MCQOPTIONS
Saved Bookmarks
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.
| 1001. |
A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60°. What is the height of the flagstaff? |
| A. | 9 m |
| B. | 10.5 m |
| C. | 13.5 m |
| D. | 15 m |
| Answer» D. 15 m | |
| 1002. |
In the given figure, if PQ = 13 cm and PR = 12 cm then the value of sin θ + tan θ = ? |
| A. | 218/5 |
| B. | 213/5 |
| C. | 216/13 |
| D. | 216/65 |
| Answer» E. | |
| 1003. |
A simplified value of sinθ + cosθ + 1 + cosθsinθtanθ + cos2θ - sinθ is: |
| A. | 2sinθ |
| B. | cosθ |
| C. | 2 + cosθ |
| D. | sinθ |
| Answer» D. sinθ | |
| 1004. |
ΔDEF is right angled at E. If sinD = 15/17, then what is the value of cotF ? |
| A. | 15/17 |
| B. | 8/17 |
| C. | 15/8 |
| D. | 17/15 |
| Answer» D. 17/15 | |
| 1005. |
If 0 < θ < 90°, 0 < φ < 90° and cos θ < cos φ, then which one of the following is correct? |
| A. | θ < φ |
| B. | θ > φ |
| C. | θ + φ = 90° |
| D. | No conclusion can be drawn |
| Answer» C. θ + φ = 90° | |
| 1006. |
If \(sin x=\frac{12}{37}\), then what is the value of tan x? |
| A. | \(\frac{35}{37}\) |
| B. | \(\frac{35}{12}\) |
| C. | \(\frac{12}{35}\) |
| D. | \(\frac{37}{12}\) |
| Answer» D. \(\frac{37}{12}\) | |
| 1007. |
If sin θ + sin 2θ = 1, then what is the value of (cos12θ + 3cos10θ + 3cos8θ + cos6θ - 1)? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 1008. |
In ∆ABC measure of angle B is 90o. If secA = 25/7, and AB = 14 cm, then what is the length (in cm) of side BC? |
| A. | 50 |
| B. | 48 |
| C. | 20 |
| D. | 26 |
| Answer» C. 20 | |
| 1009. |
ΔPQR is right angled at Q. If ∠R = 60°, then find the value of (sec P - 1/√3). |
| A. | (√6 - 6)/3√3 |
| B. | (1 - 3√2)/3 |
| C. | 1/√3 |
| D. | 2/√3 |
| Answer» D. 2/√3 | |
| 1010. |
ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are \({\rm{co}}{{\rm{t}}^{ - 1}}\left( {3\sqrt 2 } \right){\rm{\;and\;cose}}{{\rm{c}}^{ - 1}}\left( {2\sqrt 2 } \right)\) respectively, then the height of the tower (in meters) is: |
| A. | \(\frac{{100}}{{3\sqrt 3 }}\) |
| B. | \(10\sqrt 5\) |
| C. | 20 |
| D. | 25 |
| Answer» D. 25 | |
| 1011. |
From a point A, the distance of a tower is 3 m. If the angle of elevation from point A to the tower is 30°, then find the height (in m) of the tower. |
| A. | √7 |
| B. | √5 |
| C. | √3 |
| D. | 2√3 |
| Answer» D. 2√3 | |
| 1012. |
If 6 + 8 tan θ = sec θ and 8 - 6 tan θ = k sec θ, then what is the value of k2? |
| A. | 11 |
| B. | 22 |
| C. | 77 |
| D. | 99 |
| Answer» E. | |
| 1013. |
If sin(A + B) = √3/2 and tan(A – B) = 1/√3, then (2A + 3B) is equal to∶ |
| A. | 120° |
| B. | 135° |
| C. | 130° |
| D. | 125° |
| Answer» C. 130° | |
| 1014. |
If tanθ = 2/3, then \(\frac{{3\sin \theta - 4\cos \theta }}{{3\sin \theta {\rm{\;}} + {\rm{\;}}4{\rm{\;}}\cos \theta }}\) is equal to: |
| A. | 2/3 |
| B. | -1/3 |
| C. | 1/3 |
| D. | -2/3 |
| Answer» C. 1/3 | |
| 1015. |
If \(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0° |
| A. | 1 |
| B. | 5 |
| C. | 0 |
| D. | 2 |
| Answer» B. 5 | |
| 1016. |
An observer who is 1.62 m tall is 45 m away from a pole. The angle of elevation of the top of the pole from his eyes is 30°. The height (in m) of the pole is closest to: |
| A. | 26.8 |
| B. | 25.8 |
| C. | 26.2 |
| D. | 27.6 |
| Answer» E. | |
| 1017. |
P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are 60° and 30°, respectively and the distance between them is 84√3 m. What is the height (in m) of the pole? |
