MCQOPTIONS
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MCQOPTIONS
This section includes 65 Mcqs, each offering curated multiple-choice questions to sharpen your GEOMETRY knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the value of : (sin 35º / cos 55º)2 + (cos 55º / sin 35º)2 – 2 cos 30º |
| A. | 0 |
| B. | 1 – √3 |
| C. | 2 – √3 |
| D. | 3 |
| Answer» D. 3 | |
| 2. |
If sin 21° = x/y, then sec 21° – sin 69° is equal to |
| A. | x2 / y √(y2 –x2) |
| B. | y2 / y √(y2 – x2) |
| C. | x2 / y √(x2 – y2) |
| D. | y / x √(x2 – y2) |
| Answer» B. y2 / y √(y2 – x2) | |
| 3. |
Find the value of: cos2Θ {√(1 + sin Θ / 1 – sin Θ) + √(1 – sing Θ / 1 + sin Θ)} |
| A. | cos Θ |
| B. | cos θ /2 |
| C. | 2 cosΘ |
| D. | √2 cos Θ |
| Answer» D. √2 cos Θ | |
| 4. |
Find the value of 16/ √3 (Cos50°Cos10°Cos110°Cos60°) |
| A. | 1 |
| B. | 2 |
| C. | – 1 |
| D. | – 2 |
| Answer» D. – 2 | |
| 5. |
Find the value of sin2 10 + sin2 20 + sin2 30 + ....... + sin2 80. |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | 4 |
| Answer» E. | |
| 6. |
If cot A + cosec A = 3 and A is an acute angle, then the value of cos A is |
| A. | 4/5 |
| B. | 1 |
| C. | 1/2 |
| D. | 1/√3 |
| Answer» B. 1 | |
| 7. |
The value of sin (45° + θ) – cos (45° – θ) is |
| A. | 1 |
| B. | 0 |
| C. | 2 cos θ |
| D. | 2 sin θ |
| Answer» C. 2 cos θ | |
| 8. |
If tan4θ + tan2θ = 1, then the value of cos4θ + cos2θ is |
| A. | 8 |
| B. | 10 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 9. |
If cot {(π / 2) – θ} = √3,then the value of cos θ is |
| A. | 0 |
| B. | 1/√2 |
| C. | 1/2 |
| D. | 1 |
| Answer» D. 1 | |
| 10. |
If {(2 sin θ – cos θ) / (cos θ + sin θ)} = 1,then the value of cot θ is |
| A. | 1/2 |
| B. | 1/3 |
| C. | 3 |
| D. | 2 |
| Answer» B. 1/3 | |
| 11. |
If x = a cos3 Θ and y = b sin3 Θ, then (x / a)2/3 + (y / b)2/3 = ? |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | 4 |
| Answer» B. 0 | |
| 12. |
If cosΘ + secΘ = 2 ,then the value of cos68Θ + sec68Θ equal to |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 68 |
| Answer» C. 3 | |
| 13. |
If 7 sin2θ + 3 cos2θ = 4 and 0 ≤ θ ≤ (π / 2), then the value of tan θ is: |
| A. | √(3 / 7) |
| B. | √(2 / 7) |
| C. | 1 / √3 |
| D. | 1 / √7 |
| Answer» D. 1 / √7 | |
| 14. |
Evaluate : ( Cot4Θ–Cosec4Θ + Cot2Θ + Cosec2Θ) |
| A. | 1 |
| B. | 0 |
| C. | – 1 |
| D. | 2 |
| Answer» C. – 1 | |
| 15. |
If cos X = m cos Y and where X and Y are not equal to each other and values of angle X and Y range from 0°to 90°, then |
| A. | cot (X + Y / 2) = [(m + 1) / (m – 1)] tan (Y – X / 2) |
| B. | tan (X + Y / 2) = [(m + 1) / (m – 1)] cot (Y – X / 2) |
| C. | cot (X + Y / 2) = [(m + 1) / (m – 1)] tan (X – Y / 2) |
| D. | cot (X + Y / 2) = [(m – 1) / (m + 1)] tan (X – Y / 2) |
| Answer» B. tan (X + Y / 2) = [(m + 1) / (m – 1)] cot (Y – X / 2) | |
| 16. |
If x = a (sin Θ + cos Θ), y = b (sin Θ – cos Θ) then the value of (x2/ a2) + (y2/ b2) is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | – 2 |
