Explore topic-wise MCQs in Aptitude.

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.

401.

The value of tan 4 .tan 43 .tan 47 .tan 86 is

A. 2
B. 3
C. 1
D. 4
Answer» D. 4
Discussion
402.

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
Discussion
403.

The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are

A. 16 , 56 , 88
B. 18 , 63 , 99
C. 20 , 70 , 90
D. 25 , 175 , 105
Answer» C. 20 , 70 , 90
Discussion
404.

If cos x + cos y = 2, the value of sin x + sin y is

A. 0
B. 1
C. 2
D. -1
Answer» B. 1
Discussion
405.

If 0 < A < 90 , the value of tan A sec A 1 istan A + sec A + 1

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>sin A 1 </center></td><td rowspan="2"></td></tr><td align="center">cos A</td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - sin A </center></td><td rowspan="2"></td></tr><td align="center">cos A</td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - cos A </center></td><td rowspan="2"></td></tr><td align="center">sin A</td></table>
D.
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>sin A + 1 </center></td><td rowspan="2"></td></tr><td align="center">cos A</td></table>
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - sin A </center></td><td rowspan="2"></td></tr><td align="center">cos A</td></table>
Discussion
406.

Iftan + cot = 2, (0 90 ),then the value of sin istan - cot

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <span style=" text-decoration: overline;">3</span></center></td></tr><td align="center">2</td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
D. 1
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
Discussion
407.

If tan 15 = 2

A. 14
B. 12
C. 10
D. 8
Answer» B. 12
Discussion
408.

The numerical value of cot18

A. 1
B.
C. <span style=" text-decoration: overline;">2</span>
D. 3
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
Answer» B.
Discussion
409.

A man on the top of a tower, standing on the sea shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30 to 60 . How soon the boat reach the seashore?

A. 5 minutes
B. 7 minutes
C. 10 minutes
D. 15 minutes
Answer» B. 7 minutes
Discussion
410.

The value of sin 1 + sin 5 + sin 9 + .... + sin 89 is

A. <table><tr><td rowspan="2">11</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
B. 11
C. <span style=" text-decoration: overline;">2</span>
D. 11
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>11</center></td></tr><td align="center"> <span style=" text-decoration: overline;">2</span></td></table>
Answer» B. 11
Discussion
411.

If the sum and difference of two angles are 135 and ( / 12) respectively, then the value of the angles in degree measure are

A. 70 , 65
B. 75 , 60
C. 45 , 90
D. 80 , 55
Answer» C. 45 , 90
Discussion
412.

The value of (sin 39 / cos 51 ) + 2 tan 11 tan 31 tan 45 tan 59 tan 79 3 (sin 21 + sin 69 ) is :

A. 2
B. - 1
C. 1
D. 0
Answer» E.
Discussion
413.

sin 5 + sin 10 + sin 15 + .... + sin 85 + sin 90 is equal to

A. <table><tr><td rowspan="2">7</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
B. <table><tr><td rowspan="2">8</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
C. 9
D. <table><tr><td rowspan="2">9</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
Answer» E.
Discussion
414.

If x = a sec and y = b tan then

A. 1
B. 2
C. 3
D. 4
Answer» B. 2
Discussion
415.

Two ships are sailing in the sea on the two sides of a light house. The angles of elevation of the top of the light house as observed from the two ships are 30 and 45 respectively. If the light house is 100m high, the distance between the two ships is : (take

A. 173 metre
B. 200 metre
C. 273 metre
D. 300 metre
Answer» D. 300 metre
Discussion
416.

The value ofsin 43 +cos 19 - 8 cos 60 iscos 47 sin 71

A. 0
B. 1
C. 2
D. - 1
Answer» B. 1
Discussion
417.

sin 5 + sin 6 + ... + sin 84 + sin 85 = ?

A. <table><tr><td rowspan="2">39</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
B. <table><tr><td rowspan="2">40</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
C. 40
D. <table><tr><td rowspan="2">39</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span><br></td></table>
Answer» C. 40
Discussion
418.

