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.
| 701. |
5cos20° - 4sin230° + 6cosec245° = ?A. 12B. 8C. 4D. 16 |
| A. | C |
| B. | A |
| C. | D |
| D. | B |
| Answer» D. B | |
| 702. |
If 2cos2θ + 3sin θ = 3, where 0° < θ |
| A. | 35/12 |
| B. | 29/6 |
| C. | 35/6 |
| D. | 29/3 |
| Answer» D. 29/3 | |
| 703. |
Find the value of sin 15°. |
| A. | \(\frac{{\sqrt 6 - \sqrt 2 }}{4}\) |
| B. | √3 - √2 |
| C. | \(\frac{{\sqrt 3 - \sqrt 2 }}{2}\) |
| D. | \(\frac{{\sqrt 6 + \sqrt 2 }}{4}\) |
| Answer» B. √3 - √2 | |
| 704. |
If \(x\sin \theta = y\sin \left( {\theta + \frac{{2\pi }}{3}} \right) = z\sin \left( {\theta + \frac{{4\pi }}{3}} \right)\), Then xy + yz + zx is equal to |
| A. | 1 |
| B. | \(\frac{1}{2}\) |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 705. |
If Cot θ = 21/20, then what is the value of Sec θ? |
| A. | 29/21 |
| B. | 21/29 |
| C. | 29/20 |
| D. | 20/29 |
| Answer» B. 21/29 | |
| 706. |
If cosec θ - sin θ = p3 and sec θ - cos θ = q3, then what is the value of tan θ ? |
| A. | \(\dfrac{p}{q}\) |
| B. | \(\dfrac{q}{p}\) |
| C. | pq |
| D. | p2q2 |
| Answer» C. pq | |
| 707. |
A 14 foot ladder rests against a wall. The base of the ladder is 7 feet from the wall. What angle does the ladder makes with the ground? |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» D. 90° | |
| 708. |
If secθ = 13/5, then tan θ – sin θ + cos θ is equal to∶ |
| A. | 118/65 |
| B. | 124/65 |
| C. | 121/65 |
| D. | 23/13 |
| Answer» D. 23/13 | |
| 709. |
ΔPQR is right angled at Q. If sec P = 13/5, then what is the value of sin R? |
| A. | 5/13 |
| B. | 5/12 |
| C. | 13/5 |
| D. | 13/12 |
| Answer» B. 5/12 | |
| 710. |
If θ is an acute angle and tanθ – cotθ = 0, then what is the value of tan26θ + cot100θ? |
| A. | –2 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 711. |
Find the value of.\(\frac{{\sin \theta }}{{\cos \left( {90^\circ + \theta } \right)}} + \frac{{\sin \theta }}{{\sin \left( {180^\circ + \theta } \right)}} + \frac{{\tan \left( {90^\circ + \theta } \right)}}{{\cot \theta }}\) |
| A. | 0 |
| B. | - 1 |
| C. | - 3 |
| D. | 2 |
| Answer» D. 2 | |
| 712. |
If sec4θ – sec2θ = 3 then the value of tan4θ + tan2θ is: |
| A. | 8 |
| B. | 4 |
| C. | 6 |
| D. | 3 |
| Answer» E. | |
| 713. |
Consider the following statements:1) cos θ + sec θ can never be equal to 1.5.2) sec2 θ + cosec2 θ can never be less than 4.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 | |
| 714. |
A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30° with the ground. How high on the wall does the ladder reach?A. 10 mB. 17.32 mC. 34.64 mD. 30 m |
| A. | C |
| B. | D |
| C. | B |
| D. | A |
| Answer» E. | |
| 715. |
If A and B are acute angles and sec A = 3; cot B = 4, then the value of \(\frac {{\rm cosec}^2 A + \sin^2 B}{\cot^2 A + \sec^2B}\) is: |
| A. | 2 |
| B. | \(\frac {322}{323}\) |
| C. | \(\frac {1}{261}\) |
| D. | \(\frac {25}{261}\) |
| Answer» C. \(\frac {1}{261}\) | |
| 716. |
ΔDEF is right-angled at E. If cosD = 8/17, then what is the value of sec F? |
| A. | 17/8 |
| B. | 8/17 |
| C. | 17/15 |
| D. | 15/17 |
| Answer» D. 15/17 | |
| 717. |
Choose one of the following options which is equal to: \(\frac{{1\; + \;\cos \theta }}{{\sin \theta }}\) |
| A. | \(\frac{{\sin \theta }}{{1 - \cos \theta }}\) |
| B. | \(\frac{{1\; + \;{{\sin }^2}\theta }}{{\sin \theta \cos \theta }}\) |
| C. | \(\frac{{1\; + \;2\cos \theta }}{{\sin \theta \cos \theta }}\) |
| D. | \(\frac{{1 - 2{{\sin }^2}\theta }}{{\cos \theta }}\) |