| Answer» D. – 2 | |
| 17. |
Value of sec2θ – (sin2θ – 2sin4θ) / (2 cos4θ – cos2θ) is |
| A. | 1 |
| B. | 2 |
| C. | – 1 |
| D. | 0 |
| Answer» B. 2 | |
| 18. |
If sin 3A = cos (A – 26°), where 3A is an acute angle then the value of A is |
| A. | 29° |
| B. | 26° |
| C. | 23° |
| D. | 28° |
| Answer» B. 26° | |
| 19. |
In a ΔABC, ∠B =π/3, ∠C =π/4and D divides BC internally in the ratio 1 : 3 then (sin ∠BAD) / (sin ∠CAD)is equal to |
| A. | (1 / √2) |
| B. | (1 / √3) |
| C. | ( 1 / √6) |
| D. | √6 |
| Answer» D. √6 | |
| 20. |
For any real values of √(secΘ – 1 ) / (secΘ + 1) = ? |
| A. | cot Θ – cosec Θ |
| B. | sec Θ – tan Θ |
| C. | cosec Θ – cot Θ |
| D. | tan Θ – sec Θ |
| Answer» D. tan Θ – sec Θ | |
| 21. |
The expression (tan 57 º + cot 37º) / (tan 33º + cot 53º) is equal to |
| A. | tan 33° cot 57° |
| B. | tan 57° cot 37° |
| C. | tan 33° cot 53° |
| D. | tan 53° cot 37° |
| Answer» C. tan 33° cot 53° | |
| 22. |
If sin 17° = x / y, then the value of (sec 17° – sin 73°) is |
| A. | y2 / x √(y2 – x2) |
| B. | y2 / y √(y2 – x3) |
| C. | x2 / y √(x2– y2) |
| D. | y2 / x√(x2 – y2) |
| Answer» C. x2 / y √(x2– y2) | |
| 23. |
If A = tan 11° tan 29° and B = 2 cot 61° cot 79°, then : |
| A. | A = 2B |
| B. | A = – 2B |
| C. | 2A = B |
| D. | 2A = – B |
| Answer» D. 2A = – B | |
| 24. |
Ifcos2Θ / (cot2Θ – cos2Θ)= 3 and 0° < Θ < 90°, then the value of Θ is: |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | None of these |
| Answer» D. None of these | |
| 25. |
The value of (sin 39°) / (cos 51°) + 2 tan11° tan31° tan45° tan59° tan79° – 3 (sin2 21° + sin2 69°) is : |
| A. | 2 |
| B. | – 1 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 26. |
The numerical value of cot 18º { cot 72º cos2 22º + (1 / tan 72º sec2 68º)} is |
| A. | 1 |
| B. | √2 |
| C. | 3 |
| D. | 1/√3 |
| Answer» B. √2 | |
| 27. |
The value of sin21° + sin25° + sin29° + ..... + sin289° is |
| A. | |
| B. | 11√2 |
| C. | 11 |
| D. | 11/√2 |
| Answer» B. 11√2 | |
| 28. |
If Θ be an acute angle and 7 sin2Θ + 3 cos2Θ = 4, then the value of tan Θ is |
| A. | √3 |
| B. | 1/√3 |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 29. |
The value of cot 10° . cot 20° . cot 60° . cot 70° . cot 80° is |
| A. | 1 |
| B. | – 1 |
| C. | √3 |
| D. | 1/√3 |
| Answer» E. | |
| 30. |
The angles of a triangle are (x + 5)°, (2x – 3)° and (3x + 4)°. The value of x is |
| A. | 30 |
| B. | 31 |
| C. | 29 |
| D. | 28 |
| Answer» D. 28 | |
| 31. |
The minimum value of 2 sin2Θ + 3 cos2Θ is |
| A. | 0 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» D. 1 | |
| 32. |
If the sum of two angles is 135° and their difference is (π/12), then the circular measure of the greater angle is |
| A. | (2π / 3) |
| B. | (3π / 6) |
| C. | (5π / 12) |
| D. | (π / 3) |
| Answer» D. (π / 3) | |
| 33. |
If x sin2 60º – (3/2) sec 60º tan2 30º + (4/5) sin2 45º tan2 60 = 0 then x is |
| A. | – (1/15) |
| B. | – 4 |
| C. | –(4/15) |
| D. | – 2 |
