JEE Advanced (Fill in the Blanks): Differentiation | Mathematics for Airmen Group X - Airforce X Y / Indian Navy SSR PDF Download

Fill in the Blanks

Q. 1.  and f '(x) = sin x² , then   ....................

Ans. 

Solution. 

Q. 2. If f_r (x), g (x), h_r (x) r , r = 1, 2, 3 are polynomials in x such that fr(a) = g_r (a) = h_r(a), r = 1, 2, 3

....................

Ans. 0 

Solution. 

Where f_r(x), g_r(x), h_r(x), r = 1, 2, 3, are polynominals in x and hence differentiable and

f_r(a) = gr(a) = hr(a), r = 1, 2, 3 … (2)

Differentiating eq. (1) with respect to x, we get

Using eq. (2) we get D₁ = D₂ = D₃ = 0 [By the property of determinants that D = 0 if two rows in D are identical]
∴ F'  (a) = 0.

Q. 3. If f(x) = log_x (ln x), then f '(x) at x = e is ....................

Ans. 1/e

Solution. Given that

Q. 4. The derivative of at = 1/2 is .......

Ans. 4

Solution.

Q. 5.  If f (x) = | x – 2 | and g(x) = f [f(x)], then g'(x) = .................... for x > 20

Ans. 1

Solution. f (x) = | x – 2 |
⇒ g (x) = f (f (x)) = | f (x) – 2 | as x > 20
= || x - 2| -2 | = |x - 2- 2| as x > 20 = | x – 4 |
= x – 4 as x > 20  
∴ g' (x) = 1

Q. 6. If xe^xy = y + sin² x, then at x = 0, dy/dx = ......

Ans. 1

Solution. Given : xe^xy = y + sin² x

Differentiating both sides w. r.to x, we get

True/ False

Q. 1. The derivative of an even function is always an odd function.

Ans. T

Solution.  , which is an even function