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.
| 851. |
Find the value of sin(60 + θ) - cos(30 - θ). |
| A. | 0 |
| B. | 1 |
| C. | \(\frac{1}{2}\) |
| D. | -1 |
| Answer» B. 1 | |
| 852. |
In triangle ABC, if \(\frac{{{{\sin }^2}A + {{\sin }^2}B + {{\sin }^2}C}}{{{{\cos }^2}A + {{\cos }^2}B + {{\cos }^2}C}} = 2\) then the triangle is |
| A. | right-angled |
| B. | equilateral |
| C. | isosceles |
| D. | obtuse-angled |
| Answer» B. equilateral | |
| 853. |
∆DEF is right angled at E. If m∠F = 60°, then find the value of (cotD - 2/√3). |
| A. | 1-√2 |
| B. | 1/√3 |
| C. | (2-√3)/2√3 |
| D. | (2-2√3)/√3 |
| Answer» C. (2-√3)/2√3 | |
| 854. |
Evaluate: (sinθ/cosθ) × (cotθ/cosecθ) |
| A. | cosθ |
| B. | sinθ |
| C. | tanθ |
| D. | secθ |
| Answer» C. tanθ | |
| 855. |
If A + B = 45°, then the value of 2(1 + tan A) (1 + tan B) is: |
| A. | 4 |
| B. | 1 |
| C. | 0 |
| D. | 2 |
| Answer» B. 1 | |
| 856. |
In ∆XYZ measure of angle Y is 90°. If sinX = 4/5, and XY = 6cm, then what is the length (in cm) of side YZ? |
| A. | 10 |
| B. | 5 |
| C. | 8 |
| D. | 4 |
| Answer» D. 4 | |
| 857. |
If sin θ + cos θ = √2, then what is sin6 θ + cos6 θ + 6 sin2 θ cos2 θ equal to? |
| A. | \(\frac{1}{{4}}\) |
| B. | \(\frac{3}{{4}}\) |
| C. | 1 |
| D. | \(\frac{7}{{4}}\) |
| Answer» E. | |
| 858. |
Mohit is standing at some distance from a 60 meters tall building. Mohit is 1.8 meters tall. When Mohit walks towards the building, then the angle of elevation from his head becomes 60° from 45°. How much distance (in metres) Mohit covered towards the building? |
| A. | 18.6 (4 - √3) |
| B. | 58.2 - 24.6√3 |
| C. | 19.4 (√3 + 1) |
| D. | 19.4 (3 - √3) |
| Answer» E. | |
| 859. |
If cos2 θ – sin2 θ = tan2 ϕ, then which of the following is true? |
| A. | cos θ cos ϕ = 1 |
| B. | cos θ cos ϕ = √2 |
| C. | cos2 ϕ – sin2 ϕ = cot2 θ |
| D. | cos2 ϕ – sin2 ϕ = tan2 θ |
| Answer» E. | |
| 860. |
If sinθ = 15/17, then cot θ = ?A. 8/17B. 15/8C. 8/15D. 17/8 |
| A. | C |
| B. | B |
| C. | D |
| D. | A |
| Answer» B. B | |
| 861. |
If \(\sin \theta = - \frac{1}{2}\) and \(\tan \theta = \frac{1}{{\sqrt 3 }}\), then in which quadrant does θ lie? |
| A. | First |
| B. | Second |
| C. | Third |
| D. | Fourth |
| Answer» D. Fourth | |
| 862. |
If 3cosθ + 4sinθ = 5, then find the value of 4cosθ – 3sinθ. |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | 3 |
| Answer» D. 3 | |
| 863. |
\(\left( {\frac{{2\tan 30^\circ }}{{1 - {{\tan }^2}30^\circ }}} \right){\rm{}} = {\rm{}}?\) |
| A. | √3 |
| B. | 1/3 |
| C. | 1/√3 |
| D. | 3 |
| Answer» B. 1/3 | |
| 864. |
In a ΔABC, right angled at B, AB = 7 cm and (AC – BC) = 1 cm. The value of (sec C + cot A) is∶ |
| A. | 3/4 |
| B. | 4/3 |
| C. | 19/24 |
| D. | 1 |
| Answer» C. 19/24 | |
| 865. |
If tan A + cot A = 2, then find the value of tan2 A + cot2 A.A. 4B. 2C. 1D. 1/2 |
| A. | C |
| B. | B |
| C. | D |
| D. | A |
| Answer» C. D | |
| 866. |
If \(\tan X = \frac{m}{n}\) and 0° ≤ X ≤ 90°, then the value of (sin X + cos X) is: |
| A. | \(\frac{1}{{\sqrt {{m^2} + {n^2}} }}\) |
| B. | \(\sqrt {{m^2} - \;{n^2}} \) |
| C. | \(\frac{1}{{\sqrt {{m^2}\; - \;{n^2}} }}\) |