If A and B are complementary to each other, then the value of sec A + sec B sec A . sec B is

A. 1
B. - 1
C. 2
D. 0
Answer» E.
Discussion
419.

If sin (3x 20 ) = cos (3y + 20 ), then the value of (x + y) is

A. 20
B. 30
C. 40
D. 45
Answer» C. 40
Discussion
420.

The value of cot .tan(90 ) sec(90 ) cosec + (sin 25 + sin2 65 ) +

A. 1
B. - 1
C. 2
D. 0
Answer» B. - 1
Discussion
421.

If 0 < q < 90 , the value of sin q + cos q is

A. equal to 1
B. greater than 1
C. less than 1
D. equal to 2
Answer» C. less than 1
Discussion
422.

If sec (7 + 28 ) = cosec (30 3 ) then the value of is

A. 8
B. 5
C. 60
D. 9
Answer» B. 5
Discussion
423.

The value of (tan35 tan45 tan55 ) is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
B. 2
C. 0
D. 1
Answer» E.
Discussion
424.

If 2 (cos sin ) = 1, is a positive acute angle, then the value of is

A. 60
B. 30
C. 45
D. <table><tr><td rowspan="2">22</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> </td></tr><td align="center">2</td></table>
Answer» C. 45
Discussion
425.

If A = tan 11 tan 29 , B = 2 cot 61 cot 79 , then :

A. A = 2B
B. A = 2B
C. 2A = B
D. 2A = B
Answer» D. 2A = B
Discussion
426.

If cos cosec 23 = 1, the value of is

A. 23
B. 37
C. 63
D. 67
Answer» E.
Discussion
427.

If sec + tan = &radic

A. undefined
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center"> <span style=" text-decoration: overline;">2</span></td></table>
D.
E. 3
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
Discussion
428.

If sin (60 ) = cos (&psy; 30 ), then the value of tan (&psy; ) is (assume that and &psy; are both positive acute angles with < 60 and &psy; > 30 ).

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
B. 0
C.
D. <span style=" text-decoration: overline;">3</span>
E. 1
Answer» D. <span style=" text-decoration: overline;">3</span>
Discussion
429.

If + = 90 , then the value of (1 sin ) (1 cos ) (1 + cot ) (1 + tan ) is

A. 1
B. - 1
C. 0
D. 2
Answer» B. - 1
Discussion
430.

The value of (1 + sec 20 + cot 70 ) (1 cosec 20 + tan 70 ) is equal to

A. 0
B. 1
C. 2
D. - 1
Answer» D. - 1
Discussion
431.

sin 3 sin + 2 = 0 will be true if

A. 0 < 90
B. 0 < < 90
C. = 0
D. = 90
Answer» E.
Discussion
432.

Evaluate : 3 cos 80 cosec 10 + 2 cos 59 cosec 31

A. 1
B. 3
C. 2
D. 5
Answer» E.
Discussion
433.

From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are 45 and 60 respectively. The height of the tower is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>100</center></td><td rowspan="2">(3 - <span style=" text-decoration: overline;">3</span>) metre</td></tr><td align="center">3</td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>100</center></td><td rowspan="2">( <span style=" text-decoration: overline;">3</span> - 1) metre</td></tr><td align="center">3</td></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>100</center></td><td rowspan="2">(2 <span style=" text-decoration: overline;">3</span> - 1) metre</td></tr><td align="center">3</td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>100</center></td><td rowspan="2"> <span style=" text-decoration: overline;">3</span> - <span style=" text-decoration: overline;">2</span> metre</td></tr><td align="center">3</td></table>
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>100</center></td><td rowspan="2">( <span style=" text-decoration: overline;">3</span> - 1) metre</td></tr><td align="center">3</td></table>
Discussion
434.

