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.
| 201. |
Find the value of sin 30°. |
| A. | 0 |
| B. | 1/√2 |
| C. | 1/2 |
| D. | √3/2 |
| Answer» D. √3/2 | |
| 202. |
If sin(A + B) = cos(A - B) = \(\frac{\sqrt 3}{2}\) and A and B are acute angle. The measures of angles A and B (in degrees) will be: |
| A. | A = 60 and B = 30 |
| B. | A = 45 and B = 15 |
| C. | A = 45 and B = 45 |
| D. | A = 15 and B = 45 |
| Answer» C. A = 45 and B = 45 | |
| 203. |
ABC is a right angles triangle with base BC and height AB. The hypotenuse AC is four times the length of the perpendicular drawn to it from opposite vertex. What is tan C equal to? |
| A. | 2 – √3 |
| B. | √3 – 1 |
| C. | 2 + √3 |
| D. | √3 + 1 |
| Answer» B. √3 – 1 | |
| 204. |
If \(\cot x = \dfrac{5}{12}\), then sin x - sec x =?A. \(-\dfrac{229}{65}\)B. \(\dfrac{229}{65}\)C. \(\dfrac{109}{65}\)D. \(-\dfrac{109}{65}\) |
| A. | B |
| B. | D |
| C. | C |
| D. | A |
| Answer» C. C | |
| 205. |
ABC is a triangle inscribed in a semicircle of diameter AB. What is cos(A+B) + sin(A + B) equal to ? |
| A. | 0 |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{2}\) |
| D. | 1 |
| Answer» E. | |
| 206. |
If a ladder of 10 m long reaches a window 8 m above the ground, then the distance of the foot of the ladder from the base of the wall is |
| A. | 18 m |
| B. | 8 m |
| C. | 4 m |
| D. | 6 m |
| Answer» E. | |
| 207. |
If cosec4θ - cosec2θ = 1.24, then cot4θ + cot2θ = ? |
| A. | 1.24 |
| B. | 1.86 |
| C. | 2.48 |
| D. | 0.62 |
| Answer» B. 1.86 | |
| 208. |
If x = a (sinθ + cosθ) and y = b (sinθ - cosθ) then (x2/ a2) + (y2/b2) = ? |
| A. | 3 |
| B. | 1 |
| C. | 4 |
| D. | 2 |
| Answer» E. | |
| 209. |
If cos(A–B) –cos(A + B) = x, then the value of x is |
| A. | 2sinAsinB |
| B. | 2cosAcosB |
| C. | 2cosAsinB |
| D. | 2sinAcosB |
| Answer» B. 2cosAcosB | |
| 210. |
If [1/(1 + cosec θ) - 1/(1 - cosecθ)]cosθ = 2, 0° < θ < 90°, then the value of sin2θ + cot2θ + sec2θ is: |
| A. | 2 |
| B. | 212 |
| C. | 7/2 |
| D. | 1 |
| Answer» D. 1 | |
| 211. |
If Sec θ = 5/3, then what is the value of Cosec θ? |
| A. | 0.8 |
| B. | 1.25 |
| C. | 4/3 |
| D. | 3/4 |
| Answer» C. 4/3 | |
| 212. |
A man standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N β° W. From the observation what is the breadth of the river will be(Given that the tanα° = 2 and tanβ° = 0.5) |
| A. | 60 m |
| B. | 70 m |
| C. | 80 m |
| D. | 90 m |
| Answer» D. 90 m | |
| 213. |
Find cos4 A – sin4 A. |
| A. | 0 |
| B. | 2 |
| C. | cos 2A |
| D. | sin2 A + cos2 A |
| Answer» D. sin2 A + cos2 A | |
| 214. |
If Sin θ = 8/17, thenSec θ = ? |
| A. | 17/8 |
| B. | 17/15 |
| C. | 8/15 |
| D. | 15/17 |
| Answer» C. 8/15 | |
