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.
| 501. |
If sin x = 4/5, then sec x/sin x = |
| A. | 23/12 |
| B. | 25/4 |
| C. | 4/5 |
| D. | 25/12 |
| Answer» E. | |
| 502. |
If \({\sin ^{ - 1}}\frac{{2p}}{{1 + p2}} - {\cos ^{ - 1}}\frac{{1 - {q^2}}}{{1 + {q^2}}} = {\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}}\), then what is x equal to? |
| A. | \(\frac{{p + q}}{{1 + pq}}\) |
| B. | \(\frac{{p - q}}{{1 + pq}}\) |
| C. | \(\frac{{pq}}{{1 + pq}}\) |
| D. | \(\frac{{p + q}}{{1 - pq}}\) |
| Answer» C. \(\frac{{pq}}{{1 + pq}}\) | |
| 503. |
\({{\left( \frac{\sqrt{3}+2\cos A}{1-2\sin A} \right)}^{-3}}+{{\left( \frac{1+2\sin A}{\sqrt{3}-2\cos A} \right)}^{-3}}=?\) |
| A. | 1 |
| B. | √3 |
| C. | -1 |
| D. | 0 |
| Answer» E. | |
| 504. |
Consider the following statements :1. \(co{s^2}\theta = 1 - \frac{{{p^2} + {q^2}}}{{2pq}},\) where p, q are non-zero real numbers, is possible only when p = q.2. \({\tan ^2}\theta = \frac{{4pq}}{{{{\left( {p + q} \right)}^2}}} - 1\), where p, q are non-zero real numbers, is possible only when p = q.Which of the statements given above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 505. |
ΔDEF is right angled at E. If ∠F = 30°, then find the value of (cos D – 1/√2). |
| A. | -1/2 |
| B. | (√6 – 1)/√3 |
| C. | (√2 – 2)/2√2 |
| D. | √3 – 2 |
| Answer» D. √3 – 2 | |
| 506. |
ΔABC is right angled at B. If m∠A = 60°, then find the value of (sec C + 2). |
| A. | (2 + 2√3)/√2 |
| B. | 4/3 |
| C. | (2 + 2√3)/√3 |
| D. | 4/√3 |
| Answer» D. 4/√3 | |
| 507. |
If cosx + sinx = √2cosx then the value of cot x is: |
| A. | √2 + 1 |
| B. | 1 |
| C. | √2 – 1 |
| D. | √2 |
| Answer» B. 1 | |
| 508. |
If cot52° = b, tan38° = ?A. √bB. √b/2C. – bD. b |
| A. | C |
| B. | D |
| C. | B |
| D. | A |
| Answer» C. B | |
| 509. |
ΔPQR is right angled at Q. If m∠R = 45°, then find the value of (tan P - 1/2). |
| A. | (2 - √3)/√3 |
| B. | (2√3 - √6)/2√2 |
| C. | 1/2 |
| D. | (√6 - 6)/3√3 |
| Answer» D. (√6 - 6)/3√3 | |
| 510. |
If 12cot2 θ – 31cosec θ + 32 = 0, 0° < θ < 90°, then the values of tan θ will be: |
| A. | 4/5, 5√7/7 |
| B. | 4/3, 3√7/7 |
| C. | 4/5, 4/3 |
| D. | 5/4, 4/3 |
| Answer» C. 4/5, 4/3 | |
| 511. |
On simplifying \(\frac{{{{\sin }^3}{\rm{A}} + \sin 3{\rm{\;A}}}}{{\sin {\rm{A}}}} + \frac{{{{\cos }^3}{\rm{A}} - \cos 3{\rm{\;A}}}}{{\cos {\rm{A}}}}\) we get |
| A. | sin 3 A |
| B. | cos 3 A |
| C. | sin A + cos A |
| D. | 3 |
| Answer» E. | |
| 512. |
If a pole of 6 m height caste a shadow of 2√3 m long on the ground then the sun’s angle of elevation at that instant is |
| A. | 30° |
| B. | 60° |
| C. | 45° |
| D. | 90° |
| Answer» C. 45° | |
| 513. |
