65/36 |
| C. | 36/65 |
| D. | 60/65 |
| Answer» D. 60/65 | |
| 834. |
If the value of θ = 30°, then value of tan2 θ + cot2θ |
| A. | 1/3 |
| B. | 4/3 |
| C. | 9/3 |
| D. | 10/3 |
| Answer» E. | |
| 835. |
If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the angles A, B and C respectively. If \(s=\dfrac{a+b+c}{2}=6\), then the product \(\dfrac{1}{3}s^2 (s-a)(s-b)(s-c)\) is equal to |
| A. | 2Δ |
| B. | 2Δ2 |
| C. | \(\sqrt{2}\Delta\) |
| D. | Δ2 |
| Answer» C. \(\sqrt{2}\Delta\) | |
| 836. |
If tan θ = 5/12, then cosec θ = ? |
| A. | 5/13 |
| B. | 12/5 |
| C. | 13/5 |
| D. | 13/12 |
| Answer» D. 13/12 | |
| 837. |
If tan(A + B) = 0, then – |
| A. | tan A + tan B = 0 |
| B. | tan A = tan B |
| C. | \(\frac{{2\tan A\; + \;\tan B}}{{1\; - \;\tan A\tan B}} = 1\) |
| D. | \(\frac{{2\tan A\; + \;\tan B}}{{1\; + \;\tan A\tan B}} = 0\) |
| Answer» B. tan A = tan B | |
| 838. |
From the top of a tower, the angles of depression two objects on the ground on the same side of it, observed to be 60° and 30° respectively and the distance between the objects is 400√3 m. The height (in m) of the tower is∶ |
| A. | 600√3 |
| B. | 800 |
| C. | 800√3 |
| D. | 600 |
| Answer» E. | |
| 839. |
If tan x = cot (60° + 6x), then what is the value of x? |
| A. | 15°/2 |
| B. | 10° |
| C. | 12° |
| D. | 30°/7 |
| Answer» E. | |
| 840. |
ΔDEF is right angled at E. If m∠F = 300, then find the value of (sin D - 1/3). |
| A. | -1/2√3 |
| B. | (3√3 - 2)/6 |
| C. | (√2 - √3)/√6 |
| D. | (2√2 - 1)/√2 |
| Answer» C. (√2 - √3)/√6 | |
| 841. |
Angle α is divided into two parts A and B such that A – B = x and tan A: tan B = p : q. The value of sin x is equal to |
| A. | \(\frac{{\left( {p + q} \right)\sin \alpha }}{{p - q}}\) |
| B. | \(\frac{{p\sin \alpha }}{{p + q}}\) |
| C. | \(\frac{{p\sin \alpha }}{{p - q}}\) |
| D. | \(\frac{{\left( {p - q} \right)\sin \alpha }}{{p + q}}\) |
| Answer» E. | |
| 842. |
If (1 + tan2θ) + [1 + (tan2 θ)-1] = k, then √k = ? |
| A. | sin θ cos θ |
| B. | cosec θ cos θ |
| C. | sin θ sec θ |
| D. | cosec θ sec θ |
| Answer» E. | |
| 843. |
A ladder 5 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75°. What is the height of the Flagstaff? |
| A. | 11 m |
| B. | 9 m |
| C. | (6 + √3) m |
| D. | (6 + 3√3) m |
| Answer» B. 9 m | |
| 844. |
If secθ + tanθ = x then secθ |
| A. | \(\frac{{{x^2} - 1}}{{2x}}\) |
| B. | \(\frac{{{x^2} + 1}}{x}\) |
| C. | \(\frac{{{x^2} - 1}}{x}\) |
| D. | \(\frac{{{x^2} + 1}}{{2x}}\) |
| Answer» E. | |
| 845. |
In ΔABC, right angled at B, if sin A = \(\frac{1}{\sqrt2}\), then the value of \(\frac{sin A(cos C + cos A)}{cos C (sin C + sin A)}\) is: |
| A. | \(2 \sqrt{5}\) |
| B. | 1 |
| C. | 3 |
| D. | 2 |
| Answer» C. 3 | |
| 846. |
If θ = 9°, then what is the value of Cot θ cot 2 θ cot 3 θ cot 4 θ cot 5 θ cot 6 θ cot 7 θ cot 8 θ cot 9 θ ? |
| A. | 13 |
| B. | 3 - 1 |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 847. |
If 9cosA + 12sinA = 15, find the value of cotA.A. 3/4B. 12/13C. 1/3D. 3/5 |
| A. | A |
| B. | D |
| C. | B |
| D. | C |
| Answer» B. D | |
| 848. |
If sin θ = 12 / 37, then tan θ = ? |
| A. | 12 / 35 |
| B. | 35 / 12 |
| C. | 37 / 12 |
| D. | 35 / 37 |
| Answer» B. 35 / 12 | |
| 849. |
Consider the following:\(1.{\rm{\;}}\frac{{{\rm{cos}}75^\circ }}{{{\rm{sin}}15^\circ }} + \frac{{{\rm{sin}}12^\circ }}{{{\rm{cos}}78^\circ }} - \frac{{{\rm{cos}}18^\circ }}{{{\rm{sin}}72^\circ }}{\rm{\;}} = {\rm{\;}}1\)\(2.\;\frac{{{\rm{cos}}35^\circ }}{{{\rm{sin}}55^\circ }} - \frac{{{\rm{sin}}11^\circ }}{{{\rm{cos}}79^\circ }} + {\rm{cos}}28^\circ .{\rm{cosec}}62^\circ {\rm{\;}} = {\rm{\;}}1\)\(3.\;\frac{{{\rm{sin}}80^\circ }}{{{\rm{cos}}10^\circ }} - {\rm{sin}}59^\circ .{\rm{sec}}31^\circ {\rm{\;}} = {\rm{\;}}0\)Which of the above are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 850. |
From an aeroplane vertically over a straight horizontal road, the angle of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be α and β. The height of the aeroplane above the road is |
| A. | \(\frac{{{\rm{tan\;\alpha }} + {\rm{tan\;\beta }}}}{{{\rm{tan\;\alpha \;tan\;\beta }}}}\) |
| B. | \(\frac{{{\rm{tan\;\alpha \;tan\;\beta }}}}{{{\rm{tan\;\alpha }} + {\rm{\;tan\;\beta }}}}\) |
| C. | \(\frac{{{\rm{cot\;\alpha \;cot\;\beta }}}}{{{\rm{cot\;\alpha }} + {\rm{\;cot\;\beta }}}}\) |
| D. | \(\frac{{{\rm{cot\;\alpha }} + {\rm{\;cot\;\beta }}}}{{{\rm{cot\;\alpha \;cot\;\beta }}}}\) |
| Answer» C. \(\frac{{{\rm{cot\;\alpha \;cot\;\beta }}}}{{{\rm{cot\;\alpha }} + {\rm{\;cot\;\beta }}}}\) | |