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.
| 1051. |
If cosecθ – cotθ = t, then the value of cotθ is: |
| A. | (1 – t2) /2t |
| B. | (t2 + 1)/2t |
| C. | (t2 + 1)/t |
| D. | (t2 – 1)2t |
| Answer» B. (t2 + 1)/2t | |
| 1052. |
If x sin 45° = y cosec 30°, then \(\frac{x^4}{y^4}\) is equal to |
| A. | 43 |
| B. | 63 |
| C. | 23 |
| D. | 83 |
| Answer» B. 63 | |
| 1053. |
Let cos α + cos β = 2 and sin α + sin β = 0, where 0 ≤ α ≤ 90°, 0 ≤ β ≤ 90°. What is the value of cos 2α - cos 2β? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | Cannot be determined due to insufficient data |
| Answer» B. 1 | |
| 1054. |
If Cot θ = 15/8, then Cosec θ =? |
| A. | 8/17 |
| B. | 8/15 |
| C. | 15/17 |
| D. | 17/8 |
| Answer» E. | |
| 1055. |
If sin x = 4/5, then sec x + tan x = ? |
| A. | 37/20 |
| B. | 31/12 |
| C. | 3 |
| D. | 1/3 |
| Answer» D. 1/3 | |
| 1056. |
Express \({\pi\over 12}\) radians in degrees. |
| A. | -15 |
| B. | 30 |
| C. | -30 |
| D. | 15 |
| Answer» E. | |
| 1057. |
Sine rule for a triangle states that |
| A. | a/sin A = b/sin B = c/sin C |
| B. | sin A/a = sin B/b = sin C/c |
| C. | a/sin A + b/sin B + c/sin C |
| D. | 2a/sin A = 2b/sin B = 2c/sin C |
| Answer» C. a/sin A + b/sin B + c/sin C | |
| 1058. |
Considering Cosine Rule of any triangle ABC, possible measures of angle A includes |
| A. | angle A is acute |
| B. | angle A is obtuse |
| C. | angle A is right-angle |
| D. | all of above |
| Answer» E. | |
| 1059. |
In a triangle ABC, if angle A = 72° , angle B = 48° and c = 9 cm then Ĉ is |
| A. | 60° |
| B. | 63° |
| C. | 66° |
| D. | 69° |
| Answer» D. 69° | |
| 1060. |
For Cosine Rule of any triangle ABC, c² is equal to |
| A. | a² - b² + 2ab sin A |
| B. | a² + b² + 2ab cos A |
| C. | a² + b² - 2ab cos C |
| D. | c² + a² + 2ac cos C |
| Answer» D. c² + a² + 2ac cos C | |
| 1061. |
For Cosine Rule of any triangle ABC, b² is equal to |
| A. | a² - c² 4bc cos A |
| B. | a² + c² - 2ac cos B |
| C. | a² - c² + 2ab cos A |
| D. | a³ + c³ - 3ab cos A |
| Answer» C. a² - c² + 2ab cos A | |
| 1062. |
Solve for A for the given equation cos 2A = 1 – cos 2A |
| A. | 45, 125, 225, 315 degrees |
| B. | 45, 125, 225, 335 degrees |
| C. | 45, 135, 225, 315 degrees |
| D. | 45, 150, 220, 315 degrees |
| Answer» D. 45, 150, 220, 315 degrees | |
| 1063. |
Solve for x in the equation: arc tan (x + 1) + arc tan (x – 1) = arc tan (12) |
| A. | 1.20 |
| B. | 1.25 |
| C. | 1.34 |
| D. | 1.5 |
| Answer» D. 1.5 | |
| 1064. |
Solve for x in the given equation: Arc tan (2x) + arc tan (x) = π/4 |
| A. | 0.149 |
| B. | 0.281 |
| C. | 0.316 |
| D. | 0.421 |
| Answer» C. 0.316 | |
| 1065. |
Evaluate arc cot [2cos (arc sin 0.5)] |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» B. 45° | |
| 1066. |
Arc tan [2 cos (arc sin [(3^(1/2))/2]) / 2]) is equal to |
| A. | π/2 |
| B. | π/3 |
| C. | π/4 |
| D. | π/16 |
| Answer» D. π/16 | |
| 1067. |
Simplify the expression sec θ – (sec θ)sin^2θ |
| A. | sin θ |
| B. | cos θ |
| C. | cos^2θ |
| D. | sin^2θ |
| Answer» C. cos^2θ | |
| 1068. |
Simplify the equation sin^2θ(1 + cot^2θ) |
| A. | 1 |
| B. | sin^2θ |
| C. | sec^2θ |
| D. | sin^2θsec^2θ |
| Answer» B. sin^2θ | |
| 1069. |