| Answer» B. \(\frac{{1\; + \;{{\sin }^2}\theta }}{{\sin \theta \cos \theta }}\) | |
| 718. |
A 18 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground? |
| A. | 9√2 |
| B. | 9√3 |
| C. | 9 |
| D. | (9√3)/2 |
| Answer» D. (9√3)/2 | |
| 719. |
If sec 4θ = cosec (θ + 20°), then θ is equal to: |
| A. | 22° |
| B. | 18° |
| C. | 20° |
| D. | 14° |
| Answer» E. | |
| 720. |
If Sec θ = 25/24, then what is the value of Sin θ? |
| A. | 24/25 |
| B. | 7/25 |
| C. | 24/7 |
| D. | 25/7 |
| Answer» C. 24/7 | |
| 721. |
If 2ycos θ = xsin θ and 2xsec θ – ycosec θ = 3, then the value of x2 + 4y2 is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 722. |
If sinx = cosx, and x is acute, the value of 2sin2x - 3cos2x is: |
| A. | 1/2 |
| B. | 1 |
| C. | -1 |
| D. | -1/2 |
| Answer» E. | |
| 723. |
If the angles of a triangle ABC are in the ratio 1 : 2 : 3, then the corresponding sides are in the ratio |
| A. | 1 : 2 : 3 |
| B. | 3 : 2 : 1 |
| C. | 1 : √3 : 2 |
| D. | 1 : √3 : √2 |
| Answer» D. 1 : √3 : √2 | |
| 724. |
In a triangle ABC, a = 4, b = 3, ∠BAC = 60°, then the education for which c is the root, is |
| A. | c2 + 3c + 7 = 0 |
| B. | c2 + 3c - 7 = 0 |
| C. | c2 - 3c + 7 = 0 |
| D. | c2 - 3c - 7 = 0 |
| Answer» E. | |
| 725. |
ΔPQR is right angled at Q. If ∠P = 60°, then find the value of (cotR + √3/2). |
| A. | 3√3/2 |
| B. | 1 + √3 |
| C. | (2√2 + 1)/2 |
| D. | (3√3 + 1)/6 |
| Answer» B. 1 + √3 | |
| 726. |
Cot θ /[(1 – sin θ) (sec θ + tan θ)] is equal to: |
| A. | sin θ |
| B. | cosec θ |
| C. | 1 |
| D. | sec θ |
| Answer» C. 1 | |
| 727. |
If \(\cot x = \dfrac{5}{12}\) , then sin x + cos x = ?A. \(\dfrac{31}{17}\)B. \(\dfrac{27}{13}\)C. \(\dfrac{13}{17}\)D. \(\dfrac{17}{13}\) |
| A. | B |
| B. | D |
| C. | C |
| D. | A |
| Answer» C. C | |
| 728. |
Consider the following:(1) \(\sqrt {\frac{{1\; - \;\cos \theta }}{{1\; + \;\cos \theta }}}\) = cosec θ – cot θ(2) \(\sqrt {\frac{{1\; + \;\cos \theta }}{{1\; - \;\cos \theta }}}\) = cosec θ + cot θWhich of the above is/are identity/identities? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 729. |
From the top of a platform 5 m high, the angle of elevation of a tower was 30°. If the platform was positioned 40√3 m away from the tower, how tall was the tower? |
| A. | 45 m |
| B. | 30√3 m |
| C. | 40 m |
| D. | 20√3 m |
| E. | 30 m |
| Answer» B. 30√3 m | |
| 730. |
Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180 / π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π / 9 results. The angle θ must be equal to |
| A. | 30° |
| B. | 45° |
| C. | 50° |
| D. | 60° |
| Answer» D. 60° | |
| 731. |
If 2 cos2x – sin2x = -0.25 and 0° ≤ x < 90°, then find the value of x. |
| A. | 30° |
| B. | 60° |
| C. | 90° |
| D. | 40° |
| Answer» C. 90° | |
| 732. |
If A greater than 0° and less than equal to 90° then find the minimum value of (4 cosec2 2A + 9 sin2 2A)? |
| A. | 6 |
| B. | -12 |
| C. | 12 |
| D. | -18 |
| Answer» D. -18 | |
| 733. |
A moving boat is observed from the top of a cliff of 150 m height. The angle of depression of the boat changes from 60° to 45° in 2 minutes, what is the speed of the boat in metres per hour? |
| A. | \(\frac{{4500}}{{\sqrt 3 }}\) |
| B. | \(\frac{{4500\left( {\sqrt 3 - 1} \right)}}{{\sqrt 3 }}\) |
| C. | 4500√3 |
| D. | \(\frac{{4500\left( {\sqrt 3 + 1} \right)}}{{\sqrt 3 }}\) |
| Answer» C. 4500√3 | |
| 734. |
If cos x = -1/2 and π < x < 3π/2, then the value of 2 tan2x + 3 cosec2x is: |
| A. | 4 |
| B. | 16 |
| C. | 8 |
| D. | 10 |
| Answer» E. | |
| 735. |