| 215. |
If \(\operatorname{cosec} \theta-\sin \theta=m \) and \(\sec \theta-\cos \theta=\mathbf{n}\) then what is \(m^{\frac{4}{3}} n^{\frac{2}{3}}+m^{\frac{2}{3}} n^{\frac{4}{3}}\) equal to ? |
| A. | 0 |
| B. | 1 |
| C. | mn |
| D. | m2n2 |
| Answer» C. mn | |
| 216. |
If sin (2x - 45°) = cosx and angle x and (2x - 45°) (in degrees) are acute angles, then the value of cot x is: |
| A. | 0 |
| B. | \(\frac{1}{2}\) |
| C. | 1 |
| D. | \(\frac{1}{\sqrt{2}}\) |
| Answer» D. \(\frac{1}{\sqrt{2}}\) | |
| 217. |
If sec2θ + tan2θ = 5/3, then what is the value of tan2θ? |
| A. | 2√3 |
| B. | √3 |
| C. | 1/√3 |
| D. | Cannot be determined |
| Answer» C. 1/√3 | |
| 218. |
If \(\cos \theta =4x~and~\sin \theta =\frac{4}{x}\left( x\ne 0 \right),\)then the value of \(\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\) is: |
| A. | 1/16 |
| B. | 1/2 |
| C. | 1/3 |
| D. | 1/4 |
| Answer» B. 1/2 | |
| 219. |
If Cosec θ = 25/7, then what is the value of Cos θ? |
| A. | 25/24 |
| B. | 7/24 |
| C. | 24/25 |
| D. | 7/25 |
| Answer» D. 7/25 | |
| 220. |
If \(\cos θ = \frac 5 {13},\) then the value of tan2 θ + sec2 θ is equal to: |
| A. | \(\frac {313}{25}\) |
| B. | \(\frac {323}{25}\) |
| C. | \(\frac {233}{25}\) |
| D. | \(\frac {303}{25}\) |
| Answer» B. \(\frac {323}{25}\) | |
| 221. |
If \(\tan x=\dfrac{b}{a}\), then \(\sqrt{\dfrac{a+b}{a-b}}+\sqrt{\dfrac{a-b}{a+b}}\) is equal to : |
| A. | \(\dfrac{2 \sin x}{\sqrt{\sin 2x}}\) |
| B. | \(\dfrac{2 \cos x}{\sqrt{\cos 2x}}\) |
| C. | \(\dfrac{2 \cos x}{\sqrt{\sin 2x}}\) |
| D. | \(\dfrac{2\sin x}{\sqrt{\cos 2x}}\) |
| Answer» C. \(\dfrac{2 \cos x}{\sqrt{\sin 2x}}\) | |
| 222. |
If 2cos2θ - 1 = 0 and θ is acute, then what is the value of (cot2θ - tan2θ)? |
| A. | 0 |
| B. | 2 |
| C. | 10/3 |
| D. | 1 |
| Answer» B. 2 | |
| 223. |
If sinA = 12/13, then the value of (secA + cosecA) is∶ |
| A. | 67/20 |
| B. | 221/60 |
| C. | 11/3 |
| D. | 211/60 |
| Answer» C. 11/3 | |
| 224. |
If sinθ = 3x and cosθ = 3/x, (x ≠ 0) then the value of 6(x2 + 1/x2) is: |
| A. | 1/3 |
| B. | 1/4 |
| C. | 2/3 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 225. |
\(\frac{{\cot x}}{{1 + cosec\;x}} + \frac{{1\; + \;cosec\;x}}{{\cot x}}\) is equal to: |
| A. | 2 sin x |
| B. | 2 cos x |
| C. | 2 cosec x |
| D. | 2 sec x |
| Answer» E. | |
| 226. |
If cosec2 θ = 625/576, then what is the value of [(sin θ – cos θ)/(sin θ + cos θ)]? |
| A. | 1 |
| B. | 31/17 |
| C. | 17/31 |
| D. | 14/25 |
| Answer» D. 14/25 | |
| 227. |
A ladder leaning against a wall makes an angle θ with the horizontal ground such that \(\cos \theta = \dfrac{5}{13}\). If the height of the top of the ladder from the foot of the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall? |
