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**Q.1. The number of real roots of the equation is (2020)****(1) 1****(2) 3****(3) 2(4) 4**

The given equation is

Let e

Dividing both sides of the equation by t

Again,

Let

Then, y

â‡’ y = -2, 3

Now, and (not possible)

Hence, e

(1) 3/4

(2)

We have,

(1)

(2)

From Eqs. (1) and (2), we have

Now,

Ans.

Solution.

(1) -4

(2) 30

(3) -2

(4) 8

Solution.

x log

Differentiate both sides w.r.t. x,

(4) x log

(2x)

â‡’

(1) 2e

(2) 4e

(3) 2e

(4) 4e

Since, f'(x) = f(x)

Since, the given condition

f(1) = 2

From eq

f(x) = e

Then, f(1) = e

â‡’ 2 = e

â‡’ 2/e = e

Then, from eq

â‡’

Now

â‡’

(1) 33

(2) 12

(3) 15

(4) 9

Solution.

Given, e

Putting x = 0 in (i), â‡’ e

On differentiating (i) w. r. to x

...(ii)

Putting y = 1 and x= 0 in (ii),

On differentiating (ii) w. r. to x,

(1) y/x

(1) - y/x

(1) - x/y

(1) x/y

Ans:

(1) -34

(2) -2

(3) 4

(4) -32

Ans:

Solution:

(1) f(2) + f'(2) = 28

(2) f"(2) - f'(2) = 0

(3) f(2) - f'(2) + f"(2) = 10

(4) f"(2) - f(2) = 4

(1) 4/3

(2) 1/3

(3) 5/3

(4) 8/3

Ans.

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