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

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# Limits and Derivatives

#### Multiple Choice Questions

1. • π/2

• 1

301 Views

2. • -1/4

• 1/2

• 1

• 1

188 Views

3.

The equation of the tangent to the curve y = x +4/x2, that is parallel to the x-axis, is

• y= 0

• y= 1

• y= 2

• y= 2

162 Views

4.

Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0 ≤α,β ≤ π/4. Then tan 2α is equal to

• 25/16

• 56/33

• 19/12

• 19/12

145 Views

5. • 1/4

• 1/24

• 1/16

• 1/16

396 Views

# 6.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 = -1/3 542 Views

7.

The differential equation which represents the family of curves y=c1ec2xe, where c1 and c2 are arbitrary constants, is

• y' =y2

•  y″ = y′ y

• yy″ = y′

• yy″ = y′

120 Views

8.

The solution of the differential equation satisfying the condition y (1) = 1 is

• y = ln x + x

• y = x ln x + x2

•  y = xe(x−1)

•  y = xe(x−1)

128 Views

9.

If then the values of a and b, are

• • • • 117 Views

10.

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