InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the magnitude, in radians and degrees, of the interior angle of aregular(i)pentagon (ii)octagon(iii) heptagon (iv) duodecagon. |
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Answer» Sum of the interior angles of n-sided polygon is given as `(n-2)*pi`. `:.` Interior angle of regular polygon `= ((n-2)*pi)/n` (i) Interior angle of regular pentagon `= ((5-2)*pi)/5 = (3pi)/5` radians Interior angle in degrees `= 3/5*180 = 108^@` (ii) Interior angle of regular octagon`= ((8-2)*pi)/8 = (6pi)/8 = (3pi)/4` radians Interior angle in degrees `= 3/4*180 = 135^@` (iii) Interior angle of regular heptagon `= ((7-2)*pi)/7 = (5pi)/7` radians Interior angle in degrees `= 5/7*180 = (900/7) ^@` (iv) Interior angle of regular duodecagon`= ((12-2)*pi)/12 = (5pi)/6` radians Interior angle in degrees `= 5/6*180 = 150 ^@` |
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| 2. |
In a right-angled triangle, the difference between the two acute angles is `(pi/15)^(c )`. Find the angle in degrees. |
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Answer» Clearly, the sum of the two acute anles of a right triangleis `90^(@)`. Difference between the acute angles `= (pi/15)^(c )= (pi/15 xx 180/pi)^(@) = 12^(@)`. Let the two acute be `x^(@)` and `y^(@)` . Then, `x + y= 90 "…….."(i)` `x- y = 12 "............" (ii)` Solving (i) and (ii), we get `x = 51` and `y = 39`. Hence, the angles of triangleare `51^(@), 39^(@)` and `90^(@)`. |
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| 3. |
Find the angle between the minute hand and the hour hand of a clock at 7.20 am |
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Answer» Angle traced by the hour hand in `12` hours `= 360^(@)`, Angle traced by it in `7 h 20` min i.e., in `22/3` ho `= (360/12 xx 22/3)^(@) = 220^(@)` Angle traced by the minute hand in `60` min `= 360^(@)`. Angle traced by the minute hand in `20` min `(360/12 xx 20)^(@) = 120^(@)`. Hence, the required anle between the two hands. `= (220^(@) - 120^(@)) = 100^(@)`. |
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| 4. |
A wheel makes 360 revolutions in one minute.Through how many radians does it turn in one second? |
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Answer» Number of revolutions made in 60 secons `= 360`. Number of revolutions made in `1` second = `(360)/(60) = 6`. Angle moved in 1 revolutions made in 1 second` = (360)/(60) = 6`. Angle moved in 1 revolution `= (2pi)^(c )` Angle moved in 6 revolutions `= (2pi xx 6)^(c) = (12pi)^(c )`. |
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| 5. |
The large hand of a clock is 42 cm long. How many centimetres does its extremity move in 20 minutes. |
| Answer» Correct Answer - `88 cm` | |
| 6. |
The angles of a quadrilateral are in AP, and the greatest angle is double the least. Express the least angle in radians. |
| Answer» Correct Answer - `((pi)/3)^(c )` | |
| 7. |
Find in degrees the angle through which a pendulum swings if its lengthis `50c m`and the tip describes an arc of length `10c m`. |
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Answer» Here, length of arc, `l = 10cm` Length of pendulam, `r = 50cm` We know, `rtheta = l` `=>50theta = 10` `=>theta = 1/5 radian` `=>theta = 1/5(360/(2pi))^@ = (36/pi)^@` |
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