In ΔABC, ∠C = 54°, the perpendicular bisector of AB at D meets BC at E. If ∠EAC = 42°, then what is the value (in degrees) of ∠ABC? |
| A. | 25 |
| B. | 42 |
| C. | 50 |
| D. | 60 |
| Answer» C. 50 | |
| 514. |
\({\left( {\frac{{1 - tan\theta }}{{1 - \cot \theta }}} \right)^2} + 1 = ?\) |
| A. | cos2 θ |
| B. | sin2 θ |
| C. | cosec2 θ |
| D. | sec2 θ |
| Answer» E. | |
| 515. |
Find x if sin x = \( - \frac{1}{2}\). |
| A. | \( \frac{{11\,\pi }}{6}\) |
| B. | \( \frac{{17\,\pi }}{6}\) |
| C. | \( \frac{{\,\pi }}{6}\) |
| D. | \( \frac{{5\,\pi }}{6}\) |
| Answer» B. \( \frac{{17\,\pi }}{6}\) | |
| 516. |
If sin α + cos α = p, then what is cos2 (2α) equal to? |
| A. | p2 |
| B. | p2 - 1 |
| C. | p2(2- p2) |
| D. | p2 + 1 |
| Answer» D. p2 + 1 | |
| 517. |
If (cosecθ - sinθ) (secθ - cosθ) (tanθ + cotθ) - tanθ = 0, 0° |
| A. | 3/4 |
| B. | 2/3 |
| C. | 5/5 |
| D. | 1 |
| Answer» B. 2/3 | |
| 518. |
If tan θ + sec θ = (x - 2)/(x + 2), then what is the value of cos θ? |
| A. | (x2 - 1)/(x2 + 1) |
| B. | (2x2 - 4)/(2x2 + 4) |
| C. | (x2 - 4)/(x2 + 4) |
| D. | (x2 - 2)/(x2 + 2) |
| Answer» D. (x2 - 2)/(x2 + 2) | |
| 519. |
If cosec θ = b/a, then \(\frac{\sqrt{3} cot \theta + 1}{tan \theta + \sqrt{3}}\) is equal to: |
| A. | \(\frac{\sqrt{b^2 - a^2}}{a}\) |
| B. | \(\frac{\sqrt{b^2 + b^2}}{b}\) |
| C. | \(\frac{\sqrt{a^2 + b^2}}{b}\) |
| D. | \(\frac{\sqrt{b^2 - a^2}}{b}\) |
| Answer» B. \(\frac{\sqrt{b^2 + b^2}}{b}\) | |
| 520. |
If A lies in the first quadrant and 6 tan A = 5, then the value of \(\frac{{8\sin A - 4\cos A}}{{\cos A + 2\sin A}}\) is |
| A. | 4 |
| B. | 1 |
| C. | 16 |
| D. | -2 |
| Answer» C. 16 | |
| 521. |
If sin 3θ = cos(20° – θ), then θ is equal to∶ |
| A. | 30 |
| B. | 25 |
| C. | 35 |
| D. | 28 |
| Answer» D. 28 | |
| 522. |
In a triangle PQR, the length of the side PQ is 4m, the angle of R is 60o and the angle at Q is 30o, what is the length of side PR? |
| A. | 4√2 m |
| B. | 4 / √3 m |
| C. | 4√3 m |
| D. | √3 / 2 m |
| Answer» C. 4√3 m | |
| 523. |
If 0 < x < π/2, then (sin x + cosec x) is |
| A. | > 2 |
| B. | < 2 |
| C. | ≥ 2 |
| D. | ≤ 2 |
| Answer» B. < 2 | |
| 524. |
If cos (A + B) = \(\frac{3}{5}\) and sin (A - B) = \(\frac{5}{13}\), where 0 ≤ A, \(B \le \frac{\pi}{4}\), then tan 2B is equal to |
| A. | \(\frac{11}{34}\) |
| B. | \(\frac{21}{56}\) |
| C. | \(\frac{33}{56}\) |
| D. | 1 |
| Answer» D. 1 | |
| 525. |
Δ DEF is right angled at E. If m∠F = 45°, then what is the value of cosec F × cot D? |
| A. | 1/√2 |
| B. | 2 |
| C. | 1/2 |
| D. | √2 |
| Answer» E. | |
| 526. |
For θ being an acute angle, it is given that, 3 (cosec2 θ + cot2 θ) = 5. Then θ is equal to: |
| A. | 0° |