| A. | 60 |
| B. | 52.5 |
| C. | 73.5 |
| D. | 63 |
| Answer» E. | |
| 1018. |
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. |
| A. | 10 m |
| B. | 20 m |
| C. | 30 m |
| D. | 40 m |
| Answer» B. 20 m | |
| 1019. |
If cosec 39° = x, then the value of \(\frac 1 {\rm cosec^2\;51^\circ} + \sin^2 39^\circ + \tan^2 51^\circ - \frac 1 {\sin^2 51^\circ\sec^2 39^\circ}\) is: |
| A. | \(\sqrt {x^2 - 1}\) |
| B. | x2 - 1 |
| C. | 1 - x2 |
| D. | \(\sqrt {1 - x^2}\) |
| Answer» C. 1 - x2 | |
| 1020. |
If sinθ + cosecθ = 2 then sin2θ + cosec2θ = ? |
| A. | 1 |
| B. | 4 |
| C. | 2 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 1021. |
If A is an acute angle and cosec A = √2, then the value of 4sin2A ÷ secA is: |
| A. | \(2\sqrt 2 \) |
| B. | \(\frac{1}{{\left( {\sqrt 2 } \right)}}\) |
| C. | \(4\sqrt 2 \) |
| D. | \(4 - \sqrt 2 \) |
| Answer» B. \(\frac{1}{{\left( {\sqrt 2 } \right)}}\) | |
| 1022. |
If tan A - tan B = x and cot B - cot A = y, then what is the value of cot (A - B)? |
| A. | \(\frac{1}{x}+\frac{1}{y}\) |
| B. | \(\frac{1}{y}-\frac{1}{x}\) |
| C. | \(\frac{xy}{x+y}\) |
| D. | \(1+\frac{1}{xy}\) |
| Answer» B. \(\frac{1}{y}-\frac{1}{x}\) | |
| 1023. |
If (cos2θ – 3cosθ + 2) /sin2θ = 1, where 0 < θ < π/2,which of the following statement(s) is/are correct?(1) There are two values of θ satisfying the above equation(2) θ = 60° is satisfied by the above equation.Select the correct answer using the code given below |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 1024. |
An observer 1.6 m tall is 20√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: |
| A. | 21.6 m |
| B. | 23.2 m |
| C. | 24.72 m |
| D. | None of these |
| Answer» B. 23.2 m | |
| 1025. |
In a ΔABC, if \(\dfrac{\tan A- \tan B}{\tan A + \tan B}=\dfrac{c-b}{c}\), then A is equal to |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» D. 90° | |
| 1026. |
If cosθ = 2p/(p2 + 1), p≠0 then tan θ is equal to: |
| A. | (p2 – 1)/2p |
| B. | (p2 + 1)/(p2 – 1) |
| C. | 2p/(p2 + 1) |
| D. | 2p/(p2 – 1) |
| Answer» B. (p2 + 1)/(p2 – 1) | |
| 1027. |
3[sinx – cosx]4 + 6[sinx + cosx]2 + 4[sin6x + cos6x] = ? |
| A. | 6 |
| B. | 4 |
| C. | 3 |
| D. | 13 |
| Answer» E. | |
| 1028. |
If \(\frac{{cos\theta \;}}{{1\; + \;sin\theta }} +\frac{{cos\theta \;}}{{1 - sin\theta }} =2\surd 2\) and θ is acute, then what is the value (in degrees) of θ? |
| A. | 30 |
| B. | 45 |
| C. | 60 |
| D. | 90 |
| Answer» C. 60 | |
| 1029. |
Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30°, and the angle of elevation to the top of the tower at C is 45°. What is the ratio of the height of towers at B and C? |
| A. | 1 : √3 |
| B. | 1 : 3 |
| C. | 1 : 2 |
| D. | 1 : 2√3 |
| Answer» C. 1 : 2 | |
| 1030. |
If (1 − cosA)/2 = x, then the value of x is |
| A. | cos2(A/2) |
| B. | √sin(A/2) |
| C. | √cos(A/2) |
| D. | sin2(A/2) |
| Answer» E. | |
| 1031. |
If sinθ = 40/41, then cotθ isA. 40/9B. 9/40C. 9/41D. 41/9 |
| A. | D |
| B. | A |
| C. | B |
| D. | C |
| Answer» D. C | |
| 1032. |
If sin θ + cosec θ = 2, then the value of sin2 θ + cosec2 θ is: |
| A. | 4 |
| B. | 8 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 1033. |
If \(\tan a = \frac{2}{{\sqrt {13} }}\), then the value of \(\frac{{cosec^2a\ +\ 2{{\sec }^2}a}}{{cosec^2a\ -\ 3{{\sec }^2}a}}\) is: |
| A. | 14 |
| B. | 21 |
| C. | 32 |
| D. | 16 |