| A. | 19.5 |
| B. | 7.5 |
| C. | 13 |
| D. | 18 |
| Answer» C. 13 | |
| 228. |
∆DEF is right angled at E. If tanD = 12/5, then what is the value of secF? |
| A. | 5/12 |
| B. | 13/5 |
| C. | 5/13 |
| D. | 13/12 |
| Answer» E. | |
| 229. |
Find the value of \(\frac{{\sqrt {cose{c^2}A - 1} }}{{\cot A\; + \;\tan A}}?\) |
| A. | sin2A |
| B. | cos A sin A |
| C. | cos2 A |
| D. | sec A cosec A |
| Answer» D. sec A cosec A | |
| 230. |
If 0 ≤ θ ≤ 90°, and sec107 θ + cos107 θ = 2, then, (sec θ + cos θ) is equal to: |
| A. | 2 |
| B. | 1 |
| C. | 2-107 |
| D. | 1/2 |
| Answer» B. 1 | |
| 231. |
A man on the top of a tower, standing on the sea-shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° to 60°. How soon the boat reach the sea-shore? |
| A. | 5 minutes |
| B. | 7 minutes |
| C. | 10 minutes |
| D. | 15 minutes |
| E. | 9 minutes |
| Answer» B. 7 minutes | |
| 232. |
A pole stands vertically on a road, which goes in the north-south direction. P, Q are two points towards the north of the pole, such that PQ = b, and the angles of elevation of the top of the pole at P, Q are α, β respectively. Then the height of the pole is: |
| A. | \(\frac{b}{{\tan \beta + \tan \alpha }}\) |
| B. | \(\frac{b}{{\tan \beta - \tan \alpha }}\) |
| C. | \(\frac{b}{{\cot \beta - \cot \alpha }}\) |
| D. | \(\frac{{b\tan \alpha }}{{\tan \beta }}\) |
| Answer» D. \(\frac{{b\tan \alpha }}{{\tan \beta }}\) | |
| 233. |
Find the value of sin 120° sin 240° sin 270°. |
| A. | 1/8 |
| B. | -1/8 |
| C. | -1/2 |
| D. | 3/4 |
| Answer» E. | |
| 234. |
Consider the following statements:1. The number of circles that can be drawn through three non-collinear points is infinity.2. Angle formed in minor segment of a circle is acute.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. | |
| 235. |
Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h2 equal to? |
| A. | 2l2 |
| B. | l2/2 |
| C. | 3l2/2 |
| D. | 2l3/3 |
| Answer» C. 3l2/2 | |
| 236. |
In ∆DEF measure of angle E is 90°. If sec D = 25/7, and DE = 1.4 cm, then what is the length (in cm) of side DF? |
| A. | 5 |
| B. | 4.8 |
| C. | 4 |
| D. | 5.6 |
| Answer» B. 4.8 | |
| 237. |
ΔDEF is right angled at E. If sec D = 25/7, then what is the value of cosec F? |
| A. | 7/25 |
| B. | 24/7 |
| C. | 25/7 |
| D. | 7/24 |
| Answer» D. 7/24 | |
| 238. |
If α + β = 90° and α = 2β, then the value of cos2α + sin2β is: |
| A. | \(\frac{1}{5}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{2}\) |
| D. | 1 |
| Answer» D. 1 | |
| 239. |
If sinθ and cosθ is the solution of the quadratic equation \({x^2} + ax + b = 0\), then, which of the following option is correct? |
