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.
| 301. |
If secθ + tanθ = 2, then secθ – tanθ = ? |
| A. | 1.5 |
| B. | 1 |
| C. | 0.5 |
| D. | 0.75 |
| Answer» D. 0.75 | |
| 302. |
If sec θ + tan θ = m (>1), then the value of sin θ is (0° < θ < 90°) |
| A. | \(\frac{{1 - {m^2}}}{{1 + {m^2}}}\) |
| B. | \(\frac{{{m^2} - 1}}{{{m^2} + 1}}\) |
| C. | \(\frac{{{m^2} + 1}}{{{m^2} - 1}}\) |
| D. | \(\frac{{1 + {m^2}}}{{1 - {m^2}}}\) |
| Answer» C. \(\frac{{{m^2} + 1}}{{{m^2} - 1}}\) | |
| 303. |
If 5 cot θ = 12, the value of cosec θ + sec θ is close to |
| A. | 3.68 |
| B. | 2.48 |
| C. | 6.28 |
| D. | 5.38 |
| Answer» B. 2.48 | |
| 304. |
If 2 tan A = 3 tan B = 1, then what is tan (A - B) equal to? |
| A. | \(\frac{1}{5}\) |
| B. | \(\frac{1}{6}\) |
| C. | \(\frac{1}{7}\) |
| D. | \(\frac{1}{9}\) |
| Answer» D. \(\frac{1}{9}\) | |
| 305. |
If A + B = 90°, then which of the following is correct?A. sin A = cos BB. sin A + cos B = 0C. sin A – cos B = 1D. sin A – cos B = 2 |
| A. | C |
| B. | A |
| C. | B |
| D. | D |
| Answer» C. B | |
| 306. |
∆DEF is right angled at E. If m∠F = 45°, then find the value of (cosec D - 1/√3). |
| A. | (√6 - 1)/√3 |
| B. | (1 - √6)/√2 |
| C. | √3 - 2 |
| D. | (2 - √3)/2√3 |
| Answer» B. (1 - √6)/√2 | |
| 307. |
In Δ ABC, ∠B = 90º, AC = 29 cm and BC = 20 cm. Then \(\frac{{1 - \sin A + \cos A}}{{1 + \sin A + \cos A}}\) is equal to: |
| A. | 3/8 |
| B. | 3/7 |
| C. | 1/2 |
| D. | 1/4 |
| Answer» C. 1/2 | |
| 308. |
An 18 feet high electric pole is located along a 6 feet tall tree at a distance of 10 feet from. What will be the length of the tree's shadow?A. 10 feetB. 7.5 feetC. 6 feetD. 5 feet |
| A. | A |
| B. | D |
| C. | B |
| D. | C |
| Answer» C. B | |
| 309. |
If θ lies in the first quadrant and \(\cot \theta = \frac{{63}}{{16}}\), then what is the value of (sin θ + cos θ)? |
| A. | 1 |
| B. | \(\frac{{69}}{{65}}\) |
| C. | \(\frac{{79}}{{65}}\) |
| D. | 2 |
| Answer» D. 2 | |
| 310. |
From the top of a hill 240 m high, the angles of depression of the top and bottom of a pole are 30° and 60°, respectively. The difference (in m) between the height of the pole and its distance form the hill is: |
| A. | 80(√3 - 1) |
| B. | 120 (2 - √3) |
| C. | 120 (√3 - 1) |
| D. | 80 (2 - √3) |
| Answer» E. | |
| 311. |
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 18 m. Find the height of the tree (in metres) |
| A. | 24√3 |
| B. | 9 |
| C. | 9√3 |
| D. | 18√3 |
| Answer» E. | |
| 312. |
In the equation\({\cos ^{ - 1}}\left( {\frac{{1 - {a^2}}}{{1 + {a^2}}}} \right) - {\cos ^{ - 1}}\left( {\frac{{1 - {b^2}}}{{1 + {b^2}}}} \right) = 2{\tan ^{ - 1}}x\)value of x is |
| A. | \(\frac{{a + b}}{{1 + ab}}\) |
| B. | \(\frac{{a - b}}{{1 + ab}}\) |
| C. | \(\frac{{a - b}}{{1 - ab}}\) |
