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.

601.

A kite is flying at a height of 50 metre. If the length of string is 100 metre then the inclination of string to the horizontal ground in degree measure is

A. 90
B. 60
C. 45
D. 30
Answer» E.
Discussion
602.

If 3 sin + 5 cos = 5, then the value of 5 sin 3 cos q will be

A. 3
B. 5
C. 2
D. 1
Answer» B. 5
Discussion
603.

If sec + tan = 2, then the value of sin is

A. 0.4
B. 0.5
C. 0.6
D. 0.8
Answer» D. 0.8
Discussion
604.

If sin 21 =
x
 , then sec 21 sin 69 is equal to
y
A. <table><tr><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></tr><td align="center">y <span style=" text-decoration: overline;">y - x </span></td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2"></td></tr><td align="center">x <span style=" text-decoration: overline;">y - x </span></td></table>
C. <table><tr><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></tr><td align="center">y <span style=" text-decoration: overline;">x - y </span></td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2"></td></tr><td align="center">x <span style=" text-decoration: overline;">x - y </span></td></table>
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>y </center></td><td rowspan="2"></td></tr><td align="center">x <span style=" text-decoration: overline;">y - x </span></td></table>
Discussion
605.

The shadow of a tower is

A. 45
B. 30
C. 60
D. 90
Answer» C. 60
Discussion
606.

The value of
sin 65
is
cos 25

A. 0
B. 1
C. 2
D. Not defined
Answer» C. 2
Discussion
607.

The value of the expression (1 + sec 22 + cot 68 ) (1 cosec22 + tan 68 ) is

A. 0
B. 1
C. 1
D. 2
Answer» E.
Discussion
608.

If x sin 60 (3 / 2) sec 60 tan 30 + (4 / 5) sin 45 tan 60 = 0 then x 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">15</td></table>
B.
C. 4
D. <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">15</td> <li style="display: list-item;border:none; list-style-type: upper-alpha;color:#EB586F;font-size:20px;padding: 10px 10px 10px 0px; margin: 0 0 0 30px;font-weight: normal;"> <span style="color:#888; font-size:16px;"> 2 </span> </li> <div id="answer" style="margin-right:10px;"> <div class="well" style="border: 2px solid #DED6DA;background-color:#FFF"> <h5 style="font-weight:bold;color:#EB586F;padding:20px 0px 0px 8px;">Correct Option: <span style="color:#888;">C</span></h5> <p style="color:#888;font-size:14px;padding:0px 0px 0px 15px;"></p><table><tr><td rowspan="2"> x sin 60 </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2">sec 60 . tan 30 </td></tr><td align="center">2</td></table><br><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"> sin 45 . tan 60 = 0<br></td></tr><td align="center">5</td></table><br><img src="http://images.interviewmania.com/wp-content/uploads/2019/09/166a1.png"><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">-<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"> 2 <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1<center><td rowspan="2">+</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"> <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> 3 = 0<br></td></center></center></td></tr><td align="center">4</td><td align="center">2</td><td align="center">3</td><td align="center">5</td><td align="center">2</td></table><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">- 1 +<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>6</center></td><td rowspan="2">= 0</td></tr><td align="center">4</td><td align="center">5</td></table><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">= 1 -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>6</center></td><td rowspan="2">=<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5 - 6<center><td rowspan="2">=</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>- 1</center></td><td rowspan="2"><br></td></center></center></td></tr><td align="center">4</td><td align="center">5</td><td align="center">5</td><td align="center">5</td></table><br><table><tr><td rowspan="2"> x = -</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>- 4<center><td rowspan="2"><br></td></center></center></td></tr><td align="center">5</td><td align="center">3</td><td align="center">15</td></table><br> 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E. 2
Answer» D. <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">15</td> <li style="display: list-item;border:none; list-style-type: upper-alpha;color:#EB586F;font-size:20px;padding: 10px 10px 10px 0px; margin: 0 0 0 30px;font-weight: normal;"> <span style="color:#888; font-size:16px;"> 2 </span> </li> <div id="answer" style="margin-right:10px;"> <div class="well" style="border: 2px solid #DED6DA;background-color:#FFF"> <h5 style="font-weight:bold;color:#EB586F;padding:20px 0px 0px 8px;">Correct Option: <span style="color:#888;">C</span></h5> <p style="color:#888;font-size:14px;padding:0px 0px 0px 15px;"></p><table><tr><td rowspan="2"> x sin 60 </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2">sec 60 . tan 30 </td></tr><td align="center">2</td></table><br><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"> sin 45 . tan 60 = 0<br></td></tr><td align="center">5</td></table><br><img src="http://images.interviewmania.com/wp-content/uploads/2019/09/166a1.png"><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">-<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2"> 2 <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1<center><td rowspan="2">+</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"> <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> 3 = 0<br></td></center></center></td></tr><td align="center">4</td><td align="center">2</td><td align="center">3</td><td align="center">5</td><td align="center">2</td></table><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">- 1 +<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>6</center></td><td rowspan="2">= 0</td></tr><td align="center">4</td><td align="center">5</td></table><br><table><tr><td rowspan="2"> </td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3x</center></td><td rowspan="2">= 1 -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>6</center></td><td rowspan="2">=<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5 - 6<center><td rowspan="2">=</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>- 1</center></td><td rowspan="2"><br></td></center></center></td></tr><td align="center">4</td><td align="center">5</td><td align="center">5</td><td align="center">5</td></table><br><table><tr><td rowspan="2"> x = -</td><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>- 4<center><td rowspan="2"><br></td></center></center></td></tr><td align="center">5</td><td align="center">3</td><td align="center">15</td></table><br> 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Discussion
609.