Find the value of (sin θ + cos θ tanθ)/cos θ |
| A. | 2 sin θ |
| B. | 2 tan θ |
| C. | 2 cos θ |
| D. | 2 cot θ |
| Answer» C. 2 cos θ | |
| 1070. |
Find the value of y in the given: y = (1 + cos θ) tan θ |
| A. | sin θ |
| B. | cos θ |
| C. | sin 2θ |
| D. | cos 2θ |
| Answer» D. cos 2θ | |
| 1071. |
If tan x =1/2, tan y = 1/3, what is the value of tan (x + y)? |
| A. | 1 |
| B. | 2 |
| C. | 1/2 |
| D. | 1/6 |
| Answer» B. 2 | |
| 1072. |
If conversed sin θ= 0.134, find the value of θ |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» D. 90° | |
| 1073. |
If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.39x, find the value of x? |
| A. | 0.256 |
| B. | 0.265 |
| C. | 0.562 |
| D. | 0.625 |
| Answer» B. 0.265 | |
| 1074. |
Solve for the value of A° when sin A = 3.5 x and cos A = 5.5 x |
| A. | 32.47° |
| B. | 33.68° |
| C. | 34.12° |
| D. | 35.21° |
| Answer» B. 33.68° | |
| 1075. |
Evaluate: (2sinθcosθ-cosθ)/(1 – sin θ+ sin^2θ – cos^2θ) |
| A. | sin θ |
| B. | cos θ |
| C. | tan θ |
| D. | cot θ |
| Answer» E. | |
| 1076. |
Simplify the following: [(cos A + cos B)/(sin A – sin B)] + [(sin A + sin B)/(cos A – cos B)] |
| A. | 0 |
| B. | 1 |
| C. | sin A |
| D. | cos A |
| Answer» B. 1 | |
| 1077. |
An aero lift airplane can fly at airspeed of 300 mph. If there is a wind blowing towards the cast at 50 mph, what should be the plane’s compass heading in order for its course to be 30°? What will be |
| A. | 19.7°, 307.4 mph |
| B. | 20.1°, 309.1 mph |
| C. | 21.7°, 321.8 mph |
| D. | 22.3°, 319.2 mph |
| Answer» D. 22.3°, 319.2 mph | |
| 1078. |
A ship started sailing S 42°35’ W at the rate of 5 kph. After 2 hours, ship B started at the same port going N 46°20’ W at the rate of 7 kph. After how many hours will the second ship be exactly north |
| A. | 3.68 |
| B. | 4.03 |
| C. | 4.83 |
| D. | 5.12 |
| Answer» C. 4.83 | |
| 1079. |
Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the |
| A. | 3 and 9 |
| B. | 4 and 10 |
| C. | 5 and 11 |
| D. | 6 and 12 |
| Answer» C. 5 and 11 | |
| 1080. |
Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32° W of N and from B the bearing of C is 26° N of E. Approximate the shortest |
| A. | 364 m |
| B. | 374 m |
| C. | 384 m |
| D. | 394 m |
| Answer» C. 384 m | |
| 1081. |
A man standing on a 48.5 meter building high, has an eyesight height of 1.5m from the top of the building, took a depression reading from the top of another building and wall, which are 50° & 80° |
| A. | 35.50 |
| B. | 36.50 |
| C. | 39.49 |
| D. | 42.55 |
| Answer» D. 42.55 | |
| 1082. |
If an equivalent triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle. |
| A. | 32.10 cm |
| B. | 34.64 cm |
| C. | 36.44 cm |
| D. | 64.12 cm |
| Answer» C. 36.44 cm | |
| 1083. |
A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13° and 35° respectively. The height of the |
| A. | 29.13 m |
| B. | 30.11 m |
| C. | 32.12 m |
| D. | 33.51 m |
| Answer» E. | |
| 1084. |
A wire supporting a pole is fastened to it 20 feet from the ground and to the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole. |
| A. | 24 ft, 36.87° |
| B. | 24 ft, 53.13° |
| C. | 25 ft, 36.87° |
| D. | 25 ft, 53.13° |
| Answer» D. 25 ft, 53.13° | |
| 1085. |
