Question 1 :
If {tex} f: R \rightarrow R {/tex} and {tex} g: R \rightarrow R {/tex} are defined by {tex} f ( x ) = | x | {/tex} and {tex} g ( x ) = [ x - 3 ] {/tex} for {tex} x \in R , {/tex} then {tex} \left\{ g ( f ( x ) ): - \frac { 8 } { 5 } < x < \frac { 8 } { 5 } \right\} {/tex} is equal to
Question 2 :
If {tex} y = \log _ { 2 } \left\{ \log _ { 2 } ( x ) \right\} , {/tex} then {tex} \frac { d y } { d x } {/tex} is
Question 3 :
Let {tex} y = \sin ^ { 2 } x + \cos ^ { 4 } x . {/tex} Then for all real {tex} x {/tex}
Question 4 :
The function {tex} f ( x ) = [ x ] ^ { 2 } - \left[ x ^ { 2 } \right] {/tex} (where [y] is the greatest integer less than or equal to y), is discontinuous at
Question 5 :
{tex} \operatorname { Let } f ( x ) = | x - 1 | . {/tex} Then
Question 6 :
The domain of the function {tex} f ( x ) = \sqrt { x - \sqrt { 1 - x ^ { 2 } } } {/tex} is
Question 7 :
If {tex}\mathrm A {/tex} and {tex}\mathrm B {/tex} are two events such that {tex}\mathrm P (\mathrm A ) = \frac { 1 } { 2 } {/tex} and {tex}\mathrm P (\mathrm B ) = \frac { 2 } { 3 } , {/tex} then
Question 8 :
A survey shows that {tex} 63 \% {/tex} of the Americans like cheese whereas {tex} 76 \% {/tex} like apples.If {tex} x \% {/tex} of the Americans like both cheese and apples, then
Question 9 :
The angle between the pair of tangents drawn to the ellipse {tex} 3 \mathrm { x } ^ { 2 } + 2 \mathrm { y } ^ { 2 } = 5 {/tex} from the point {tex}(1,2){/tex} is
Question 10 :
If {tex} \sin ^ { - 1 } \frac { 2 a } { 1 + a ^ { 2 } } + \sin ^ { - 1 } \frac { 2 b } { 1 + b ^ { 2 } } = 2 \tan ^ { - 1 } x {/tex} then {tex} x {/tex} is equal to<br>
Question 11 :
The sum of the series {tex} 3 + 33 + 333 + \ldots \ldots + n {/tex} terms is
Question 12 :
The set of points where {tex} f ( x ) = {/tex} {tex} ( x - 1 ) ^ { 2 } ( x + | x - 1 | ) {/tex} is thrice differentiable, is
Question 13 :
If a positive integer {tex} n {/tex} is divisible by 9 , then the sum of the digits of {tex} n {/tex} is divisible by 9 . So which statement is it contrapositive.
Question 14 :
If {tex} \vec { a } + \vec { b } + \vec { c } = 0 , | \vec { a } | = 3 , | \vec { b } | = 5 , | \vec { c } | = 7 , {/tex} then the angle between {tex} \vec { a } {/tex} and {tex} \vec { b } {/tex} is :
Question 15 :
{tex} \int \frac { d x } { \cos x + \sqrt { 3 } \sin x } {/tex} equals
Question 16 :
If {tex} f ( x ) {/tex} is differentiable and strictly increasing function, then the value of {tex} \lim _ { x \rightarrow 0 } \frac { f \left( x ^ { 2 } \right) - f ( x ) } { f ( x ) - f ( 0 ) } {/tex} is
Question 17 :
The order of the differential equation<br>{tex} \left[ 1 + 5 \left( \frac { \mathrm { dy } } { \mathrm { dx } } \right) ^ { 2 } \right] ^ { 3 / 2 } = 11 \left( \frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } \right) ^ { 5 } \mathrm { is } {/tex}<br>
Question 18 :
The inverse of the statement {tex} ( p \wedge \sim q ) \rightarrow r {/tex} is
Question 19 :
The negation of the compound proposition {tex} p \vee ( \sim p \vee q ) {/tex} is
Question 20 :
