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MCQOPTIONS
This section includes 639 Mcqs, each offering curated multiple-choice questions to sharpen your Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The angles of elevation of an aeroplane flying vertically above the ground, as observed from the two consecutive stones, 1 km apart; are 45 and 60 aeroplane from the ground is : |
| A. | ( |
| B. | + 1) km. |
| C. | ( |
| D. | + 3) km. |
| Answer» E. | |
| 2. |
If the angle of elevation of the top of a pillar from the ground level is raised from 30 to 60 , the length of the shadow of a pillar of height 50 3 will be decreased by |
| A. | 60 metre |
| B. | 75 metre |
| C. | 100 metre |
| D. | 50 metre |
| Answer» D. 50 metre | |
| 3. |
From a point P on a level ground, the angle of elevation to the top of the tower is 30 . If the tower is 100 metre high, the distance of point P from the foot of the tower is (Take 3 = 1.73) |
| A. | 149 metre |
| B. | 156 metre |
| C. | 173 metre |
| D. | 188 metre |
| Answer» D. 188 metre | |
| 4. |
Find the angular elevation of the Sun when the shadow of a 15 metre long pole is (15 / 3) metre. |
| A. | 45 |
| B. | 60 |
| C. | 30 |
| D. | 90 |
| Answer» C. 30 | |
| 5. |
If A is an acute angle and cot A + cosec A = 3, then the value of sin A is |
| A. | 1 |
| B. | |
| C. | |
| D. | 0 |
| Answer» C. | |
| 6. |
If x = a sec and y = b tan then a -b = ?x y |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 7. |
The value of tan 11 tan 17 tan 79 tan 73 is |
| A. | |
| B. | 0 |
| C. | 1 |
| D. | |
| Answer» D. | |
| 8. |
If sin + sin = 1, then the value of cos2 + 3 cos10 + 3 cos8 + cos6 1 is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» E. | |
| 9. |
If for any acute angle A, sin A + sin A = 1, then the value of cos A + cos4 A is |
| A. | - 1 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» C. 2 | |
| 10. |
If 0 90 and 4 cos 4 3 cos + 3 = 0 then the value of is |
| A. | 30 |
| B. | 45 |
| C. | 90 |
| D. | 60 |
| Answer» B. 45 | |
| 11. |
If sin ( + 30 ) =3, then the value of cos is 12 |
| A. | |
| B. | |
| Answer» D. | |
| 12. |
If a sin + b cos = c, then a cos b sin is equal to |
| A. | |
| B. | |
| C. | |
| D. | |
| E. | |
| Answer» D. | |
| 13. |
If x = a sec , y = b tan , then x -y isa b |
| A. | - 1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 14. |
If sin (60 x) = cos (y + 60 ), then the value of sin (x y) is |
| A. | |
| B. | |
| C. | 1 |
| Answer» C. 1 | |
| 15. |
If sin (3 ) = 1 and cos (2 + ) = (1 / 2) , then the value of tan is |
| A. | 0 |
| B. | |
| C. | 1 |
| D. | |
| E. | |
| Answer» C. 1 | |
| 16. |
If cos4 sin4 = (2 / 3) , then the value of 1 2 sin2 is |
| A. | |
| B. | 1 |
| C. | 0 |
| Answer» B. 1 | |
| 17. |
If cos + sec = 3 , then the value of cos3 + sec3 is |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | 4 |
| Answer» D. 4 | |
| 18. |
If is a positive acute angle and cosec + cot = 3 , then the value of cosec is |
| A. | |
| B. | |
| C. | 1 |
| Answer» D. | |
| 19. |
If x cos 30 . sin 60 = tan 45 . sec 60 then the value of x iscosec 60 |
| A. | |
| B. | |
| C. | |
| Answer» D. | |
| 20. |
If tan (A + B) = AAAA and tan (A B) = (1 / 3) , A + B) < 90 , A B, then A is |
| A. | 90 |
| B. | 30 |
| C. | 45 |
| D. | 60 |
| Answer» D. 60 | |
| 21. |
If tan = 2, then the value of cosec - sec iscosec + sec |
| A. | |
| B. | |
| Answer» C. | |
| 22. |
If 3 tan = 3 sin , then the value of (sin cos ) is |
| A. | 1 |
| B. | 3 |
| C. | |
| D. | None |
| Answer» D. None | |
| 23. |
If tan =3, then the value of 4sin - 2cos is equal to44sin + 3cos |
| A. | |
| B. | |
| C. | |
| D. | |
| Answer» B. | |
| 24. |
