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.
| 951. |
If sin 3x = cot 30° × sin 150°, then x is |
| A. | 20° |
| B. | 15° |
| C. | 30° |
| D. | 60° |
| Answer» B. 15° | |
| 952. |
If cos 37˚ = a/b then what is the value of cosec37˚ - cos53˚ = ? |
| A. | (b2 - a2)/ab |
| B. | a2/(b√(a2 + b2)) |
| C. | b√(a2 + b2)/a |
| D. | a2/b√(b2 - a2) |
| Answer» E. | |
| 953. |
If the elevation of the top of the tree of point E due east of the tree is 60° and a point S due west of the tree is 30° then, elevation at the midpoint of ES is: |
| A. | 90° |
| B. | 45° |
| C. | 30° |
| D. | 60° |
| Answer» E. | |
| 954. |
If tan 6θ = cot 2θ, where \(0 < 6\theta < \frac{\pi }{2}\), then what is the value of sec 4θ? |
| A. | \(\sqrt 2 \) |
| B. | 2 |
| C. | \(\frac{2}{{\sqrt 3 }}\) |
| D. | \(\frac{4}{{3}}\) |
| Answer» B. 2 | |
| 955. |
If 2 sin θ – 8 cos2 θ + 5 = 0, 0° < θ < 90°, then what is the value of (tan 2θ + cosec 2θ)? |
| A. | 3√3 |
| B. | \(\frac{{4\sqrt 3 }}{3}\) |
| C. | \(\frac{{5\sqrt 3 }}{3}\) |
| D. | 2√3 |
| Answer» D. 2√3 | |
| 956. |
If a triangle has 5, 13 and 12 units and θ is the acute angle of the triangle, then what is the value of (sin θ + cos θ)? |
| A. | 5/13 |
| B. | 7/13 |
| C. | 12/13 |
| D. | 17/13 |
| Answer» E. | |
| 957. |
If cosθ1 + cosθ2 + cosθ3 = 3 then sinθ1 + sinθ2 + sinθ3 = ? |
| A. | 1 |
| B. | 3 |
| C. | 2 |
| D. | 0 |
| Answer» E. | |
| 958. |
If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ = |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{\sqrt3}{2}\) |
| C. | \(\frac{1}{\sqrt3}\) |
| D. | \(\frac{1}{\sqrt2}\) |
| Answer» E. | |
| 959. |
Find the value of tan 10° tan 15° tan 80° tan 75°. |
| A. | 2/3 |
| B. | 1/2 |
| C. | 1 |
| D. | 1/3 |
| Answer» D. 1/3 | |
| 960. |
If cos θ = 1/√5, where 0 < θ < π/2. Then \(\frac{{2\tan \theta }}{{1 - {{\tan }^2}\theta }}\) is equal to: |
| A. | 4/3 |
| B. | -4/3 |
| C. | 1/3 |
| D. | -2/3 |
| Answer» C. 1/3 | |
| 961. |
If sinx + cosx = √2sinx, then the value of tanx is: |
| A. | √2 + 1 |
| B. | 1 |
| C. | √2 |
| D. | √2 – 1 |
| Answer» B. 1 | |
| 962. |
If \(\rm tan\:x=-\dfrac{3}{4}\) and x is in the second quadrant, then what is the value of sin x ⋅ cos x? |
| A. | \(\dfrac{6}{25}\) |
| B. | \(\dfrac{12}{25}\) |
| C. | \(-\dfrac{6}{25}\) |
| D. | \(-\dfrac{12}{25}\) |
| Answer» E. | |
| 963. |
If 0 ≤ θ ≤ 90°, and sin (2θ + 50°) = cos (4θ + 16°), then what is the value of θ (in degrees)? |
| A. | 10° |
| B. | 12° |
| C. | 8° |
| D. | 4° |
| Answer» E. | |
| 964. |
If f(x) = cos hx + sin hx, then which one of the following is correct? |
| A. | f(x) f(y) = f(x) + f(y) |
| B. | f(x) f(y) = f(xy) |
| C. | f(x) f(y) = f(x + y) |
| D. | \(f(x)f(y) = f(\frac{x}{y})\) |
| Answer» D. \(f(x)f(y) = f(\frac{x}{y})\) | |
| 965. |
A and B are standing on the same side of a wall and observe that the angles of elevation to the top of the wall are 45° and 60° respectively. If the height of the wall is 50 m, the distance between A and B is : (Use √3 = 1.73 and √2 = 1.41) |
| A. | 25.07 m |
| B. | 21. 10 m |
| C. | 17.38 m |
| D. | 14.65 m |
| Answer» C. 17.38 m | |
| 966. |
A ladder leaning against a wall makes an angle θ with the horizontal ground such that sin θ = 12/13 If the foot of the ladder is 7.5 m from the wall, then what is the height of the point where the top of the ladder touches the wall? |
| A. | 15 m |
| B. | 8 m |
| C. | 18 m |
| D. | 12 m |
| Answer» D. 12 m | |
| 967. |
On a plane area there are two vertical towers separated by 100 feet apart. The shorter tower is 40 feet tall. A pole of length 6 feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is 75 feet, then what is the height of the taller tower (approximately)? |