If sin =
5
 and is acute, what is the value of (cot + tan ) ?
13
A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">5</span></td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>13</center></td></tr><tr><td style="text-align: center;">2 <span style=" text-decoration: overline;">15</span></td></tr></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>-2</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">5</span></td></tr></table>
D. Cannot be determined
Answer» C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>-2</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">5</span></td></tr></table>
Discussion
610.

The expression of
cot + cosec - 1
 is equal to
cot - cosec + 1
A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 + cos </center></td></tr><tr><td style="text-align: center;">sin </td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - cos </center></td></tr><tr><td style="text-align: center;">sin </td></tr></table>
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>cot + 1</center></td></tr><tr><td style="text-align: center;">cosec </td></tr></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>cot - 1</center></td></tr><tr><td style="text-align: center;">cosec </td></tr></table>
E. None of these
Answer» F.
Discussion
611.

If 2y cos = x sin and 2x sec ycosec = 3, then the value of (x

A. 1
B. 2
C. 3
D. 4
Answer» E.
Discussion
612.

If
sinx
 +
sinx
 = 4 ; and 0 < x < 90 , then find the value of x
1 + cosx1 - cosx
A. 10
B. 15
C. 45
D. 30
Answer» E.
Discussion
613.

Find the value of tan (1 + sec2 )(1 + sec 4 ) (1 + sec8 ).

A. tan 10
B. tan8
C. tan 12
D. 1
Answer» C. tan 12
Discussion
614.

2sin
simplifies to:
cos (1 + tan2 )
A. cos
B. cos2
C. sin2
D. sin
Answer» D. sin
Discussion
615.

The value of cos 1 cos 2 cos 3 ... cos 180 is

A. 0
B. 1
C. <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><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» B. 1
Discussion
616.

If sin (90 ) + cos = 2 cos(90 ), then the value of cosec is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;">3</td></tr></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><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">2</span></td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">2</span></td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span></td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">2</span></td></tr></table>
Discussion
617.

If tan 1 = 1, sin 2 =
1
 , then the value of sin ( 1 + 2) equal to
2
A. 1
B. 0
C. 1
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
618.

If sec + tan = m (>1), then the value of sin is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - m<sup>2</sup></center></td></tr><tr><td style="text-align: center;">1 + m<sup>2</sup></td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>m<sup>2</sup> - 1</center></td></tr><tr><td style="text-align: center;">m<sup>2</sup> + 1</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>m<sup>2</sup> + 1</center></td></tr><tr><td style="text-align: center;">m<sup>2</sup> - 1</td></tr></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 + m<sup>2</sup></center></td></tr><tr><td style="text-align: center;">1 - m<sup>2</sup></td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>m<sup>2</sup> + 1</center></td></tr><tr><td style="text-align: center;">m<sup>2</sup> - 1</td></tr></table>
Discussion
619.

If cos 27 = x, the value of tan63 is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">1 - x </span></td></tr></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">1 + x </span></td></tr></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;">1 - x </span></center></td></tr><tr><td style="text-align: center;">x</td></tr></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;">1 + x </span></center></td></tr><tr><td style="text-align: center;">x</td></tr></table>
Answer» B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>x</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">1 + x </span></td></tr></table>
Discussion
620.

If tan (5x 10 ) = cot (5y + 20 ), then the value of (x + y) is

A. 15
B. 16
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></tr><tr><td style="text-align: center;">2</td></tr></table>
D. 24
Answer» 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></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
621.

If x = a sec , y = b tan , then

A. - 1
B. 0
C. 1
D. 2
Answer» D. 2
Discussion
622.

If cos 20 = m and cos 70 = n, then the value of m

A. 1
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span></td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
623.