| D. | \(\frac{{m + n}}{{\sqrt {{m^2}\; + {n^2}\;} }}\) |
| Answer» E. | |
| 867. |
PQR is a triangle in which PR = QR. Side PR is extended to S, such that QR = RS. If ∠QPR = 40°, then what is the value (in degrees) of ∠QSR? |
| A. | 45 |
| B. | 50 |
| C. | 55 |
| D. | 41 |
| Answer» C. 55 | |
| 868. |
If tan (α + β) = 2 and tan (α - β) = 1, then tan (2α) is equal to |
| A. | -3 |
| B. | -2 |
| C. | \(- \frac{1}{3}\) |
| D. | 1 |
| Answer» B. -2 | |
| 869. |
ΔABC is right angled at B. If ∠A = 60°, then what is the value of 1/√3 Cosec C? |
| A. | 2/√3 |
| B. | 2/3 |
| C. | √2/√3 |
| D. | √2/3 |
| Answer» B. 2/3 | |
| 870. |
If tanθ + cotθ = 2 and θ is acute, then the value of tan100θ + cot100θ is equal to: |
| A. | 0 |
| B. | √3 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 871. |
If sinθ + cosθ = (1 + √3)/2 where 0 < θ < π/2, then what is tanθ + cotθ equal to? |
| A. | √3/4 |
| B. | 1/√3 |
| C. | √3 |
| D. | 4/√3 |
| Answer» E. | |
| 872. |
From the top of a house A in a street, the angles of elevation and depression of the top and foot of another house B on the opposite side of the street are 60° and 45°, respectively. If the height of house A is 36m, then what is the height of house B?(Your answer should be nearest to an integer.) |
| A. | 93 m |
| B. | 94 m |
| C. | 91 m |
| D. | 98 m |
| Answer» E. | |
| 873. |
Let sin (A + B) = √3/2 and cos B = √3/2, where A, B are acute angles. What is tan (2A – B) equal to? |
| A. | 1/2 |
| B. | √3 |
| C. | 1/√3 |
| D. | 1 |
| Answer» D. 1 | |
| 874. |
If \(\frac{1}{{sin\theta + cosec\theta }} = \frac{1}{2}\), then what is the value of sin100θ + cosec100θ? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 875. |
If A + B + C = 180° then what is sin 2A – sin 2B – sin 2C equal to? |
| A. | -4 sin A sin B sin C |
| B. | -4 cos A sin B cos C |
| C. | -4 cos A cos B sin C |
| D. | -4 sin A cos B cos C |
| Answer» E. | |
| 876. |
A boy is standing near a pole which is 2.7 m high and the angle of elevation is 30°. The distance of the boy from the pole is (√3 = 1.73): |
| A. | 4.68 m |
| B. | 4.63 m |
| C. | 4.53 m |
| D. | 4.42 m |
| Answer» B. 4.63 m | |
| 877. |
Find the value of sin 60°cos 30° + cos 60° sin 30°. |
| A. | 1/2 |
| B. | 3/4 |
| C. | 1/4 |
| D. | 1 |
| Answer» E. | |
| 878. |
If \(\frac {\sec θ + \tan θ }{\sec θ - \tan θ } = 2 \frac {51}{79},\) then the value of sin θ is equal to: |
| A. | \(\frac {35}{72}\) |
| B. | \(\frac {91}{144}\) |
| C. | \(\frac {65}{144}\) |
| D. | \(\frac {39}{72}\) |
| Answer» D. \(\frac {39}{72}\) | |
| 879. |
If cot 60° + cosec 60° = x, then the value of x is |
| A. | (1 - 2√2)/√2 |
| B. | (√3 - 4)/2√3 |
| C. | 1 |
| D. | √3 |
| Answer» E. | |
| 880. |
If the value of sec B + tan B = r, then the value of sec B - tan B is equal to: |
| A. | 0 |
| B. | -r |
| C. | \(\frac{1}{r}\) |
| D. | r2 |
| Answer» D. r2 | |
| 881. |
If cosec 4θ = sec (60° – 2θ), then θ is equal to: |
| A. | 18° |
| B. | 20° |
| C. | 25° |
| D. | 15° |
| Answer» E. | |
| 882. |
