Question 1 :
In order that the function f(x) = (x + 1)<sup>cotx</sup> is continuous at x = 0, f(0) must be defined as
Question 2 : The point of discontinuity of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c8619f8d44d3a17fadb' height='37' width='95' > is -
Question 4 :
The number of points of discontinuity of f(x) = [x<sup>3</sup> +1] in<br>(1, 2) is/are
Question 5 : If x is real number in [0, 1], then the value of <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cf275ed294f2c7c42ed' height='27' width='55' >[1 + cos<sup>2m</sup> (n!πx)] is given by
Question 6 : At the point x = 1, the function f(x) =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c8be6d3604eaa92ed3f' height='47' width='117' > is:
Question 7 :
If A and B are square Matrices of order 3 such that |A| = -1 , |B| = 3 then |3AB| = ---------
Question 8 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c8419f8d44d3a17fad6' height='41' width='100' >
then the function is non differentiable at -
Question 9 : If <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c87e6d3604eaa92ed33' height='68' width='161' >
then at x = 1 f(x) is continuous if -
Question 10 : <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cec75ed294f2c7c42db' height='27' width='57' >, where [.] is GIF, is
Question 12 : Let f(x)=4 and f'(x)= 4. Then <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d2d75ed294f2c7c439c' height='51' width='179' > is given by
Question 14 :
f is defined in [-5, 5] as F(x)= x if x is rational = -x if x is irrational. Then
Question 15 : <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870a8475ed294f2c7c3bd7' height='27' width='25' ><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870bea75ed294f2c7c3fa7' height='40' width='93' > equals -
Question 16 :
Let f:R →R be a function defined as f(x)= Min{ 1 +x, 1 + |x|} then which of the following is correct
Question 17 :
Let f(x) = [tan<sup>2</sup>x], where [.] denotes the greatest integer function. Then
Question 18 : Function f (x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c7419f8d44d3a17faac' height='39' width='68' > where [.] is GIF. is
Question 20 : A function f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d0375ed294f2c7c431a' height='44' width='79' >, α ≠ mπ is continuous at x = α then
Question 21 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c76e6d3604eaa92ed0c' height='41' width='176' >Where [.] is G.I.F. then -
Question 22 : Which point is not a point of discontinuity of the function f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c98e6d3604eaa92ed6b' height='37' width='57' >
Question 23 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cfbe6d3604eaa92eea7' height='68' width='91' >
is continuous " x ∈ R then (A, B) is-
Question 24 :
Consider the function f(x) = |x - 1| + |x - 2|
Question 25 : The value of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870bee19f8d44d3a17f909' height='56' width='109' > is -
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 : If f is a real valued differentiable function satisfying <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d42e6d3604eaa92ef8a' height='29' width='402' >, then f(1) equals
Question 28 :
{tex}\underset { x \rightarrow 0 }\lim \frac { \sin x + \log ( 1 - x ) } { x ^ { 2 } } {/tex} is equal to
Question 29 : Let ƒ(x) = x - [x], where [x] denotes the greatest integer ≤ x and g(x) =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870a8e75ed294f2c7c3be7' height='28' width='29' ><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cdf75ed294f2c7c42b3' height='44' width='72' > , then g(x) is equal to -
Question 30 :
If {tex} f ( x ) = \left\{ \begin{array} { c c } { \frac { 1 - \sin x } { \pi - 2 x } , } & { x \neq \frac { \pi } { 2 } } \\ { \lambda , } & { x = \frac { \pi } { 2 } } \end{array} , \text { be continuous at } x = \pi / 2 , \text { } \right. {/tex} then value of {tex} \lambda {/tex} is<br>
Question 31 :
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 32 :
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 33 :
{tex}\underset{ x \rightarrow 0 } \lim \left( \frac { 1 + \tan x } { 1 + \sin x } \right) ^ { cosec x } {/tex} is equal to
Question 34 :
The domain of definition of the function f(x) given by the equation 2<sup>x</sup> + 2<sup>y</sup> = 2 is
Question 35 : The point of discontinuity in <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c6fe6d3604eaa92ecf5' height='39' width='53' > of f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c6f19f8d44d3a17fa9f' height='35' width='57' > is
Question 36 :
{tex} \underset{{ x \rightarrow 0 }}\lim \frac { \sqrt { \frac { 1 } { 2 } ( 1 - \cos 2 x ) } } { x } = {/tex}
Question 37 : 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 39 :
The function {tex} y = | \sin x | {/tex} is continuous for any {tex} x {/tex} but it is not differentiable at
Question 40 :
Function {tex} y = \sin ^ { - 1 } \left( \frac { 2 x } { 1 + x ^ { 2 } } \right) {/tex} is not differentiable for
Question 41 :
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 42 : If f(x) = sin<sup>-1</sup><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c7919f8d44d3a17fabd' height='41' width='51' >, then f(x) is differentiable on :
Question 43 :
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 44 :
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 45 :
{tex}\underset{ x \rightarrow 0 } \lim \frac { 1 + \sin x - \cos x + \log ( 1 - x ) } { x ^ { 3 } } {/tex} equals
Question 46 :
{tex}\underset{ x \rightarrow 0 }\lim x ^ { x } = {/tex}
Question 47 : <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870b8219f8d44d3a17f7a4' height='43' width='147' > , given that f'(2) = 6 and f'(1) = 4
Question 48 : 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 49 :
A point where function ƒ(x) is not continuous where ƒ(x) = [sin [x]] in (0, 2π) [.] denotes greatest integer ≤ x is -
Question 50 :
A function {tex} f ( x ) = \left\{ \begin{array} { l l } { 1 + x , } & { x \leq 2 } \\ { 5 - x , } & { x > 2 } \end{array} \right. {/tex}
