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.
| 901. |
If p = sec θ - tan θ and q = cosec θ + cot θ, then what is p + q(p - 1) equal to? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» B. 0 | |
| 902. |
If a SinA + b cosA = c, then a cosA - b sinA is equal to: |
| A. | \(\sqrt {{a^2} + {b^2} + {c^2}}\) |
| B. | \(\sqrt {{a^2} - {b^2} + {c^2}}\) |
| C. | \(\sqrt {{a^2} + {b^2} - {c^2}}\) |
| D. | \(\sqrt {{a^2} - {b^2} - {c^2}}\) |
| Answer» D. \(\sqrt {{a^2} - {b^2} - {c^2}}\) | |
| 903. |
\(\left( {\frac{1}{{1{\rm{\;}} + {\rm{\;}}{{\sin }^2}{\rm{\theta }}}}{\rm{}} + {\rm{}}\frac{1}{{1{\rm{\;}} + {\rm{\;\;cose}}{{\rm{c}}^2}{\rm{\theta }}}}} \right){\rm{}} = {\rm{}}?\) |
| A. | 2 |
| B. | 1 |
| C. | cosec2 θ |
| D. | sin2 θ |
| Answer» C. cosec2 θ | |
| 904. |
For 0° < θ < 90°, if\(\frac{{sec\theta \left( {1 - sin\theta } \right)\left( {sec\theta \; + \;tan\theta } \right)}}{{{{\left( {sec\theta - tan\theta } \right)}^2}}} = \frac{{1\; + \;k}}{{1 - k}}\;\)then k is equal to: |
| A. | sin θ |
| B. | sec θ |
| C. | cos θ |
| D. | cosec θ |
| Answer» B. sec θ | |
| 905. |
ΔDEF is right angled at E. If cosec D = 5/4, then what is the value of cosec F? |
| A. | 5/3 |
| B. | 3/4 |
| C. | 4/5 |
| D. | 4/3 |
| Answer» B. 3/4 | |
| 906. |
\(\frac{4}{3}{\tan ^2}60^\circ + 3{\cos ^2}30^\circ - 2{\sec ^2}30^\circ - \frac{3}{4}{\cot ^2}60^\circ \) is equal to∶ |
| A. | \(\frac{8}{3}\) |
| B. | \(\frac{5}{4}\) |
| C. | \(\frac{{10}}{3}\) |
| D. | \(\frac{7}{3}\) |
| Answer» D. \(\frac{7}{3}\) | |
| 907. |
In ΔUVW measure of angle V is 90°. If tan U = 12/5, and UV = 10 cm, then what is the length (in cm) of side VW? |
| A. | 26 |
| B. | 24 |
| C. | 25 |
| D. | 5 |
| Answer» C. 25 | |
| 908. |
If 4 – 2sin2 θ – 5cos θ = 0, 0° |
| A. | \(\dfrac{1-2\sqrt{3}}{2}\) |
| B. | \(\dfrac{2-\sqrt{3}}{2}\) |
| C. | \(\dfrac{1+2\sqrt{3}}{2}\) |
| D. | \(\dfrac{2+\sqrt{3}}{2}\) |
| Answer» D. \(\dfrac{2+\sqrt{3}}{2}\) | |
| 909. |
If tan2A + cot2A + 2 = x, then the value of x is |
| A. | tan2Acosec2A |
| B. | secAcosecA |
| C. | sec2Acosec2A |
| D. | tanAcosecA |
| Answer» D. tanAcosecA | |
| 910. |
ΔPQR is right angled at Q. If m∠R = 30°, then find the value of (cosP - 1/3). |
| A. | 1/6 |
| B. | (2√2-1) /√2 |
| C. | -1/√3 |
| D. | (√3-4) /2√3 |
| Answer» B. (2√2-1) /√2 | |
| 911. |
A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge form the balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge? |
| A. | 122 sin 48° m |
| B. | 122 tan 42° m |
| C. | 122 cos 48° m |
| D. | 122 tan 48° m |
| Answer» C. 122 cos 48° m | |
| 912. |