If sin 60° + cos 45° = x, then the value of x is |
| A. | 1/√2 |
| B. | (√3 + √2)/2 |
| C. | √2 - 1 |
| D. | √3 |
| Answer» C. √2 - 1 | |
| 736. |
If \(\sin A = \dfrac{4}{5}\) and \(\sin B = \dfrac{5}{13}\), then Sin (A + B) = ?A. \(\dfrac{63}{65}\)B. \(\dfrac{16}{65}\)C. \(\dfrac{33}{65}\)D. \(\dfrac{56}{65}\) |
| A. | A |
| B. | B |
| C. | C |
| D. | D |
| Answer» B. B | |
| 737. |
If cos θ + sin θ = m, sec θ + cosec θ = n, what is m/n?A. 1B. sin θ cos θC. sec θ cosec θD. cot θ tan θ |
| A. | B |
| B. | A |
| C. | C |
| D. | D |
| Answer» B. A | |
| 738. |
If the data given to construct a triangle ABC are a = 5, b = 7, \(\sin A = \frac{3}{4}\), then it is possible to construct |
| A. | only one triangle |
| B. | two triangle |
| C. | infinitely many triangle |
| D. | no triangle |
| Answer» E. | |
| 739. |
In ∆UVW measure of angle V is 90°. If Cosec U = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW? |
| A. | 6.5 |
| B. | 6 |
| C. | 4 |
| D. | 5.6 |
| Answer» C. 4 | |
| 740. |
If cos x = -1/2 and π < x < 3π/2, then the value of 2tan2x – 3cosec2x is: |
| A. | 2 |
| B. | 10 |
| C. | 4 |
| D. | 8 |
| Answer» B. 10 | |
| 741. |
If A = 30°, then find the value of cos2 A + cos2 (60° + A) + cos2 (60° – A). |
| A. | -3/2 |
| B. | 1 |
| C. | 3/2 |
| D. | √3/2 |
| Answer» D. √3/2 | |
| 742. |
From the top of a 12 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is θ, such that tan θ = 3/4. What is the height of the tower (√3 = 1.73)? |
| A. | 36.22 m |
| B. | 41.41 m |
| C. | 37.95 m |
| D. | 39.68 m |
| Answer» E. | |
| 743. |
In ΔABC measure of angle B is 90°. If cot A = 7/24, and AB = 1.4 cm, then what is the length (in cm) of side AC? |
| A. | 5 |
| B. | 4.8 |
| C. | 4 |
| D. | 5.6 |
| Answer» B. 4.8 | |
| 744. |
If \(\sec^2 x - 3 \sec x + 2 = 0\), then the value of \(x(0 < x < 90^\circ)\)is: |
| A. | 30° |
| B. | 15° |
| C. | 60° |
| D. | 45° |
| Answer» D. 45° | |
| 745. |
A rectangle is 48 cm long and 14 cm wide. If the diagonal makes an angle θ with the longer side, then what is (sec θ + cosec θ) equal to? |
| A. | \(\frac{{775}}{{168}}\) |
| B. | \(\frac{{725}}{{168}}\) |
| C. | \(\frac{{375}}{{84}}\) |
| D. | \(\frac{{325}}{{84}}\) |
| Answer» B. \(\frac{{725}}{{168}}\) | |
| 746. |
If angle C of a triangle ABC is a right angle, then what is tan A + tan B equal to? |
| A. | \(\frac{{{a}^{2}}-{{b}^{2}}}{ab}\) |
| B. | \(\frac{{{a}^{2}}}{bc}\) |
| C. | \(\frac{{{b}^{2}}}{ca}\) |
| D. | \(\frac{{{c}^{2}}}{ab}\) |
| Answer» E. | |
| 747. |
If cosec ( - 4π/3) = x, then the value of x is? |
| A. | √2 |
| B. | 2/√3 |
| C. | √3 |
| D. | 1/√3 |
| Answer» C. √3 | |
| 748. |
cosec (90° - θ) = ? |
| A. | tan θ |
| B. | cot θ |
| C. | sec θ |
| D. | cos θ |
| Answer» D. cos θ | |
| 749. |
From the top of a cliff 100-metre high, the angles of depression of the top and bottom of a tower are 45° and 60° respectively. The height of the tower is |
| A. | \(\frac{{100}}{3}\left( {3 - \sqrt 3 } \right)\;{\rm{metre}}\) |
| B. | \(\frac{{100}}{3}\left( {\sqrt 3 - 1} \right)\;{\rm{metre}}\) |
| C. | \(\frac{{100}}{3}\left( {2\sqrt 3 - 1} \right){\rm{metre}}\) |
| D. | \(\frac{{100}}{3}\left( {\sqrt 3 - \sqrt 2 } \right){\rm{metre}}\) |
| Answer» B. \(\frac{{100}}{3}\left( {\sqrt 3 - 1} \right)\;{\rm{metre}}\) | |
| 750. |
\(\frac{{\left( {2\sin A} \right)\left( {1 + \sin A} \right)}}{{1 + \sin A + \cos A}}\) is equal to∶ |
| A. | 1 + sin A cos A |
| B. | 1 + sin A - cos A |
| C. | 1 - sin A cos A |
| D. | 1 + cos A - sin A |
| Answer» C. 1 - sin A cos A | |