| B. | 30° |
| C. | 45° |
| D. | 60° |
| Answer» E. | |
| 527. |
A 12 m high pole is tied with a rope to make it vertical to the ground. If the rope makes an angle of 30° with the ground, what is the length of the rope? |
| A. | \(6\sqrt 3 \;m\) |
| B. | \(12\sqrt 2 \;m\) |
| C. | 18 m |
| D. | 24 m |
| Answer» E. | |
| 528. |
If cot4θ + cot2θ = 2.2, then cosec4θ - cosec2θ = ? |
| A. | 1.1 |
| B. | 0 |
| C. | 2.2 |
| D. | 3.3 |
| Answer» D. 3.3 | |
| 529. |
In a triangle ABC, the length of the side AB, is 2 cm, the angle at C is 600 and the angle at B is 300, what is the length of side AC? |
| A. | √2 cm |
| B. | 2 / √3 cm |
| C. | √3 cm |
| D. | √3 / 2 cm |
| Answer» C. √3 cm | |
| 530. |
If 3 sec2 θ + tan θ = 7, 0° < θ < 90°, then the value of \(\frac{{cosec2\theta + cos\theta }}{{sin2\theta + cot\theta }}is:\) |
| A. | \(\frac{{2 + \sqrt 2 }}{4}\) |
| B. | \(\frac{{2 + 3\sqrt 2 }}{4}\) |
| C. | \(\frac{{3 + \sqrt 2 }}{2}\) |
| D. | \(\frac{{2 + \sqrt 3 }}{2}\) |
| Answer» B. \(\frac{{2 + 3\sqrt 2 }}{4}\) | |
| 531. |
If 4 cos2θ - 3 sin2θ + 2 = 0, then the value of tanθ is (where 0 ≤ θ < 90°) |
| A. | \(\sqrt{2}\) |
| B. | \(\sqrt{6}\) |
| C. | \(\dfrac{1}{\sqrt{3}}\) |
| D. | 1 |
| Answer» C. \(\dfrac{1}{\sqrt{3}}\) | |
| 532. |
If secθ + tanθ = 2 +√5 and θ is an acute angle, then the value of sin θ is: |
| A. | \(\frac{{\sqrt 5 }}{5}\) |
| B. | \(\frac{{2\sqrt 5 }}{5}\) |
| C. | \(\frac{{3}}{5}\) |
| D. | \(\frac{{1 }}{5}\) |
| Answer» C. \(\frac{{3}}{5}\) | |
| 533. |
Δ PQR is right angled at Q. If ∠R = 30°, then what is the value of Cot P? |
| A. | 1/2 |
| B. | 1/√2 |
| C. | 1/√3 |
| D. | 2 |
| Answer» D. 2 | |
| 534. |
If \(u = \log \left\lfloor {\tan \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right\rfloor\), then cosh u is |
| A. | sec θ |
| B. | sin θ |
| C. | cos θ |
| D. | None of these |
| Answer» B. sin θ | |
| 535. |
If sin θ - cos θ = \(\frac{7}{17}\), then find the value of sin θ + cos θ. |
| A. | \(\frac{23}{13}\) |
| B. | \(\frac{23}{17}\) |
| C. | \(\frac{8}{17}\) |
| D. | \(\frac{8}{13}\) |
| Answer» C. \(\frac{8}{17}\) | |
| 536. |
If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is |
| A. | 50 |
| B. | 60 |
| C. | 45 |
| D. | 42 |
| Answer» B. 60 | |
| 537. |
∆ABC is similar to ∆PQR. If ratio of perimeters of ∆ABC and ∆PQR is 1 : 2 and if PQ = 10 cm then what is the length of AB (in cm)? |
| A. | 5 |
| B. | 20 |
| C. | 25 |
| D. | 15 |
| Answer» B. 20 | |
| 538. |
Δ DEF is right angled at E. If m ∠D = 30°. What is the length (in cm) of DE, if EF = 2√3 cm? |
| A. | 3 |
| B. | 4 |
| C. | 6 |
| D. | 2 |
| Answer» D. 2 | |
| 539. |
If \(2{\cos ^2}θ - 5\cos θ + 2 = 0\), 0º |