| A. | a2 – 2b – 1 = 0 |
| B. | a2 + 2b – 1 = 0 |
| C. | a2 – 2b + 1 = 0 |
| D. | a2 –b – 1 = 0 |
| Answer» B. a2 + 2b – 1 = 0 | |
| 240. |
If \(\frac{{\cos A}}{{\cos ecA + 1}} + \frac{{\cos A}}{{\cos ecA - 1}} = 2,0^\circ \le A \le 90^\circ \), then A is equal to: |
| A. | 60° |
| B. | 45° |
| C. | 90° |
| D. | 30° |
| Answer» C. 90° | |
| 241. |
If \(x\sin {30^ \circ }cos{60^ \circ } = \sin {45 }\cos {45 }\), then the value of x is: |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | 3 |
| Answer» B. 0 | |
| 242. |
∆XYZ is right angled at Y. If cotX = 5/12, then what is the value of sec Z? |
| A. | 5/12 |
| B. | 13/5 |
| C. | 13/12 |
| D. | 12/5 |
| Answer» D. 12/5 | |
| 243. |
\({\left( {\frac{{\sin {\rm{\theta }} - 2{{\sin }^3}{\rm{\theta }}}}{{2{{\cos }^3}{\rm{\theta }} - \cos {\rm{\theta }}}}} \right)^2}{\rm{}} + {\rm{}}1,{\rm{\;\theta }} \ne 45^\circ ,\) is equal to: |
| A. | cot2 θ |
| B. | cosec2 θ |
| C. | 2tan2 θ |
| D. | sec2 θ |
| Answer» E. | |
| 244. |
A ladder leaning against a window of a house makes an angle of 60° with the ground. If the distance of the foot of the ladder from the wall is 4.2 m, then the height of the point, where the ladder touches the window from the ground is closest to: |
| A. | 7.3 m |
| B. | 6.8 m |
| C. | 7.8 m |
| D. | 7 m |
| Answer» B. 6.8 m | |
| 245. |
Δ PQR is right angled at Q. If m∠R = 30o then Cos P x Cosec P = ? |
| A. | √3 |
| B. | √2 |
| C. | 1 / √3 |
| D. | 1 / √2 |
| Answer» D. 1 / √2 | |
| 246. |
In a triangle, ∠C = 90° and ∠A = 60° then sin A/2 + cosecA = ? |
| A. | (√3 + 4)/2 |
| B. | (√3 + 4)/2√3 |
| C. | (√2 + 4)/3√3 |
| D. | (√3 + 4)/√3 |
| Answer» C. (√2 + 4)/3√3 | |
| 247. |
If cos x = (-√3/2) and π < x < 3π/2 then the value of 2cot2x + 3sec2x is: |
| A. | 10 |
| B. | 16 |
| C. | 8 |
| D. | 4 |
| Answer» B. 16 | |
| 248. |
In ΔPQR, ∠Q = 90°. If cot R=\(\frac{1}{3},\) then what is the value of \(\frac{secP(cosR+sinP)}{cosecR(sinR-cosec P)}\)? |
| A. | \(\frac{2}{7}\) |
| B. | \(-\frac{2}{3}\) |
| C. | \(-\frac{2}{7}\) |
| D. | \(\frac{2}{3}\) |
| Answer» D. \(\frac{2}{3}\) | |
| 249. |
A flag is placed on the top of a temple. The angles of elevation of the top of the flag and the top of the temple from point 15 m away from the base of the temple are 60° and 45°, respectively. What is the length of the pole of the flag? |
| A. | 15(√3 - 1) m |
| B. | 16(√3 - 1) m |
| C. | 17 (√3 - 1) m |
| D. | 14 (√3 - 1) m |
| Answer» B. 16(√3 - 1) m | |
| 250. |
If sin θ = cos θ, then what will be the value of sec θ? |
| A. | \({{\sqrt 2 }}\) |
| B. | \(\frac{1}{{\sqrt 2 }}\) |
| C. | 1 |
| D. | 2 |
| Answer» B. \(\frac{1}{{\sqrt 2 }}\) | |