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.

351.

If + = and sin =1, then the value of sin is22

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"> <span style=" text-decoration: overline;">2</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">2</td></table>
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;">3</span></center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
Answer» E.
Discussion
352.

If cos sin = tan , then the value of cos sin is

A. cot
B. cot
C. tan
D. tan
Answer» D. tan
Discussion
353.

If tan 2 . tan 3 = 1, where 0 < < 90 then the value of is

A. <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>
B. 18
C. 24
D. 30
Answer» C. 24
Discussion
354.

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60 with the ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30 with ground. How much did the ladder slip from the top of the wall?

A. 12 ft
B. 20 ft
C. 7.32 ft
D. 18 ft
Answer» D. 18 ft
Discussion
355.

If 0 < < 90 and 2 sin + 3 cos = 3, then the value of is

A. 30
B. 60
C. 45
D. 75
Answer» C. 45
Discussion
356.

If sin 5 = cos 20 ( 0 < < 90 ) then the value of is

A. 4
B. 22
C. 10
D. 14
Answer» E.
Discussion
357.

If r sin =7and r cos =7 3, then the value of r is22

A. 4
B. 3
C. 5
D. 7
Answer» E.
Discussion
358.

The value ofsin - 2sin3 is2 cos3 - cos

A. sin
B. cos
C. tan
D. cot
Answer» D. cot
Discussion
359.

The angle of elevation of the sun when the length of the shadow of a pole is equal to its height is :

A. 30
B. 45
C. 60
D. 90
Answer» C. 60
Discussion
360.

If x = a (sin + cos ), y = b (sin cos ) then the value of

A. 0
B. 1
C. 2
D. 2
Answer» D. 2
Discussion
361.

The value of (0 90 ) satisfying 2 sin = 3 cos is

A. 60
B. 30
C. 90
D. 45
Answer» B. 30
Discussion
362.

The angle of elevation of an aeroplane as observed from a point 30 metre above the transparent water-surface of a lake is 30 and the angle of depression of the image of the aeroplane in the water of the lake is 60 . The height of the aeroplane from the water-surface of the lake is

A. 60 metre
B. 45 metre
C. 50 metre
D. 75 metre
Answer» B. 45 metre
Discussion
363.

If2sin - cos = 1, then value of cot is :cosec + sin

A. <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>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">3</td></table>
C.
D. 3
E. 2
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">3</td></table>
Discussion
364.

If cosec sin = l and sec cos = m, then the value of l m (l + m + 3) is

A. - 1
B. 0
C. 1
D. 2
Answer» D. 2
Discussion
365.

Value of sec - sin - 2sin 4 is2cos4 - cos

A. 1
B. 2
C. - 1
D. 0
Answer» B. 2
Discussion
366.

If sin + cosec = 2, then the value of sin

A. 3
B. 2
C. 4
D. 1
Answer» C. 4
Discussion
367.

If a (tan + cot ) = 1, sin + cos = b with 0 < < 90 , then a relation between a and b is

A. b = 2 (a + 1)
B. b = 2 (a 1)
C. 2a = b 1
D. 2a = b + 1
Answer» D. 2a = b + 1
Discussion
368.

tan +cot is equal to1 - cot 1 - tan

A. 1 tan cot
B. 1 + tan cot
C. 1 tan + cot
D. 1 + tan + cot
Answer» E.
Discussion
369.

The value of4=3+ 3 sin will be1 + cot 1 + cot

A. 4
B. - 1
C. 2
D. 3
Answer» B. - 1
Discussion
370.

The angles of depression of two ships from the top of a light house are 45 and 30 toward east. If the ships are 200m apart, the height of the light house is (Take

A. 273 metre
B. 270 metre
C. 253 metre
D. 263 metre
Answer» B. 270 metre
Discussion
371.

A boat is moving away from an observation tower. It makes an angle of depression of 60 with an observer s eye when at a distance of 50 metre from the tower. After 8 seconds, the angle of depression becomes 30 . By assuming that it is running in still water, the approximate speed of the boat is :

A. 33 km/hr
B. 42 km/hr
C. 45 km/hr
D. 50 km/hr
Answer» D. 50 km/hr
Discussion
372.

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

A. 5.83 metre
B. 6.83 metre
C. 5.76 metre
D. 6.87 metre
Answer» C. 5.76 metre
Discussion
373.

From the top of a building 60 metre high, the angles of depression of the top and bottom of a tower are observed to be 30 and 60 respectively. The height of the tower in metre is :

A. 40
B. 45
C. 50
D. 55
Answer» B. 45
Discussion
374.

The value of 3 (sin x cos x)

A. 14
B. 11
C. 12
D. 13
Answer» E.
Discussion
375.

The numerical value of1=3+ 2 sin will be1 + cot 1 + tan

A. 2
B. 5
C. 6
D. 3
Answer» E.
Discussion
376.

If (l + sin ) (l + sin ) (l + sin ) = (1 sin )(l sin ) (l sin ), then each side is equal to

A. cos cos cos
B. sin sin sin
C. sin cos cos
D. sin sin cos
Answer» B. sin sin sin
Discussion
377.

The value of1-1iscosec - cot sin

A. 1
B. cot
C. cosec
D. tan
Answer» C. cosec
Discussion
378.

The numerical value of 1 +1- sec 27 +1- cosec 27 iscot 63 sin 63

A. 1
B. 2
C. - 1
D. 0
Answer» E.
Discussion
379.

If cos x = x x + (5 / 4) , the value of x will be

A. 0
B. 1
C. - 1
D. None of the above
Answer» E.
Discussion
380.

If 3sin + 5cos = 5, then 5sin 3cos is equal to

A. 3
B. 5
C. 1
D. 2
Answer» B. 5
Discussion
381.

If x =cos , thencos is equal to1 - sin 1 + sin

A. x 1
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">x</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">x + 1</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">1 - x</td></table>
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">x + 1</td></table>
Discussion
382.