| D. | None of the above |
| Answer» C. \(\frac{{a - b}}{{1 - ab}}\) | |
| 313. |
If xsin3 θ + ycos3 θ = sin θcos θ and xsin θ – ycos θ = 0, then the value of x2 + y2 equals |
| A. | 1 |
| B. | 1/2 |
| C. | 3/2 |
| D. | 2 |
| Answer» B. 1/2 | |
| 314. |
If sinx + cosecx = 2, then sin17x + cosec18x is equal to: |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | 4 |
| Answer» B. 1 | |
| 315. |
In sin (α + β) = 1, sin(α – β) = 1/2, then tan (α + 2β) tan (2α + β) = ? |
| A. | -1 |
| B. | 0 |
| C. | None of these |
| D. | 1 |
| Answer» E. | |
| 316. |
If A, B, C are the angles of a triangle, then the value of \(\frac{{\tan \left( {B + C} \right) + \tan \left( {C + A} \right) + \tan \left( {A + B} \right)}}{{\tan \left( {\pi - A} \right) + \tan \left( {\pi - B} \right) + \tan \left( {\pi - C} \right)}}\) is equal to - |
| A. | 0 |
| B. | 1 |
| C. | π/2 |
| D. | tan (A+B+C) |
| Answer» C. π/2 | |
| 317. |
If sin A = x - cos A and sec A = y - cosec A, then the value of y(x2 - 1) is equal to: |
| A. | 3x |
| B. | 2x |
| C. | 2xy |
| D. | 0 |
| Answer» C. 2xy | |
| 318. |
ABCD is a parallelogram where AC and BD are the diagonals. If ∠BAD = 60°, ∠ADB = 90°, then what is BD2 equal to? |
| A. | \(\frac{3}{5}A{B^2}\) |
| B. | \(\frac{3}{4}A{B^2}\) |
| C. | \(\frac{1}{2}A{B^2}\) |
| D. | \(\frac{2}{3}A{B^2}\) |
| Answer» C. \(\frac{1}{2}A{B^2}\) | |
| 319. |
If sin x + a cos x = b, then what is the expression for |a sin x - cos x| in terms of a and b? |
| A. | \(\rm \sqrt{a^2-b^2-1}\) |
| B. | \(\rm \sqrt{a^2+b^2-1}\) |
| C. | \(\rm \sqrt{a^2+b^2+1}\) |
| D. | \(\rm \sqrt{a^2-b^2+1}\) |
| Answer» E. | |
| 320. |
In ΔABC measure of angle B is 90o. If tan A = 12/5, and AB = 1 cm, then what is the length (in cm) of side BC? |
| A. | 2.6 |
| B. | 2.4 |
| C. | 1.5 |
| D. | 2 |
| Answer» C. 1.5 | |
| 321. |
If x/a – (y/b)tanθ = 1 and (x/a)tanθ + y/b = 1, then the value of x2/a2 + y2/b2 is |
| A. | 2sec2θ |
| B. | sec2θ |
| C. | cos2θ |
| D. | 2cos2θ |
| Answer» E. | |
| 322. |
A 1.8 m tall boy is standing at some distance from a 12 m tall building. The angle of elevation from his eyes to the top of the building increases from 45° to 60° as he walks towards the building. Find the distance (in meters) he walked towards the building. |
| A. | \(\frac{{51\left( {\sqrt 3 + 1} \right)}}{{5\sqrt 3 }}\) |
| B. | \(\frac{{51\left( {\sqrt 3 - 1} \right)}}{{5\sqrt 3 }}\) |
| C. | \(\frac{{12\left( {\sqrt 3 - 1} \right)}}{{\sqrt 3 }}\) |
| D. | \(\frac{{12\left( {\sqrt {3 + 1} } \right)}}{{\sqrt 3 }}\) |
| Answer» C. \(\frac{{12\left( {\sqrt 3 - 1} \right)}}{{\sqrt 3 }}\) | |
| 323. |
In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord? |
| A. | \(\frac{{484}}{{21}}cm\) |
| B. | \(\frac{{242}}{{21}}\;cm\) |
