Test: JEE Main 35 Year PYQs- Limits, Continuity & Differentiability - Airforce X Y / Indian Navy SSR MCQ

denotes greatest integer less than or equal to x)

If f(1) = 1, f ¹ (1) = 2, then 

f is defined in [-5, 5] as f(x) = x if x is rational = –x if x is irrational. Then

f(x) and g(x) are two differentiable functions on [0, 2] such that f ''( x) - g '' (x)= 0, f ' (1) =2g'(1)=4 f(2) =3g(2) = 9 then f(x)–g(x) at x = 3/2 is

 and f (5) = 2,f '(0)= 3 , then f ' (5) is

the value of k is

The value of 

Let f (a) = g (a) = k  and their nth derivatives

fⁿ (a) , gⁿ (a) exist and are not equal for some n. Further if

then the value of k is

then the values of a and b, are

 is continuous

equals

Let a and b be the distinct roots of ax² + bx +c = 0 , then 

Suppose f(x) is differentiable at x = 1 and 

Let f  be differentiable for all x. If f (1) = – 2 and f '(x) > 2 for x ∈ [1, 6], then

If f is a real valued differentiable function satisfying

|f (x) – f (y) | < ( x -y)² , x, y ∈ R and f (0) = 0, then f (1) equals

Let f : R → R be a function defined by f (x) = min {x + 1,x+ 1} ,Then which of the following is true ?

The function f : R /{0} → R given by

can be made continuous at x = 0 by defining f (0) as

Then which one of the following is true?

Let f : R →R be  a positive incr easing function with 

The values of p and q for which the function 

Let f : R → [0, ∞) be such that    exists and 

If f : R → R is a function defined by f (x) = [x]  where [x] denotes the greatest integer function, then f is .