If {tex} 0 < \alpha , \beta , \gamma < \frac { \pi } { 2 }{/tex} such that {tex} \alpha + \beta + \gamma = \frac { \pi } { 2 } {/tex} and {tex} \cot \alpha , \cot \beta , {/tex} cot {tex} \gamma {/tex} are in arithmetic progression, then the value of {tex} \cot \alpha \cot \gamma {/tex} is
Question 21 :
The function {tex} f ( x ) = \tan ^ { - 1 } ( \sin x + \cos x ) {/tex} is an increasing function in
Question 22 :
The value of {tex} \cos \frac { 2 \pi } { 7 } + \cos \frac { 4 \pi } { 7 } + \cos \frac { 6 \pi } { 7 } {/tex} is
Question 23 :
If {tex} y = \tan ^ { - 1 } \left( \frac { 2 ^ { x } } { 1 + 2 ^ { 2 x + 1 } } \right) , {/tex} then {tex} \frac { d y } { d x } {/tex} at {tex} x = 0 {/tex} is
Question 24 :
If {tex} \frac { \tan 3 \theta - 1 } { \tan 3 \theta + 1 } = \sqrt { 3 } , {/tex} then the general value of {tex} \theta {/tex} is
Question 25 :
If {tex} \int \frac { 1 } { 1 + \sin x } d x = \tan \left( \frac { x } { 2 } + a \right) + b {/tex} then
Question 26 :
If {tex} \Delta ( x ) = \left| \begin{array} { c c } e ^ { x } & \sin x \\ \cos x & \ln \left( 1 + x ^ { 2 } \right) \end{array} \right| , {/tex} then the value of {tex} \lim \limits_ { x \rightarrow 0 } \frac { \Delta ( x ) } { x } {/tex} is<br>
Question 27 :
The function {tex} f ( x ) = ( x - 3 ) ^ { 2 } {/tex} satisfies all the conditions of mean valuess point on theorem in {tex} \{ 3,4 \} . {/tex} A pont is {tex} y = ( x - 3 ) ^ { 2 } , {/tex} where the tangent is parallel to the chord joining ( 3,0 ) and ( 4,1 ) is
Question 28 :
The number of value(s) of x in the interval [0,5π] satisfying the inequation3sin<sup>2</sup>x – 7sinx + 2 < 0such that sinx is an integer is
Question 29 :
The value of<br>{tex} \int _ { - \pi / 4 } ^ { \pi / 4 } \left( x | x | + \sin ^ { 3 } x + x \tan ^ { 2 } x + 1 \right) d x {/tex}<br>
Question 30 : Let ABCDA'B'C'D' be a cuboid as shown in the following figure<img style='object-fit:contain' style="vertical-align: middle" alt="Image not present" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f4776d72c9e0b48ffba5033"><br>There are twelve face diagonals two on each face. (such as AC & BD, A'C' & B'D' etc)<br>How many pairs of them are skew lines (line segments) ?
Question 31 :
If {tex} ( 7 - 4 \sqrt { 3 } ) ^ { x ^ { 2 } - 4 x + 3 } + {/tex} {tex} ( 7 + 4 \sqrt { 3 } ) ^ { x ^ { 2 } - 4 x + 3 } = 14 {/tex}, then the value of {tex} x {/tex} is given by<br>
Question 32 :
The length of the perpendicular from the origin to a line is 7 and line makes an angle of {tex} 150 ^ { \circ } {/tex} with the positive direction of {tex} y {/tex}-axis, then the equation of the line is
Question 33 :
If {tex} x + y - z + x y z = 0 , {/tex} then {tex} \frac { 2 x } { 1 - x ^ { 2 } } + \frac { 2 y } { 1 - y ^ { 2 } } - \frac { 2 z } { 1 - z ^ { 2 } } {/tex} is equal to
Question 34 :
Let {tex} f ( x ) = \frac { x - \{ x + 1 \} } { x - \{ x + 2 \} } ; {/tex} where {tex} \{ \mathrm { x } \} {/tex} is the fractional part of {tex} \mathrm { x } {/tex}, then {tex} \lim _ { x \rightarrow 1 / 3 } \mathrm { f } ( \mathrm { x } ) {/tex}
Question 35 :
Let f be a real valued function defined as f : R → R f(x) = |x<sup>2</sup> – 6x + 8| sin((x – 2)π) + |e<sup>x</sup> – 1|sinx + |x<sup>2</sup>| The number of points of non-differentiability is
