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Trigonometric Functions

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Question

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$If space sin to the power of negative 1 end exponent space open parentheses straight x over 5 close parentheses space plus space cosec to the power of negative 1 end exponent space open parentheses 5 over 4 close parentheses space equals space straight pi over 2$ then the value of x

1

3

4

5

Solution

B.

3

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Question

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$limit as straight n rightwards arrow infinity of space open square brackets 1 over straight n squared sec squared space 1 over straight n squared plus 2 over straight n squared space plus 2 over straight n squared sec squared 4 over straight n squared plus.....1 over straight n squared sec squared 1 close square brackets equal$
$1 half sec space 1$
$1 half cosec space 1$

tan 1

$1 half tan space 1$

Solution

D.

1 half tan space 1

limit as straight n rightwards arrow infinity of space open square brackets 1 over straight n squared sec squared 1 over straight n squared plus 2 over straight n squared sec squared 4 over straight n squared plus 3 over straight n squared sec squared 9 over straight n squared plus..... plus 1 over straight n sec squared 1 close square brackets

is equals

limit as straight n rightwards arrow infinity of space straight r over straight n squared space sec squared space straight r squared over straight n squared space equals space limit as straight n rightwards arrow infinity of 1 over straight n. straight r over straight n space sec squared straight r squared over straight n squared

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$If space straight l subscript 1 space equals space integral subscript 0 superscript 1 space 2 to the power of straight x squared 1 end exponent space dx comma space straight I subscript 2 space equals space integral subscript 0 superscript 1 space 2 to the power of straight x cubed end exponent space dx space comma space straight I subscript 3 space equals space integral subscript 1 superscript 2 space 2 to the power of straight x squared space end exponent dx space and space straight I subscript 4 space equals space integral subscript 1 superscript 2 2 to the power of straight x cubed space end exponent space dx space then$

I₂ > I₁

I₁ > I₂

I₃ = I₄

I₃ > I₄

Solution

B.

I₁ > I₂

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Question

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A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^o. Then the time taken (in minutes) by him, from B to reach the pillar, is:

6

10

20

5

Solution

D.

5

According to given information, we have the following figure:
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Now, from ΔACD and ΔBCD, we have
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∵ speed is uniform.
∵ distance y will be cover in 5 min
∵ distance x covered in 10 min
∵ Distance x/2 will be cover in 5 min

Question

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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60^o and when he retires 40 meters away from the tree the angle of elevation becomes 30^o. The breadth of the river is

20 m

30 m

40 m

60 m

Solution

A.

20 m

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