If sec + tan = 2 + 5 , then the value of sin + cos is : |
| A. | |
| B. | |
| Answer» B. | |
| 25. |
If sin + cosec = 2, then the value of sin9 + cosec9 is : |
| A. | 3 |
| B. | 2 |
| C. | 4 |
| D. | 1 |
| Answer» C. 4 | |
| 26. |
If sec + tan = 2, then the value of sec is |
| A. | |
| B. | 5 |
| C. | |
| D. | |
| E. | |
| Answer» D. | |
| 27. |
The value of 3 (sin x cos x)4 + 6 (sin x + cos x)2+ 4 (sin6 x + cos6 x) is |
| A. | 14 |
| B. | 11 |
| C. | 12 |
| D. | 13 |
| Answer» E. | |
| 28. |
If tan + cot = 2, then the value of tan100 + cot100 is |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | |
| E. | |
| Answer» B. 0 | |
| 29. |
From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are 30 and 45 respectively. If the bridge is at a height of 2.5 m from the banks, then the width of the river is (Take 3 = 1.732) |
| A. | 5.83 metre |
| B. | 6.83 metre |
| C. | 5.76 metre |
| D. | 6.87 metre |
| Answer» C. 5.76 metre | |
| 30. |
If cos x + cos x = 1, the numerical value of (sin12x + 3 sin10x + 3 sin8x + sin6x l) is : |
| A. | - 1 |
| B. | 2 |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 31. |
If (r cos 3 ) + (r sin 1) = 0 then the value of r tan + sec is equal to r sec + tan |
| A. | |
| B. | |
| C. | |
| D. | |
| Answer» B. | |
| 32. |
If r sin = 1, r cos = 3 , then the value of ( 3 tan + 1 ) is |
| A. | |
| B. | |
| C. | |
| D. | 1 |
| E. | 2 |
| Answer» E. 2 | |
| 33. |
The greatest value of sin4 + cos4 is |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| Answer» E. | |
| 34. |
If tan cot = 0, find the value of sin + cos . |
| A. | 0 |
| B. | 1 |
| C. | |
| D. | |
| E. | 2 |
| Answer» D. | |
| 35. |
The value of1-1is(1 + tan )(1 + cot ) |
| A. | 1 |
| B. | |
| C. | |
| Answer» C. | |
| 36. |
If cos4 sin4 = (2 / 3) , then the value of 1 2 sin2 is |
| A. | |
| B. | 0 |
| C. | |
| D. | |
| Answer» D. | |
| 37. |
If sin + sin = 1, then the value of cos + cos4 is |
| A. | 2 |
| B. | 4 |
| C. | 0 |
| D. | 1 |
| Answer» E. | |
| 38. |
The simplest value of cot 9 cot 27 cot 63 cot 81 is |
| A. | 0 |
| B. | 1 |
| C. | - 1 |
| D. | |
| E. | |
| Answer» C. - 1 | |
| 39. |
If 7 sin + 3 cos = 4, (0 < < 90 ), then the value of tan is |
| A. | |
| B. | |
| C. | 1 |
| D. | |
| Answer» B. | |
| 40. |
If 0 < < 90 and 2 sec = 3 cosec , then is |
| A. | |
| B. | |
| Answer» D. | |
| 41. |
If x = a (sin + cos ), y = b (sin cos ) then the value ofx +y isa b |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 2 |
| Answer» D. 2 | |
| 42. |
If tan = 1 e , then the value of sec + tan3 cosec is |
| A. | (2 + e ) |
| B. | (2 - e ) |
| C. | (2 + e ) |
| D. | (2 - e ) |
| E. | |
| Answer» E. | |
| 43. |
If sec + tan = 5, then the value of tan (tan + 1 / tan - 1) is |
| A. | |
| B. | |
| C. | |
| Answer» E. | |
| 44. |
If q is a positive acute angle and 4 cos 4 cos + 1 = 0, then the value of tan ( 15 ) is equal to |
| A. | 0 |
| B. | 1 |
| C. | |
| D. | |
| Answer» C. | |
| 45. |
If cos sin = (1 / 3) , where 0 q ( / 2) , then the value of cos4 sin4 is |
| A. | |
| Answer» B. | |
| 46. |
The value ofcos 60 + 4sec 30 - tan 45 issin 30 + cos 30 |
| A. | |
| B. | |
| C. | |
| Answer» C. | |
| 47. |
If x = a sec cos , y = b sec sin , z = c tan , then the value of x +y -z isa b c |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | - 1 |
| Answer» D. - 1 | |
| 48. |
If sin =3, then the value of tan + cos is equal to5cot + cosec |
| A. | |
| B. | |
| Answer» C. | |
| 49. |
If tan =1and 0 , < < , then the value ofcosec - sec is 112cosec + sec |
| A. | |
| B. | |
| Answer» D. | |
| 50. |
The simple value of tan 1 . tan 2 . tan 3 ....... tan 89 is |
| A. | |
| B. | |
| C. | 0 |
| D. | 1 |
| E. | |
| Answer» D. 1 | |