The value of 152 (sin 30 + 2 cos 45 + 3 sin 30 + 4 cos 45 + .... + 17 sin 30 + 18 cos 45 ) is

A. an integer but not a perfect square
B. a rational number but not an integer
C. a perfect square of an integer
D. irrational
Answer» D. irrational
Discussion
435.

The equation cos =(x + y) is only possible when4xy

A. x = y
B. x > y
C. x = y
D. x < y
Answer» D. x < y
Discussion
436.

The value of sin 1 + sin 2 + sin 3 + .....+ sin 89 is

A. 22
B. 44
C. <table><tr><td rowspan="2">22</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
D. <table><tr><td rowspan="2">44</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
Answer» E.
Discussion
437.

2 cosec 23 cot 67 sin 23 sin 67 cot 67 is equal to

A. 1
B. sec 23
C. tan 23
D. 0
Answer» C. tan 23
Discussion
438.

If tan = 1 + 2 tan ( , are positive acute angles), then

A. 0
B.
C. <span style=" text-decoration: overline;">2</span>
D. 1
E. - 1
Answer» B.
Discussion
439.

An observer on the top of a mountain, 500 m above the sea level, observes the angles of depression of the two boats in his same place of vision to be 45 and 30 respectively. Then the distance between the boats, if the boats are on the same side of the mountain, is

A. 456 m
B. 584 m
C. 366 m
D. 699 m
Answer» D. 699 m
Discussion
440.

If sin 7x = cos 11x , then the value of tan 9x + cot 9x is

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion
441.

The minimum value of 4 tan + 9 cot is equal to

A. 0
B. 5
C. 12
D. 13
Answer» D. 13
Discussion
442.

The value of tan 10 tan 15 tan 75 tan 80 is

A. 0
B. 1
C. - 1
D. 2
Answer» C. - 1
Discussion
443.

2sin68 -2cot15 -3tan45 .tan20 .tan40 .tan50 .tan70 is equal tocos22 5tan75 5

A. - 1
B. 0
C. 1
D. 2
Answer» D. 2
Discussion
444.

If sin + cos = 2 (0 90 ), then sin (2 + / 3) =

A. <table><tr><td rowspan="2">sin</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
B. <table><tr><td rowspan="2">cos</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
C. <table><tr><td rowspan="2">sin</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
D. <table><tr><td rowspan="2">cos</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2 </center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
Answer» C. <table><tr><td rowspan="2">sin</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2"></td></tr><td align="center">3</td></table>
Discussion
445.

If sec tan =7, then sec4 - tan4 =12

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>7</center></td><td rowspan="2"></td></tr><td align="center">12</td></table>
B.
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td><td rowspan="2"></td></tr><td align="center">12</td></table>
E. 1
Answer» B.
Discussion
446.

If be acute angle and cos = (15 / 17) , then the value of cot

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2 <span style=" text-decoration: overline;">8</span></center></td><td rowspan="2"></td></tr><td align="center">15</td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>8</center></td><td rowspan="2"></td></tr><td align="center">15</td></table>
C.
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <span style=" text-decoration: overline;">2</span></center></td><td rowspan="2"></td></tr><td align="center">17</td></table>
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>8 <span style=" text-decoration: overline;">2</span></center></td><td rowspan="2"></td></tr><td align="center">17</td></table>
Answer» C.
Discussion
447.

If tan (2 + 45 ) = cot 3 where (2 + 45 ) and 3 are acute angles, then the value of is

A. 5
B. 9
C. 12
D. 15
Answer» C. 12
Discussion
448.

The product cos1 cos2 cos3 cos4 .... cos100 is equal to

A. - 1
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">4</td></table>
C. 1
D. 0
Answer» E.
Discussion
449.

If sec + tan = 7, then the value of when 0 90 , is

A. 60
B. 30
C. 0
D. 90
Answer» B. 30
Discussion
450.

If be acute and tan + cot = 2, then the value of tan

A. 1
B. 2
C. 3
D. 4
Answer» C. 3
Discussion