| Answer» C. 32 | |
| 1034. |
If \(\sin x = \frac{4}{5}\), then \(Cosecx + \cot x = \) |
| A. | 31/12 |
| B. | 35/12 |
| C. | 2 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 1035. |
If sec (θ – α), sec θ and sec (θ + α) are in AP, where cos α ≠ 1, then what is the value of sin2 θ + cos α? |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 1/2 |
| Answer» B. 1 | |
| 1036. |
∆PQR is right angled at Q. If cosec P = 17/15, then what is the value of sin R? |
| A. | 15/17 |
| B. | 8/17 |
| C. | 17/8 |
| D. | 17/15 |
| Answer» C. 17/8 | |
| 1037. |
On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45° to 60°. What will be the height (in metres) of the building? |
| A. | 50(3 + √3) |
| B. | 100(√3 + 1) |
| C. | 150 |
| D. | 100√3 |
| Answer» B. 100(√3 + 1) | |
| 1038. |
If \(\sin A = \dfrac{15}{17}\) and \(\sin B = \dfrac{7}{25}\) , then sin (A - B) =?A. \(\dfrac{304}{425}\)B. \(\dfrac{416}{425}\)C. \(\dfrac{297}{425}\)D. \(\dfrac{87}{425}\) |
| A. | A |
| B. | C |
| C. | D |
| D. | B |
| Answer» B. C | |
| 1039. |
If cos 25° + sin 25° = k, then cos 20° is equal to: |
| A. | \(\dfrac{k}{\sqrt 2}\) |
| B. | \( \pm\dfrac{k}{\sqrt 2}\) |
| C. | \(-\dfrac{k}{\sqrt 2}\) |
| D. | None of these |
| Answer» B. \( \pm\dfrac{k}{\sqrt 2}\) | |
| 1040. |
If Cos θ = 15/17, then what is the value of Cosec θ? |
| A. | 17/8 |
| B. | 8/17 |
| C. | 8/15 |
| D. | 17/15 |
| Answer» B. 8/17 | |
| 1041. |
ΔDEF is right angled at E. If m∠D = 45°, then find the value of (tanF + 1/3). |
| A. | 4/3 |
| B. | 3√3/2 |
| C. | (√2 + 1)/√2 |
| D. | (3√2 + 1)/3 |
| Answer» B. 3√3/2 | |
| 1042. |
If cos2θ – 3cosθ + 2 = sin2θ, 0° < θ < 90°, then the value of 2cosecθ + 4cotθ: |
| A. | 2√3 |
| B. | (4√3)/4 |
| C. | (8√3)/3 |
| D. | 4√3 |
| Answer» D. 4√3 | |
| 1043. |
If 5 cos θ – 12 sin θ = 0, then what is the value of \(\frac{{1\; + \;\sin \theta \; + \;\cos \theta }}{{1 - \sin \theta \; + \;\cos \theta }}?\) |
| A. | 5/4 |
| B. | 5/2 |
| C. | 3/2 |
| D. | 3/4 |
| Answer» D. 3/4 | |
| 1044. |
If 5 secθ – 3 tanθ = 5, then what is the value of 5 tanθ – 3 secθ? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 1045. |
If A = 2(sin6 θ + cos6 θ) - 3(sin4 θ + cos4 θ) then the value of 3α such that \(cos\alpha = \sqrt{\frac{3+A}{5+A}} \) is: |
| A. | 180∘ |
| B. | 90∘ |
| C. | 45∘ |
| D. | 135∘ |
| Answer» E. | |
| 1046. |
From the top of a platform 5 m high, the angle of elevation of a tower was 30°. If the tower was 45 m high, how far away from the tower was the platform positioned? |
| A. | 45√3m |
| B. | 15√3m |
| C. | 40√3m |
| D. | 40 m |
| Answer» D. 40 m | |
| 1047. |
Convert 150° in radian measure. |
| A. | \(1\frac{1}{5}\pi \) |
| B. | \(\frac{5}{{12}}\pi \) |
| C. | \(2\frac{2}{5}\pi \) |
| D. | \(\frac{5}{6}\pi \) |
| Answer» E. | |
| 1048. |
If \(\tan A=\dfrac{1}{7}\), then what is cos 2A equal to? |
| A. | \(\dfrac{24}{25}\) |
| B. | \(\dfrac{18}{25}\) |
| C. | \(\dfrac{12}{25}\) |
| D. | \(\dfrac{6}{25}\) |
| Answer» B. \(\dfrac{18}{25}\) | |
| 1049. |
∆PQR is right angled at Q. If ∠R = 45°, then find the value of (cosec P – √3/2). |
| A. | (3√3 - 1)/3 |
| B. | 2/√3 |
| C. | (2 - √3)/√3 |
| D. | (2√2 - √3)/2 |
| Answer» E. | |
| 1050. |
If p = sin2 θ + cos4 θ, for 0 ≤ θ ≤ (π/2), then consider the following statements:1. p can be less than (3/4)2. p can be more than 1Which 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. | |