From the top of a pole house A in a street, the angles of elevation and depression of the top and foot of house B on the opposite side of the street are 60° and 30°, respectively. If the height of pole house A is 21m, then what is the height (in m) of house B? (Correct to one decimal place) |
| A. | 57 |
| B. | 67 |
| C. | 84 |
| D. | 80 |
| Answer» D. 80 | |
| 883. |
If xcos A - ysinA = 1 and xsinA + ycosA = 4, then the value of 17x2 + 17y2 is: |
| A. | 7 |
| B. | 0 |
| C. | 49 |
| D. | 289 |
| Answer» E. | |
| 884. |
If A and B are supplementary angles, then find the value of \(\frac{{\tan A + \tan B}}{{1 - \tan A\tan B}}\) |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | 1/2 |
| Answer» B. -1 | |
| 885. |
If 2 cosθ = √3, cosθ x tanθ = ? |
| A. | 1 |
| B. | √3/3 |
| C. | √3/2 |
| D. | 1/2 |
| Answer» E. | |
| 886. |
ΔDEF is right angled at E. If ∠F = 45°, then what is the value of Sin F x Tan F? |
| A. | √2 |
| B. | 1/√3 |
| C. | 1/√2 |
| D. | 2/√3 |
| Answer» D. 2/√3 | |
| 887. |
If 3 sin θ = 4 cos θ, then tan2 θ + sin θ - cos θ is equal to∶ |
| A. | 2 |
| B. | 17/9 |
| C. | 89/45 |
| D. | 88/45 |
| Answer» D. 88/45 | |
| 888. |
If tan θ = 1/√5, find the value of cosec2θ – sec2θ. |
| A. | 12/5 |
| B. | 1/5 |
| C. | 13/5 |
| D. | 24/5 |
| Answer» E. | |
| 889. |
If sinθ = \(\frac{4}{5}\), Find the value of sin3θ |
| A. | \(12 \over 25\) |
| B. | \(44 \over 125\) |
| C. | \(64 \over 125\) |
| D. | \(32 \over 45\) |
| Answer» C. \(64 \over 125\) | |
| 890. |
From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower? |
| A. | 720 |
| B. | 960 |
| C. | 840 |
| D. | 1030 |
| Answer» C. 840 | |
| 891. |
If (cos2θ –1)(1 + tan2θ) + 2tan2θ = 1, 0° ≤ θ 90° then θ is: |
| A. | 90° |
| B. | 60° |
| C. | 30° |
| D. | 45° |
| Answer» E. | |
| 892. |
If sec θ = 3x and tan θ = 3/x , (x ≠ 0) then the value of 9(x2 – 1/x2) is: |
| A. | 14 |
| B. | 1 |
| C. | 13 |
| D. | 12 |
| Answer» C. 13 | |
| 893. |
If cot4θ + cot2θ = 3, then cosec4θ – cosec2θ = ? |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | 3 |
| Answer» E. | |
| 894. |
If two complimentary angles are in the ratio of 4 : 5, find the greater angle. |
| A. | 40° |
| B. | 50° |
| C. | 60° |
| D. | 30° |
| Answer» C. 60° | |
| 895. |
In ΔUVW measure of angle V is 900. If sinU = 24/25, and UV = 0.7cm, then what is the length(in cm) of side VW? |
| A. | 2.5 |
| B. | 3 |
| C. | 2.4 |
| D. | 4 |
| Answer» D. 4 | |
| 896. |
If tan 4θ = cot (40° – 2θ), then θ is equal to: |
| A. | 20° |
| B. | 35° |
| C. | 25° |
| D. | 30° |
| Answer» D. 30° | |
| 897. |
If sin x + cos x = √3 cos x, then the value of cot x is: |
| A. | \(\frac{{\sqrt 3 + 1}}{2}\) |
| B. | √3 |
| C. | 1 |
| D. | \(\frac{{\sqrt 3 -1}}{2}\) |
| Answer» B. √3 | |
| 898. |
If tan A + sin A = m and tan A - sin A = n then: |
| A. | m2 + n2 = 2mn |
| B. | m2 + n2 = mn |
| C. | \(m^2 - n^2 =4 \sqrt {mn}\) |
| D. | \(m^2 - n^2 = \sqrt {mn}\) |
| Answer» D. \(m^2 - n^2 = \sqrt {mn}\) | |
| 899. |
If tanx = √2 – 1, then the value of tanx – cotx is: |
| A. | √2 – 1 |
| B. | -2 |
| C. | 1 |
| D. | 2√2 |
| Answer» C. 1 | |
| 900. |
ΔABC is right angled at B. If ∠A = 45, then find the value of (tanC + √3/2). |
| A. | 4/√3 |
| B. | (2 + √3)/2 |
| C. | (√2 + 2)/2√2 |
| D. | (2 + √3)/3 |
| Answer» C. (√2 + 2)/2√2 | |