If \(\frac{{sec\theta + tan\theta }}{{sec\theta - tan\theta }} = 5\) and θ is an acute angle, then the value of \(\frac{{3{{\cos }^2}\theta + 1}}{{3{{\cos }^2}\theta - 1}}\) is: |
| A. | 4 |
| B. | 3 |
| C. | 1 |
| D. | 2 |
| Answer» B. 3 | |
| 913. |
If sin θ = 4 cos θ, then what is the value of sin θ cos θ? |
| A. | 4/17 |
| B. | 2/9 |
| C. | 3/4 |
| D. | 3/10 |
| Answer» B. 2/9 | |
| 914. |
ΔDEF is right angled at E. If m∠D = 30°, then find the value of (cosF + √3). |
| A. | 7/2√3 |
| B. | (1 + 2√3)/2 |
| C. | 4/√3 |
| D. | (√3 + 4)/2 |
| Answer» C. 4/√3 | |
| 915. |
Find the value of \(\sqrt {{{\cot }^2}\theta - {{\cos }^2}\theta } .\) |
| A. | cos θ cosec θ |
| B. | 1 |
| C. | cot θ cosec θ |
| D. | cot θ cos θ |
| Answer» E. | |
| 916. |
If cosec \(A = \frac{25}{7}\), then what is the value of Tan A? |
| A. | \(\frac{7}{25}\) |
| B. | \(\frac{7}{24}\) |
| C. | \(\frac{25}{24}\) |
| D. | \(\frac{24}{25}\) |
| Answer» C. \(\frac{25}{24}\) | |
| 917. |
Maximum and minimum value of 5 sin X +3 cos X respectively are |
| A. | -8 and +8 |
| B. | 2 and 8 |
| C. | \(-\sqrt{34} \ and \ \sqrt{34}\) |
| D. | None of the above |
| Answer» E. | |
| 918. |
If sin3x = cos(3x – 45°), 0° < 3x < 90°, then x is equal to: |
| A. | 27.5° |
| B. | 45° |
| C. | 35° |
| D. | 22.5° |
| Answer» E. | |
| 919. |
From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevation of the top of the tower are 30°, 45° and 60° respectively. If BC = 60 m, then AB is: |
| A. | \(\rm15\sqrt{3}\) m |
| B. | \(\rm30\sqrt{3}\) m |
| C. | \(\rm45\sqrt{3}\) m |
| D. | \(\rm60\sqrt{3}\) m |
| Answer» E. | |
| 920. |
If sin θ = cos(50° + θ), then θ is equal to: |
| A. | 30° |
| B. | 20° |
| C. | 35° |
| D. | 25° |
| Answer» C. 35° | |
| 921. |
If \(\theta + \phi = \frac{2}{3}\pi \) and \(\cos \theta = \frac{{\sqrt 3 }}{2},\) then what is the value of sin ϕ? |
| A. | 0 |
| B. | 1/2 |
| C. | 1/√2 |
| D. | 1 |
| Answer» E. | |
| 922. |
If 3 - 2sin2θ - 3cosθ = 0, 0° < θ < 90°, then find the value of (2cosecθ + tanθ) |
| A. | 7√3 |
| B. | 5√3 |
| C. | 5√3/3 |
| D. | 7√3/3 |
| Answer» E. | |
| 923. |
Find the value of sin 75°. |
| A. | \(\frac{\sqrt{3~}+~1}{2}\) |
| B. | \(\frac{\sqrt{6}~+~\sqrt{2}}{4}\) |
| C. | \(\frac{\sqrt{6~}~-~\sqrt{2}}{4}\) |
| D. | \(\frac{\sqrt{3}~-~1}{2\sqrt{2}}\) |
| Answer» C. \(\frac{\sqrt{6~}~-~\sqrt{2}}{4}\) | |
| 924. |
If \(X\sin \theta = \frac{{5\sqrt 3 }}{2}\) and \(X\cos \theta = \frac{5}{2}\) then what is the value of X? |
| A. | √3 |
| B. | 1/2 |
| C. | √3/2 |
| D. | 5 |
| Answer» E. | |
| 925. |
