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# Limits and Derivatives

#### Multiple Choice Questions

41.

is equal to

• $2\mathrm{csc}\left(2\mathrm{\alpha }\right)$

• $\frac{1}{2}\mathrm{sin}\left(2\mathrm{\alpha }\right)$

• None of these

D.

None of these

42.

For each t ∈R, let [t] be the greatest integer less than or equal to t. Then

• does not exist (in R)

• is equal to 0

• is equal to 15

• is equal to 120

D.

is equal to 120

43.
• 1/4

• 1/24

• 1/16

• 1/16

C.

1/16

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44.

If 5(tan2x – cos2x) = 2cos 2x + 9, then the value of cos4x is

• -7/9

• -3/5

• 1/3

• 1/3

A.

-7/9

⇒5(1 – t – t2) = t(4t + 7)
⇒ 9t2 + 12t – 5 = 0
⇒ 9t2 + 15t – 3t – 5 = 0
⇒ (3t – 1) (3t + 5) = 0
⇒ t = t/3 as t≠-5/3.
cos2x = 2(1/3)-1 = -1/3

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