| C. | \(\frac{{121}}{{21}}\;cm\) |
| D. | \(\frac{{44}}{7}\;cm\) |
| Answer» B. \(\frac{{242}}{{21}}\;cm\) | |
| 324. |
From a point exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 30° and 60°, respectively. The ratio of the height of P to that of Q is: |
| A. | 2 : 3√3 |
| B. | 1 : 2 |
| C. | 1 : 3 |
| D. | 1 : 2√3 |
| Answer» D. 1 : 2√3 | |
| 325. |
\(\frac{{\sin \theta cosec\theta \tan \theta \cot \theta }}{{{{\sin }^2}\theta + {{\cos }^2}\theta }}\) |
| A. | 0 |
| B. | 2 |
| C. | 3 |
| D. | 1 |
| Answer» E. | |
| 326. |
\(\frac{{\sqrt {\ cosec x - 1} }}{{\sqrt {\ cosec x + 1} }}\) is equal to: |
| A. | \(\tan x - \sec x\) |
| B. | \(\sec x.\tan x\) |
| C. | \(\tan x + \sec x\) |
| D. | \(\sec x - \tan x\) |
| Answer» E. | |
| 327. |
If tan θ =\(\frac{20}{21}\), then the value of \(\frac{{\sin \theta - \cos \theta }}{{\sin \theta + \cos \theta }}\) is: |
| A. | \(\frac{-1}{41}\) |
| B. | \(\frac{29}{35}\) |
| C. | \(\frac{27}{21}\) |
| D. | \(\frac{-29}{31}\) |
| Answer» B. \(\frac{29}{35}\) | |
| 328. |
If \(\frac{{\sin x + \cos x}}{{\sin x - \cos x}} = \frac{6}{5}\), then the value of \(\frac{{{{\tan }^2}x + 1}}{{{{\tan }^2}x - 1}}\) is: |
| A. | \(\frac{{35}}{{61}}\) |
| B. | \(\frac{{61}}{{60}}\) |
| C. | \(\frac{{60}}{{61}}\) |
| D. | \(\frac{{61}}{{35}}\) |
| Answer» C. \(\frac{{60}}{{61}}\) | |
| 329. |
Consider the following statements:1. If ABC is a right-angled triangle, right-angled at A and if sin \(\rm B = \frac 1 3,\) then cosec C = 3.2. If b cos B = c cos C and if the triangle ABC is not right-angled, then ABC must be isosceles.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» C. Both 1 and 2 | |
| 330. |
If cos x + cos2 x = 1, then what is sin2 x + sin4 x equal to? |
| A. | 1 |
| B. | 1.5 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1.5 | |
| 331. |
If tanθ + cotθ = 4/√3, where 0 < θ < π/2, then sinθ + cosθ is equal to |
| A. | 1 |
| B. | (√3 – 1) /2 |
| C. | (√3 + 1) /2 |
| D. | √2 |
| Answer» D. √2 | |
| 332. |
If cosec θ + 3 sec θ = 5 cosec θ, then what is the value of cot θ? |
| A. | 4/3 |
| B. | 3/4 |
| C. | 1/√3 |
| D. | √3 |
| Answer» C. 1/√3 | |
| 333. |
If Cos 3θ = Sin (θ - 34°), then the value of θ as an acute angle is: |
| A. | 56° |
| B. | 17° |
| C. | 31° |
| D. | 34° |
| Answer» D. 34° | |
| 334. |
\(\frac{{{{\left( {1 + \cos \theta } \right)}^2} + {{\sin }^2}\theta }}{{\left( {cose{c^2}\theta - 1} \right){{\sin }^2}\theta }} = ?\) |
| A. | cosθ (1 + sinθ) |
| B. | secθ(1 + sinθ) |
| C. | 2 cos θ(1 + secθ) |
| D. | 2 secθ(1 + secθ) |
| Answer» E. | |
| 335. |
If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)? |
| A. | 3√2 |
| B. | 3/√2 |
| C. | 1/√2 |
| D. | √2 |
| Answer» E. | |
| 336. |
ΔABC is right angled at B. If cot C = 24/7, then what is the value of cosec C? |