A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° from the vertical directly towards the sun, determine the length of the pole. |
| A. | 42.44 m |
| B. | 46.21 m |
| C. | 48.23 m |
| D. | 54.23 m |
| Answer» E. | |
| 1086. |
A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower? |
| A. | 73.16 m |
| B. | 73.31 m |
| C. | 73.61 m |
| D. | 76.31 m |
| Answer» D. 76.31 m | |
| 1087. |
If Greenwich Mean Time (GMT) is 6 A.M, what is the time at a place located 30° East longitude? |
| A. | 4 A.M. |
| B. | 7 A.M. |
| C. | 8 A.M. |
| D. | 9 A.M. |
| Answer» D. 9 A.M. | |
| 1088. |
The sides of a triangle are 8, 15, and 17 units. If each side is doubled, how many square units will the are of the new triangle be? |
| A. | 200 |
| B. | 240 |
| C. | 320 |
| D. | 420 |
| Answer» C. 320 | |
| 1089. |
The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle? |
| A. | 10,250 sq. units |
| B. | 11,260 sq. units |
| C. | 14,586 sq. units |
| D. | 73,250 sq. units |
| Answer» D. 73,250 sq. units | |
| 1090. |
The sides of a triangular lot are 130 m, 180 m and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line |
| A. | 120 m |
| B. | 125 m |
| C. | 128 m |
| D. | 130 m |
| Answer» C. 128 m | |
| 1091. |
The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26°. What is the third side? |
| A. | 197.49 m |
| B. | 218.61 m |
| C. | 282.15 m |
| D. | 341.78 m |
| Answer» E. | |
| 1092. |
Determine the spherical excess of the spherical triangle ABC given a = 56°, b = 65°, and c = 78°. |
| A. | 33°33’ |
| B. | 38°93’ |
| C. | 68°37’ |
| D. | 90°57’ |
| Answer» D. 90°57’ | |
| 1093. |
Solve for angle C of the oblique spherical triangle ABC given, a = 80°, c = 115° and A = 72° |
| A. | 61° |
| B. | 85° |
| C. | 95° |
| D. | 119° |
| Answer» D. 119° | |
| 1094. |
Solve the angle A in the spherical triangle ABC given a = 106°25’, c = 42°16’ and B = 114°53’ |
| A. | 45°54’ |
| B. | 72°43’ |
| C. | 80°42’ |
| D. | 97°09’ |
| Answer» B. 72°43’ | |
| 1095. |
Determine the value of the angle of an isosceles spherical triangle ABC whose given parts are b = c = 54°28’ and a = 92°30’. |
| A. | 41°45’ |
| B. | 55°45’ |
| C. | 84°25’ |
| D. | 89°45’ |
| Answer» E. | |
| 1096. |
Given a right spherical triangle whose parts are a = 82°, b = 62°, and C = 90°. What is the value of the side opposite the right angle? |
| A. | 83°30’ |
| B. | 84°45’ |
| C. | 85°15’ |
| D. | 86°15’ |
| Answer» E. | |
| 1097. |
Solve for side b of a right spherical triangle ABC whose parts are a = 46°, c = 75° and C = 90°. |
| A. | 48° |
| B. | 68° |
| C. | 74° |
| D. | 78° |
| Answer» B. 68° | |
| 1098. |
Solve the remaining side of the spherical triangle whose given parts are A = B = 80° and a = b = 89°. |
| A. | 158°12’ |
| B. | 162°21’ |
| C. | 168°31’ |
| D. | 172°12’ |
| Answer» D. 172°12’ | |
| 1099. |
A spherical triangle ABC has an angle C = 90° and sides a = 50° and c = 80°. Find the value of b in degrees. |
| A. | 73.22 |
| B. | 74.33 |
| C. | 75.44 |
| D. | 76.55 |
| Answer» C. 75.44 | |
| 1100. |
One degree on the equator of the earth is equivalent to _____ in time. |
| A. | 1 hour |
| B. | 30 minutes |
| C. | 4 minutes |
| D. | 1 minutes |
| Answer» B. 30 minutes | |