The greatest value of sin

A. 2
B. 3
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» E.
Discussion
383.

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
Discussion
384.

If x cos y sin = x + y cos +sin =1, then the correct relation is a b x + y

A. <table><tr><td rowspan="2"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x </center></td><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2">= 1</td></tr><td align="center">b </td><td align="center">a </td></table>
B. <table><tr><td rowspan="2"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x </center></td><td rowspan="2">+</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2">= 1</td></tr><td align="center">a </td><td align="center">b </td></table>
C.
D. <table><tr><td rowspan="2"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x </center></td><td rowspan="2">+</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2">= 1</td></tr><td align="center">b </td><td align="center">a </td></table>
E. <table><tr><td rowspan="2"></td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x </center></td><td rowspan="2">-</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2">= 1</td></tr><td align="center">a </td><td align="center">b </td></table>
Answer» C.
Discussion
385.

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

A. 1
B. 2
C. 0
D. - 1
Answer» C. 0
Discussion
386.

If sin (A B) = sin A cos B cosA sinB, then sin 15 will be

A. <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;">3</span> + 1</center></td><td rowspan="2"></td></tr><td align="center">2 <span style=" text-decoration: overline;">2</span></td></table>
B. <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;">3</span></center></td><td rowspan="2"></td></tr><td align="center">2 <span style=" text-decoration: overline;">2</span></td></table>
C. <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;">3</span> - 1</center></td><td rowspan="2"></td></tr><td align="center">- <span style=" text-decoration: overline;">2</span></td></table>
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;">3</span> - 1</center></td><td rowspan="2"></td></tr><td align="center">2 <span style=" text-decoration: overline;">2</span></td></table>
Answer» E.
Discussion
387.

If sin cos = (1 / 2) then value of sin + cos is :

A. 2
B. 2
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <span style=" text-decoration: overline;">7</span></center></td></tr><td align="center">2</td></table>
D.
E. 2
Answer» D.
Discussion
388.

From 40m away from the foot of a tower, the angle of elevation of the top of the tower is 600 . What is the height of the tower?

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>120</center></td><td rowspan="2">m.</td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>60</center></td><td rowspan="2">m.</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>50</center></td><td rowspan="2">m.</td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>130</center></td><td rowspan="2">m.</td></tr><td align="center"> <span style=" text-decoration: overline;">7</span></td></table>
E.
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>60</center></td><td rowspan="2">m.</td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
Discussion
389.

If tan + cot = 2 then the value of is

A. 45
B. 60
C. 90
D. 30
Answer» B. 60
Discussion
390.

If sin + sin = 1, then the value of cos + cos

A. 2
B. 4
C. 0
D. 1
Answer» E.
Discussion
391.

The value ofsin A+sin Ais (0 &lt; A &lt; 90 )1 + cos A1 - cos A

A. 2 cosec A
B. 2 sec A
C. 2 sin A
D. 2 cos A
Answer» B. 2 sec A
Discussion
392.

If cos x + cos x = 1, the numerical value of (sin

A. - 1
B. 2
C. 0
D. 1
Answer» D. 1
Discussion
393.

The eliminant of q from x cos y sin = 2 and x sin + y cos = 4 will give

A. x + y = 20
B. 3x + y = 20
C. x - y = 20
D. 3x - y = 10
Answer» B. 3x + y = 20
Discussion
394.

If tan + cot = 2, then the value of tan2 + cot2 is

A. 2
B. 1
C.
D. <span style=" text-decoration: overline;">2</span>
E. 0
Answer» B. 1
Discussion
395.

Ifsin =cos , then sin - cos is equal toxy

A. x - y
B. x + y
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x - y</center></td></tr><td align="center"> <span style=" text-decoration: overline;">x + y </span></td></table>
D.
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y - x</center></td></tr><td align="center"> <span style=" text-decoration: overline;">x + y </span></td></table>
Answer» D.
Discussion
396.

If x = a sec cos , y = b sec sin , z = c tan , then the value of

A. 1
B. 4
C. 9
D. 0
Answer» B. 4
Discussion
397.

If is an cute angle and 2 sin + 15 cos = 7 then the value of cot is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"></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>4</center></td><td rowspan="2"></td></tr><td align="center">5</td></table>
C. <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">4</td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"></td></tr><td align="center">4</td></table>
E.
Answer» E.
Discussion
398.

The simplest value of sin x + 2 tan x 2 sec x + cos x is

A. 1
B. 0
C. - 1
D. 2
Answer» B. 0
Discussion
399.

If sin x= x 2x + 2, then the value of x is2

A. 0
B. 1
C. 1
D. None of these
Answer» C. 1
Discussion
400.

A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60 . When he retires 36 m from the bank, he finds that the angle is 30 . The breadth of the river is

A. 15 metre
B. 18 metre
C. 16 metre
D. 11 metre
Answer» C. 16 metre
Discussion