| A. | \(\frac{{\sqrt 3 }}{3}\) |
| B. | \(\sqrt 3\) |
| C. | \(2\sqrt 3\) |
| D. | \(\frac{1}{3}\) |
| Answer» B. \(\sqrt 3\) | |
| 540. |
If tan θ = \(\frac{2}{\sqrt{11}}\), 0 |
| A. | \(\frac{11}{45}\) |
| B. | \(\frac{11}{49}\) |
| C. | \(\frac{13}{49}\) |
| D. | \(\frac{10}{49}\) |
| Answer» E. | |
| 541. |
Height of a tower is 120 metres. The angle of elevation of the top of tower from a point B is 75°. Point B is on the ground level. What is the distance (in metres) of point B from the base of tower? |
| A. | 120 (2 - √3) |
| B. | 180 (3 - √3) |
| C. | 180 (√3 - 1) |
| D. | 150 (√3 - 1) |
| Answer» B. 180 (3 - √3) | |
| 542. |
If in a triangle ∠B = 90° and ∠A = 30°, then 2sin2A – cos2A – tan2A = ? |
| A. | 1/6 |
| B. | -1/2 |
| C. | 1 |
| D. | -1/3 |
| Answer» C. 1 | |
| 543. |
If 3cos2 x – 2sin2 x = - 0.75 and 0° ≤ x ≤ 90°, then x = ? |
| A. | 60° |
| B. | 45° |
| C. | 30° |
| D. | 90° |
| Answer» B. 45° | |
| 544. |
If \(\frac{{{{\sin }^2}\phi - 3sin\;\phi + 2}}{{{{\cos }^2}\phi }} = 1,\) where 0° < ϕ < 90°, then what is the value of (cos2ϕ + sin3ϕ + cosec2ϕ)? |
| A. | \(\frac{{3 + 4\sqrt 3 }}{6}\) |
| B. | \(\frac{{2 + \sqrt 3 }}{3}\) |
| C. | \(\frac{{3 + 2\sqrt 3 }}{3}\) |
| D. | \(\frac{{9 + 4\sqrt 3 }}{6}\) |
| Answer» E. | |
| 545. |
If tan A = -3/4, then 1 – {(1 + cos A) (1 – cosA) / (1 + sinA) (1 – sinA)} + 7/16 = ? |
| A. | 5/8 |
| B. | 1 |
| C. | 0 |
| D. | 7/8 |
| Answer» E. | |
| 546. |
If \(({\cos ^2}θ - 1)(2{\sec ^2}θ ) + {\sec ^2}θ + 2{\tan ^2}θ = 2\), 0º |
| A. | 1 |
| B. | \(4\sqrt 2 \) |
| C. | \(2\sqrt 2\) |
| D. | 3 |
| Answer» E. | |
| 547. |
If \({\rm{p}} = \tan \left( { - \frac{{11{\rm{\pi }}}}{6}} \right),{\rm{\;q}} = \tan \left( {\frac{{21{\rm{\pi }}}}{4}} \right)\) and \({\rm{r}} = \cot \left( {\frac{{283{\rm{\pi }}}}{6}} \right)\), then which of the following is/are correct?1. The value of p × r is 2.2. p, q and r are in G.P.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 | |
| 548. |
Let \({\rm{a}} = \frac{{2\sin {\rm{x}}}}{{1 + \sin {\rm{x}} + \cos {\rm{x}}}}{\rm{and\;b}} = \frac{{\rm{c}}}{{1 + \sin {\rm{x}}}}\). then a = b, if c = ? |
| A. | 1 + sin x cos x |
| B. | 1 + sin x – cos x |
| C. | 1 +cos x – sin x |
| D. | 1 – sin x cos x |
| Answer» C. 1 +cos x – sin x | |
| 549. |
If \(tan \theta = \frac {4}{3}\), then \(\frac {1-sin\theta}{1+sin\theta} = \)_______ |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{9}\) |
| C. | \(\frac{1}{16}\) |
| D. | \(\frac{1}{4}\) |
| Answer» C. \(\frac{1}{16}\) | |
| 550. |
If cos θ = 24/25 then cot θ will be |
| A. | 25/24 |
| B. | 19/24 |
| C. | 24/7 |
| D. | 7/24 |
| Answer» D. 7/24 | |