| Answer» D. – 2 | |
| 34. |
The degree measure of 1 radian (taking π = 22/7) is |
| A. | 57°61'22'' (approx) |
| B. | 57°16'22''(approx) |
| C. | 57°22'16''(approx) |
| D. | 57°32'16''(approx) |
| Answer» C. 57°22'16''(approx) | |
| 35. |
If sin 21º = (x / y), then sec 21º – sin 69º is equal to |
| A. | x2 / y√(y2 – x2) |
| B. | y2 / x√(y2 – x2) |
| C. | x2 / y√(x2 – y2) |
| D. | y2 / x √(x2 – y2) |
| Answer» B. y2 / x√(y2 – x2) | |
| 36. |
If 29 tan Θ = 31, then (1 + 2 sin Θ cosΘ) / (1 – 2 sin Θ cos Θ) = ? |
| A. | 810 |
| B. | 900 |
| C. | 540 |
| D. | 490 |
| Answer» C. 540 | |
| 37. |
In circular measure, the value of the angle 11° 15' is |
| A. | (πc / 16) |
| B. | (πc / 8) |
| C. | (πc / 4) |
| D. | (πc / 12) |
| Answer» B. (πc / 8) | |
| 38. |
If 2 cot Θ = 3, so (2 cosΘ – sin Θ) / (2 cos θ + sin θ) = ? |
| A. | 2 / 3 |
| B. | 1 / 3 |
| C. | 1 / 2 |
| D. | 3 / 4 |
| Answer» D. 3 / 4 | |
| 39. |
If sin Θ.cos Θ = 1/2,then what is sin6Θ + cos6Θ equal to? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 1 4 |
| Answer» E. | |
| 40. |
What is cosec (75° + Θ) – sec (15° – Θ) – tan (55° + Θ) + cot (35° – Θ) equal to? |
| A. | –1 |
| B. | 0 |
| C. | 1 |
| D. | 3 2 |
| Answer» C. 1 | |
| 41. |
If cos A + cos2A = 1, then what is the value of 2(sin2A + sin4A)? |
| A. | 4 |
| B. | 2 |
| C. | 1 |
| D. | 1/2 |
| Answer» C. 1 | |
| 42. |
If α, β and γ are acute angles such that sin α = (√3 / 2), cos β = (√3 / 2) and tan γ = 1, then what is α + β + γ equal to? |
| A. | 105° |
| B. | 120° |
| C. | 135° |
| D. | 150° |
| Answer» D. 150° | |
| 43. |
(1 – tan A)2+ (1 + tan A)2+ (1 – cot A)2+ (1 + cot A)2is equal to |
| A. | sin2A.cos2A |
| B. | sec2A.cosec2A |
| C. | 2sec2A.cosec2A |
| D. | None of these |
| Answer» D. None of these | |
| 44. |
What is the value of {(tan A – sin A) / sin3 A} ? |
| A. | sec A / (1 – cos A) |
| B. | sec A / (1 + cos2A) |
| C. | sec A / (1 + cos A) |
| D. | None of these |
| Answer» D. None of these | |
| 45. |
If sin A = 3/5 and A is an acute angle, then tan A + sec A is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | –1 |
| Answer» D. –1 | |
| 46. |
If sin (A + B) = 1, where 0 < B < 45°, then what is cos (A – B) equal to? |
| A. | sin 2B |
| B. | sin B |
| C. | cos 2B |
| D. | cos B |
| Answer» B. sin B | |
| 47. |
The value of cos 25° – sin 25° is |
| A. | positive but less than 1 |
| B. | positive but greater than 1 |
| C. | negative |
| D. | 0 |
| Answer» B. positive but greater than 1 | |
| 48. |
Ifαandβare complementary angles, then what is cos αcosec β– cos αsin β equal to? |
| A. | sec β |
| B. | cos α |
| C. | sin α |
| D. | – tan β |
| Answer» D. – tan β | |
| 49. |
If α + β = 90°, then the value of (1 – sin2α) (1 – cos2α) × (1 + cot2β) (1 + tan2β) is |
| A. | 1 |
| B. | –1 |
| C. | 0 |
| D. | 2 |
| Answer» B. –1 | |
| 50. |
If Θ is an acute angle and tan2Θ+ 1/tan2Θ = 2then the value of Θ is: |
| A. | 60° |
| B. | 15° |
| C. | 45° |
| D. | 30° |
| Answer» D. 30° | |