| A. | 85 feet |
| B. | 110 feet |
| C. | 125 feet |
| D. | 140 feet |
| Answer» B. 110 feet | |
| 968. |
From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill? |
| A. | 48√3 |
| B. | 36 |
| C. | 36√3 |
| D. | 48 |
| Answer» E. | |
| 969. |
If \(\cos θ = \dfrac{4}{5}\) and \(\cos ϕ = \dfrac{12}{13}\), with θ and ϕ both in the fourth quadrant, the value of cos(θ + ϕ) is ? |
| A. | \(-\dfrac{16}{65}\) |
| B. | \(-\dfrac{33}{65}\) |
| C. | \(\dfrac{33}{65}\) |
| D. | \(\dfrac{16}{65}\) |
| Answer» D. \(\dfrac{16}{65}\) | |
| 970. |
In right triangle ABC, 90° at C the sides are in the ratio 1 : 1 : √2.Then find the value of cos A cos B – sin A sin B |
| A. | 1 |
| B. | 0 |
| C. | 1/2 |
| D. | 1/√2 |
| Answer» C. 1/2 | |
| 971. |
Consider the following statements:1. (sec2 θ - 1) (1 - cosec2 θ) = 12. sin θ (1 + cos θ)-1 + (1 + cos θ) (sin θ)-1 = 2 cosec θWhich of the above 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 | |
| 972. |
If tan2 θ – 3sec θ + 3 = 0, 0° |
| A. | 3√3 |
| B. | 5√3/3 |
| C. | 2√3 |
| D. | 5√3/6 |
| Answer» E. | |
| 973. |
Find the value of cosh2 x – sinh2 x |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | -2 |
| Answer» C. -1 | |
| 974. |
Find the value of Cos 225° |
| A. | 0.7071 |
| B. | -0.866 |
| C. | 0.866 |
| D. | -0.7071 |
| Answer» E. | |
| 975. |
In a triangle ∠ B = 90° and ∠ A = 30° then sin2 A – cos2 A + tan2 A: |
| A. | – 3/12 |
| B. | 1/6 |
| C. | 2/6 |
| D. | – 1/6 |
| Answer» E. | |
| 976. |
If cot (– 5π/4) = X, then the value of X is |
| A. | √3 |
| B. | 1 |
| C. | – 1 |
| D. | – ½ |
| Answer» D. – ½ | |
| 977. |
If 3sin θ = 2cos2 θ, 0° < θ < 90°, then the value of (tan2 θ + sec2 θ – cosec2 θ) is∶ |
| A. | -2 |
| B. | -7/3 |
| C. | 2 |
| D. | 7/3 |
| Answer» C. 2 | |
| 978. |
In a right-angled triangle, with right angle at A being the side AB is of length 4 cm and BC is 15 cm. what is the length of side AC? |
| A. | √(15) cm |
| B. | 14 cm |
| C. | √209 cm |
| D. | 2.09 cm |
| Answer» D. 2.09 cm | |
| 979. |
If cos (x - y) \(=\frac{\sqrt 3}{2}\) and sin (x + y) \(=\frac{1}{2}\), then the value of x (0 ≤ x ≤ 90) is: |
| A. | 45° |
| B. | 30° |
| C. | 15° |
| D. | 60° |
| Answer» C. 15° | |
| 980. |
If sec θ = 8 x and tan θ = 8/x (x ≠ 0), then the value of 16 (x2 − 1/x2) is: |
| A. | 1/4 |
| B. | 1/16 |
| C. | 1/2 |
| D. | 1/3 |
| Answer» B. 1/16 | |
| 981. |
If sin (-4π/3) = x, then the value of x is |
| A. | -2 |
| B. | -2/√3 |
| C. | √3/2 |
| D. | √2 |
| Answer» D. √2 | |
| 982. |
In ΔXYZ measure of angle Y is 90o. If sec X = 17/8, and XY = 0.8 cm, then what is the length (in cm) of side XZ? |
| A. | 1.7 |
| B. | 1.5 |
| C. | 2 |
| D. | 2.5 |
| Answer» B. 1.5 | |
| 983. |
From the top of a lighthouse, 100 m high, the angle of depression of a boat is \({\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right).\) What is the distance between the boat and the lighthouse? |
| A. | 120 m |
| B. | 180 m |
| C. | 240 m |
| D. | 360 m |
| Answer» D. 360 m | |
| 984. |
If cos θ = 0.6, then tan θ = ? |
| A. | 0.8 |
| B. | 4/3 |
| C. | 1.25 |
| D. | 3/4 |
| Answer» C. 1.25 | |
| 985. |
If 0 < θ < 90°, sinθ = 3/5 and x = cotθ, then what is the value of 1 + 3x + 9x2 + 27x3 + 81x4 + 243x5? |
| A. | 941 |
| B. | 1000 |
| C. | 1220 |
| D. | 1365 |
| Answer» E. | |
| 986. |
If sec θ – tan θ = x/y, (0 < x < y) and 0°< θ < 90°, then sinθ is equal to: |
| A. | \(\frac{{{y^2} - {x^2}}}{{{x^2} + {y^2}}}\) |
| B. | \(\frac{{{x^2} + {y^2}}}{{{y^2} - {x^2}}}\) |
| C. | \(\frac{{2xy}}{{{x^2} + {y^2}}}\) |