If \(\sec {\rm{\theta }} - {\rm{cosec\;\theta }} = \frac{4}{3}\), then what is (sin θ – cos θ) equal to? |
| A. | -2 only |
| B. | \(\frac{1}{2}\) only |
| C. | Both -2 and \(\frac{1}{2}\) |
| D. | Neither \(\frac{1}{2}\) nor -2 |
| Answer» C. Both -2 and \(\frac{1}{2}\) | |
| 926. |
If sec θ + cosec θ = √2 sec(90 - θ) then what is the value of cot θ? |
| A. | √2 |
| B. | 2 |
| C. | √2 - 1 |
| D. | √2 + 1 |
| Answer» E. | |
| 927. |
A harbour lies in a direction 60° South of West from a fort and at a distance 30 km from it, a ship sets out from the harbour at noon and sails due East at 10 km an hour. The time at which the ship will be 70 km from the fort is |
| A. | 7 PM |
| B. | 8 PM |
| C. | 5 PM |
| D. | 10 PM |
| Answer» C. 5 PM | |
| 928. |
\(\frac{{2 + {{\tan }^2}\theta + {{\cot }^2}\theta }}{{\sec \theta \;cosec\;\theta }}\) is equal to: |
| A. | sec θ cosec θ |
| B. | cos θ sin θ |
| C. | tan θ |
| D. | cot θ |
| Answer» B. cos θ sin θ | |
| 929. |
If Cos2θ – Sin θ = 1/4, then what is the value of sin θ? |
| A. | -1 |
| B. | 1/2 |
| C. | 1 |
| D. | 3/2 |
| Answer» C. 1 | |
| 930. |
If sin \({\rm{x}} = \frac{1}{{\sqrt 5 }},\) sin \({\rm{y}} = \frac{1}{{\sqrt {10} }}\), where \(0 < {\rm{x}} < \frac{{\rm{\pi }}}{2},{\rm{\;}}0 < {\rm{y}} < \frac{{\rm{\pi }}}{2},\) then what is (x + y) equal to? |
| A. | π |
| B. | π/2 |
| C. | π/4 |
| D. | 0 |
| Answer» D. 0 | |
| 931. |
If cos θ + sec θ = k, then what is the value of sin2θ - tan2θ ? |
| A. | 4 - k |
| B. | 4 - k2 |
| C. | k2 - 4 |
| D. | k2 + 2 |
| Answer» C. k2 - 4 | |
| 932. |
If \(\frac{{(\sin \;\theta - {\rm{cosec}} \ \theta )\;(\cos \theta - \sec \theta )}}{{{{\tan }^2}\;\theta - {{\sin }^2}\;\theta }} = \;{r^3}\), then r = ? |
| A. | cosec θ sec θ |
| B. | cot θ |
| C. | tan θ |
| D. | sin θ cos θ |
| Answer» C. tan θ | |
| 933. |
If \(\cos x=\frac{-\sqrt{3}}{2}~and~\pi then the value of \(2{{\cot }^{2}}x+3cose{{c}^{2}}x\) is: |
| A. | 16 |
| B. | 8 |
| C. | 14 |
| D. | 18 |
| Answer» E. | |
| 934. |
Let t = 2x + 3y be the objective function for all LPP and the corner points of the bounded feasible region are (6, 8), (6, 0), (0, 2), (0, 5). The minimum value of t occurs at: |
| A. | (0, 2) only |
| B. | (3, 0) only |
| C. | The midpoint of the line segment joining (0, 2) and (0, 3) |
| D. | Any point on the line segment joining (0, 2) and (0, 3) |
| Answer» B. (3, 0) only | |
| 935. |
If sinθ + cosθ = √7/2, then what is sinθ – cosθ equal to? |
| A. | 0 |
| B. | 1/2 |
| C. | 1 |
| D. | √2 |
| Answer» C. 1 | |
| 936. |
Fill in the blanks: sinA = ________ .cos A |
| A. | sin A |
| B. | tan A |
| C. | cot A |
