Question 1 :
Let f : R → R be a function defined by f(x) = max {x, x<sup>3</sup>}. The set of all points where f(x) is NOT differentiable is
Question 2 :
The value of {tex}\underset{ x \rightarrow 0 } \lim \frac { \log \left[ 1 + x ^ { 3 } \right] } { \sin ^ { 3 } x } = {/tex}
Question 3 :
{tex} \underset{ x \rightarrow 0 }\lim \frac { \log ( a + x ) - \log a } { x } + k \underset{ x \rightarrow e }\lim\frac { \log x - 1 } { x - e } = 1 , {/tex} then
Question 4 :
{tex} \underset{{ x \rightarrow 0 }}\lim \frac { \sqrt { \frac { 1 } { 2 } ( 1 - \cos 2 x ) } } { x } = {/tex}
Question 5 :
A point where function ƒ(x) is not continuous where ƒ(x) = [sin [x]] in (0, 2π) [.] denotes greatest integer ≤ x is -
Question 6 :
If {tex}\underset{ x \rightarrow 0 } \lim \frac { [ ( a - n ) n x - \tan x ] \sin n x } { x ^ { 2 } } = 0 , {/tex} where {tex} n {/tex} is a non-zero real number, then {tex} a {/tex} is equal to<br>
Question 7 :
Exhaustive set of values of x satisfying log<sub>|X|</sub>(x<sup>2</sup> + x +1) ≥ 0 is
Question 8 :
If {tex} f ( x ) = \left\{ \begin{align*}
x + \lambda ,\ & x < 3 \\
4 ,\ & x = 3 & \text { is continuous at } x = 3 , \text { then } \lambda \\
3 x - 5 , \ &x > 3
\end{align*} \right. {/tex}
Question 9 :
The function {tex} y = e ^ { - | x | } {/tex} is
Question 10 :
{tex}\underset{ x \rightarrow 0 }\lim x ^ { x } = {/tex}
Question 11 :
The function ƒ(x) = [x]<sup>2 </sup>- [x<sup>2</sup>] (where [y] is the greatest integer less than or equal to (y), is discontinuous at -
Question 12 :
If {tex} f ( x ) = \left\{ \begin{array} { l l } { \frac { 1 - | x | } { 1 + x } , } & { x \neq - 1 } \\ { 1 , } & { x = - 1 } \end{array} , \text { } \text { } \right. {/tex}then the value of {tex}f ( [ 2 x ] ){/tex} will be<br>(where [1 shows the greatest integer function)<br>
Question 13 :
{tex}\underset{ x \rightarrow 0 } \lim \left( \frac { 1 + \tan x } { 1 + \sin x } \right) ^ { cosec x } {/tex} is equal to
Question 14 :
The value of {tex} f {/tex} at {tex} x = 0 {/tex} so that the function {tex} f ( x ) = \frac { 2 ^ { x } - 2 ^ { - x } } { x } , x \neq 0 , {/tex} is continuous at {tex} x = 0 {/tex} is<br>
Question 15 : y = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cff19f8d44d3a17fc67' height='37' width='55' > where t =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d00e6d3604eaa92eeb5' height='36' width='31' >, then the number of points of discontinuities of y = f(x), x ∈ R is-
Question 16 :
Function {tex} y = \sin ^ { - 1 } \left( \frac { 2 x } { 1 + x ^ { 2 } } \right) {/tex} is not differentiable for
Question 17 : The range of the function <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d1719f8d44d3a17fcb4' height='32' width='112' > is [2004]
Question 18 :
The function {tex} y = | \sin x | {/tex} is continuous for any {tex} x {/tex} but it is not differentiable at
Question 19 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870b4619f8d44d3a17f6e8' height='45' width='121' >, then fof(x) is given by
Question 20 : For the function f(x) =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c93e6d3604eaa92ed59' height='92' width='84' >following are true
Question 22 : Let f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c9419f8d44d3a17fb0a' height='60' width='100' > be continuous and differentiable every where. The a and b are -
Question 23 :
The domain of definition of the function f(x) given by the equation 2<sup>x</sup> + 2<sup>y</sup> = 2 is
Question 24 :
{tex}\underset { x \rightarrow 0 }\lim \frac { \sin x + \log ( 1 - x ) } { x ^ { 2 } } {/tex} is equal to
Question 25 : If the function ƒ(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c6b75ed294f2c7c4144' height='47' width='61' > sin (x - 2) + a cos (x - 2), (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then -
Question 26 :
If {tex} f ( x ) = \left\{ \begin{array} { l l } { a x ^ { 2 } + b ; } & { x \leq 0 } \\ { x ^ { 2 } ; } & { x > 0 } \end{array} \text { possesses derivative at } x = 0 , \text { then } \right. {/tex}
Question 27 :
Given that {tex} f ^ { \prime } ( 2 ) = 6 {/tex} and {tex} f ^ { \prime } ( 1 ) = 4 , {/tex} then {tex} \underset{ h \rightarrow 0 }\lim \frac { f \left( 2 h + 2 + h ^ { 2 } \right) - f ( 2 ) } { f \left( h - h ^ { 2 } + 1 \right) - f ( 1 ) } {/tex}<br>
Question 28 :
Let a function ƒ : R→ R satisfy the equation ƒ(x + y) = ƒ(x) + ƒ(y) for all x, y. If the function ƒ(x) is continuous at x = 0, then -
Question 30 :
Let ƒ(x) = Sgn (x) and g(x) = x(x<sup>2</sup> - 5x + 6). The function f(g(x)) is discontinuous at -