| D. | \(\frac{{{x^2} + {y^2}}}{{2xy}}\) |
| Answer» B. \(\frac{{{x^2} + {y^2}}}{{{y^2} - {x^2}}}\) | |
| 987. |
Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30° , 45° and 60° respectively. The ratio of AB and BC is |
| A. | \(\sqrt{3} : 1\) |
| B. | \(\sqrt{3} : 2\) |
| C. | 1 : 2 |
| D. | \(2 : \sqrt{3}\) |
| Answer» B. \(\sqrt{3} : 2\) | |
| 988. |
Consider the following statements:(1) If 45° < θ < 60°, then sec2θ + cosec2θ = α2 for some real number α > 1(2) If 0° < θ < 45°, then (1 + cosθ)/(1 - cosθ) = x2 for some real number x > 2(3) If 0° < θ < 45°, then cosθ/(1 - tan θ) + sin θ/(1 - cot θ) ≥ 2What is the number of true statements? |
| A. | Zero |
| B. | One |
| C. | Two |
| D. | Thee |
| Answer» D. Thee | |
| 989. |
If a2sec2x - b2tan2x = c2 then the value of sec2x + tan2x is equal to (assume b2 ≠ a2) |
| A. | \(\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}\) |
| B. | \(\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}\) |
| C. | \(\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}\) |
| D. | \(\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}\) |
| Answer» C. \(\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}\) | |
| 990. |
If sec3x = cosec(3x - 45°), where 3x is an acute angle, then x is equal to: |
| A. | 35° |
| B. | 45° |
| C. | 22.5° |
| D. | 27.5° |
| Answer» D. 27.5° | |
| 991. |
If x = a cosθ + b sinθ and y = a sinθ – b cosθ, the value of x2 + y2 is: |
| A. | a2 – b2 |
| B. | a – b |
| C. | a2 + b2 |
| D. | a + b |
| Answer» D. a + b | |
| 992. |
In ΔABC measure of angle B is 90°. If cos A = 5/13, and AB = 10 cm, then what is the length (in cm) of side BC? |
| A. | 26 |
| B. | 24 |
| C. | 25 |
| D. | 5 |
| Answer» C. 25 | |
| 993. |
If angle is eight times its complementary angle, then the measurement of the angle is |
| A. | 80° |
| B. | 10° |
| C. | 180° |
| D. | 35° |
| Answer» B. 10° | |
| 994. |
In a right angled triangle ABC, if angle CAB = θ, base AB = a, perpendicular BC = b and hypotenuse AC = c, then secant θ = __________. |
| A. | \(\frac{a}{c}\) |
| B. | \(\frac{c}{a}\) |
| C. | \(\frac{c}{b}\) |
| D. | \(\frac{a}{b}\) |
| Answer» C. \(\frac{c}{b}\) | |
| 995. |
If x = 4 cos A + 5 sin A and y = 4 sin A - 5 cos A, then the value of x2 + y2 is: |
| A. | 25 |
| B. | 0 |
| C. | 16 |
| D. | 41 |
| Answer» E. | |
| 996. |
A spherical balloon of radius 150 cm subtends an angle of 60° at the eye of an observer. If the angle of elevation of its centre is 45°, what is the height of centre of the balloon?(Assume that eye of observer is at the ground level) |
| A. | 300√2 cm |
| B. | 150√2 cm |
| C. | 180√2 cm |
| D. | 300 cm |
| Answer» C. 180√2 cm | |
| 997. |
If 4tanθ = 3, \(\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta \; + \;3\;cos\theta }}\) is equal to∶ |
| A. | 1/3 |
| B. | 9 |
| C. | 3 |
| D. | 1/9 |
| Answer» E. | |
| 998. |
If 5 sin θ = 4, then the value of \(\frac{{sec\theta + 4\cot \theta }}{{4tan\theta - 5cos\theta }}\) is: |
| A. | 5/4 |
| B. | 3/2 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 999. |
If 5 sin x = 4, then the numerical value of \(\left( {\frac{{\tan x - \cot x}}{{\sec x - \tan x}}} \right)\left( {\frac{{{{\cos }^4}x - {{\sin }^4}x}}{{2{{\cos }^2}x - 1}}} \right)?\) |
| A. | \(\frac{3}{5}\) |
| B. | \(\frac{5}{4}\) |
| C. | \(\frac{7}{4}\) |
| D. | \(\frac{9}{5}\) |
| Answer» D. \(\frac{9}{5}\) | |
| 1000. |
If a flag-staff of 6 m height placed on the top of a tower throws shadow of 2√3 m along the ground, then what is the angle that the sun makes with the ground? |
| A. | 60° |
| B. | 45° |
| C. | 30° |
| D. | 15° |
| Answer» B. 45° | |