| A. | 7/25 |
| B. | 25/7 |
| C. | 24/7 |
| D. | 7/24 |
| Answer» C. 24/7 | |
| 337. |
If tanA = 15/8 and tanB = 7/24, then tan(A-B)? |
| A. | 304/297 |
| B. | 304/425 |
| C. | 416/87 |
| D. | 87/416 |
| Answer» B. 304/425 | |
| 338. |
If cosec θ = α ⇒ cosec-1α = θ and secΦ = β ⇒ sec-1β = Φ then what will be the value of cosec-1γ + sec-1γ? |
| A. | 45° |
| B. | 90° |
| C. | 60° |
| D. | 30° |
| Answer» C. 60° | |
| 339. |
If 3(cot2θ - cos2θ) = 1 - sin2θ, 0° < θ < 90°, then θ is equal to: |
| A. | 30° |
| B. | 60° |
| C. | 45° |
| D. | 15° |
| Answer» C. 45° | |
| 340. |
ΔABC is right angled at B. If m∠A = 30°. What is the length of AB (in cm), if AC = 6√2 cm? |
| A. | 3√3 |
| B. | 3√6 |
| C. | 2√3 |
| D. | 6√3 |
| Answer» C. 2√3 | |
| 341. |
If sin (x + y) = cos (x - y), then the value of cos2 x is: |
| A. | 3 |
| B. | 5 |
| C. | 1 / 4 |
| D. | 1 / 2 |
| Answer» E. | |
| 342. |
ΔPQR is right angled at Q. If cos P = 3/5, then what is the value of cos R? |
| A. | 3/4 |
| B. | 5/3 |
| C. | 4/5 |
| D. | 4/3 |
| Answer» D. 4/3 | |
| 343. |
A 22 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the ground. What is the height (in m) of the point where the ladder touches the wall from the ground? |
| A. | \(\frac{{22\sqrt 2 }}{3}\) |
| B. | 11√2 |
| C. | 11 |
| D. | 11√3 |
| Answer» E. | |
| 344. |
If tan θ = sec θ × k, 0°< θ < 90°, then k is equal to: |
| A. | cot θ |
| B. | tan θ |
| C. | cosec θ |
| D. | sin θ |
| Answer» E. | |
| 345. |
If θ lies in the first quadrant and cos2θ – sin2θ = 1/2 then the value of tan22θ + sin23θ is: |
| A. | 7/2 |
| B. | 3 |
| C. | 4/3 |
| D. | 4 |
| Answer» E. | |
| 346. |
If \(cosA = \frac{3}{4},\) then what is the value of \(\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{3A}}{2}} \right)?\) |
| A. | 5/8 |
| B. | 5/16 |
| C. | 5/24 |
| D. | 7/32 |
| Answer» C. 5/24 | |
| 347. |
If sin θ = 1/√2 then (tan θ + cos θ) = |
| A. | 1/√2 |
| B. | 2/√2 |
| C. | 3/√2 |
| D. | (1 + √2)/√2 |
| Answer» E. | |
| 348. |
If \(\tan A = \frac{{15}}{8}\) and \(\tan B = \frac{{7}}{24}\), then cos(A + B) = ?A. \(\frac{{87}}{{425}}\)B. \(\frac{{304}}{{425}}\)C. \(\frac{{297}}{{425}}\)D. \(\frac{{416}}{{425}}\) |
| A. | A |
| B. | C |
| C. | B |
| D. | D |
| Answer» B. C | |
| 349. |
Consider the following values of x: 1) 82) -43) 1/64) \(- \frac{1}{4}\)Which of the above values of x is/are the solution(s) of the equation\({\tan ^{ - 1}}\left( {2x} \right) + {\tan ^{ - 1}}\left( {3x} \right) = \frac{\pi }{4}?{\rm{\;}}\) |
| A. | 3 only |
| B. | 2 and 3 only |
| C. | 1 and 4 only |
| D. | 4 only |
| Answer» B. 2 and 3 only | |
| 350. |
cos 57° + sin 27° = |
| A. | cos 30° |
| B. | cos 3° |
| C. | sin 3° |
| D. | None of these |
| Answer» C. sin 3° | |