If (a

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2ab</center></td></tr><tr><td style="text-align: center;">a<sup>2</sup> - b<sup>2</sup></td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a<sup>2</sup> - b<sup>2</sup></center></td></tr><tr><td style="text-align: center;">2ab</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>ab</center></td></tr><tr><td style="text-align: center;">a<sup>2</sup> - b<sup>2</sup></td></tr></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a<sup>2</sup> - b<sup>2</sup></center></td></tr><tr><td style="text-align: center;">ab</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>ab</center></td></tr><tr><td style="text-align: center;">a<sup>2</sup> - b<sup>2</sup></td></tr></table>
Discussion
624.

If x sin

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></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. 2
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></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
625.

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a + b + c = ab + bc + ca, then the value of sin A + sin B + sin C is

A. <table><tr><td rowspan="2"></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">4</td></table>
B. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3 <span style=" text-decoration: overline;">3</span></center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
C. <table><tr><td rowspan="2"></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">2</td></table>
D.
E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>9</center></td><td rowspan="2"></td></tr><td align="center">4</td></table>
Answer» E. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>9</center></td><td rowspan="2"></td></tr><td align="center">4</td></table>
Discussion
626.

If sin + cos = p and sec + cosec = , then the value of (p 1) is

A. 1
B. p
C. 2p
D. 2
Answer» D. 2
Discussion
627.

If a pole of 12 m height casts a shadow of 4

A. 30
B. 60
C. 45
D. 90 16 cm is
Answer» C. 45
Discussion
628.

A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot of the tower are 60 and 30 respectively. The height of the tower is

A. 20 m
B. 30 m
C. 40 m
D. 50 m
Answer» D. 50 m
Discussion
629.

The angle of elevation of sun changes from 30 to 45 , the length of the shadow of a pole decreases by 4 metres, the height of the pole is

A. 1.464 m
B. 9.464 m
C. 3.648 cm
D. 5.464 m
Answer» E.
Discussion
630.

The angle of elevation of a ladder leaning against a house is 60 and the foot of the ladder is 6.5 metres from the house. The length of the ladder is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>13</center></td><td rowspan="2">m</td></tr><td align="center"> <span style=" text-decoration: overline;">3</span></td></table>
B. 13 metres
C. 15 metres
D. 3.25 metres
Answer» C. 15 metres
Discussion
631.

The angle of elevation of the top of a tower of height 100

A. 45
B. 60
C. 30
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. 30
Discussion
632.

A hydrogen-filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60 and 45 respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to

A. 7 km./hr.
B. 11 km./hr.
C. 26 km./hr.
D. 33 km./hr.
Answer» E.
Discussion
633.

If tan 9 = (p / q) , then the value of (sec 81 / 1 + cot 81 ) is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>q</center></td><td rowspan="2"></td></tr><td align="center">p</td></table>
B. 1
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>p </center></td><td rowspan="2"></td></tr><td align="center">q </td></table>
D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>q </center></td><td rowspan="2"></td></tr><td align="center">p </td></table>
Answer» E.
Discussion
634.

If (sin + cosec ) + (cos + sec ) = k + tan + cot , then the value of k is

A. 1
B. 7
C. 3
D. 5
Answer» C. 3
Discussion
635.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is :

A. 4 metre
B. 7 metre
C. 9 metre
D. 6 metre
Answer» E.
Discussion
636.

A telegraph post is bent at a point above the ground. Its top just touches the ground at a distance of 8

A. 12
B. 16
C. 18
D. 24
Answer» E.
Discussion
637.

The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30 . The height (in metres) that the pillar must be raised so that its angle of elevation at the same point may be 45 , is (Take,

A. 63.4
B. 86.6
C. 126.8
D. 173.2
Answer» B. 86.6
Discussion
638.

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be and ( > ). The height of the tower is h unit. A possible distance (in the same unit) between the points is

A. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h(cot - cot )</center></td><td rowspan="2">metre</td></tr><td align="center">cos( + )</td></table>
B. h (cot - cot )
C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h(tan - tan )</center></td><td rowspan="2">metre</td></tr><td align="center">tan tan )</td></table>
D. h (cot + cot )
Answer» E.
Discussion
639.

An aeroplane flying horizontally at a height of 3 km. above the ground is observed at a certain point on earth to subtend an angle of 60 . After 15 seconds of flight, its angle of elevation is changed to 30 . The speed of the aeroplane (Take,

A. 230.63 m./sec.
B. 230.93 m./sec.
C. 235.85 m./sec.
D. 236.25 m./sec.
Answer» C. 235.85 m./sec.
Discussion