| D. | cos A |
| Answer» C. cot A | |
| 937. |
If sinh x = 9, then find the value of x |
| A. | loge(9 + √10) |
| B. | 3 + √10 |
| C. | loge9 |
| D. | loge(9 + √82) |
| Answer» E. | |
| 938. |
Find (1 – cos2 θ)(cot2θ + 1) - 1. |
| A. | 2 |
| B. | sec2 θ |
| C. | -2 |
| D. | 0 |
| Answer» E. | |
| 939. |
If Cot \(x = \frac{5}{12}\), then Sec x + Cosec x = ? |
| A. | 216/60 |
| B. | 221/60 |
| C. | 313/156 |
| D. | 209/60 |
| Answer» C. 313/156 | |
| 940. |
If \(\cos \theta = \dfrac{4}{5}, \sec \theta + \tan \theta = ?\) |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | 4 |
| Answer» B. 1 | |
| 941. |
If cot A = 12/5, then (sin A + cos A) × cosec A is: |
| A. | 12/5 |
| B. | 17/5 |
| C. | 11/5 |
| D. | 2 |
| Answer» C. 11/5 | |
| 942. |
In a right-angle triangle, right-angled at A, the angle formed at B is 450, if the length of side AB is 3 cm, then what is the length of the side BC? |
| A. | 3√2 cm |
| B. | 2 cm |
| C. | 3 cm |
| D. | 1.5 cm |
| Answer» B. 2 cm | |
| 943. |
In a right-angled triangle, right angled at A, the angle formed B is 45o. If the length of side AB is 5m, then what is the length of the side AC? |
| A. | 2.5 m |
| B. | 3 m |
| C. | 5 m |
| D. | 5.5 m |
| Answer» D. 5.5 m | |
| 944. |
In a triangle ABC, if cos A = cos B × cos C, What is the value of tan A- tan B - tan C? |
| A. | - 1 |
| B. | 0 |
| C. | 1+ tan A – tan B – tan C . |
| D. | tan A tan B tan C - 1 |
| Answer» C. 1+ tan A – tan B – tan C . | |
| 945. |
If tan 60o = √3, then the value of sec 60o is |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 946. |
If \(\sin x = \frac{3}{5}\), 0 ≤ x ≤ 90º, then the value of \(\cot x.\sec x\) is: |
| A. | \(\frac{5}{3}\) |
| B. | \(\frac{3}{5}\) |
| C. | \(\frac{4}{5}\) |
| D. | \(\frac{3}{4}\) |
| Answer» B. \(\frac{3}{5}\) | |
| 947. |
ΔLMN is right angled at M. If ∠N = 60°, then tanL =______. |
| A. | 1/2 |
| B. | 1/√3 |
| C. | 1/√2 |
| D. | 2 |
| Answer» C. 1/√2 | |
| 948. |
If (x sinθ) = (y cosθ) = (2z tanθ) / (1 - tan2θ), then what is 4z2 (x2 + y2) equal to? |
| A. | (x2 + y2)3 |
| B. | (x2 - y2)2 |
| C. | (x2 - y2)3 |
| D. | (x2 + y2)2 |
| Answer» C. (x2 - y2)3 | |
| 949. |
Consider the following:1. \({\sin ^{ - 1}}\frac{4}{5} + {\sin ^{ - 1}}\frac{3}{5} = \frac{\pi }{2}\)2. \({\tan ^{ - 1}}\sqrt 3 + {\tan ^{ - 1}}1 = - {\tan ^{ - 1}}\left( {2 + \sqrt 3 } \right)\)Which of the 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 | |
| 950. |
If 7 sin2 θ + 3 cos2 θ = 4, 0° < θ < 90°, then the value of (tan2 2θ + cosec2 2θ) is: |
| A. | 13/4 |
| B. | 13/3 |
| C. | 7 |
| D. | 15/4 |
| Answer» C. 7 | |