Question 1 :
The domain of the function {tex} f ( x ) = \frac { x ^ { 2 } + 3 x + 5 } { x ^ { 2 } - 5 x + 4 } {/tex} is
Question 2 :
The period of {tex} \sin ^ { 2 } \theta {/tex} is
Question 4 :
If
{tex} f ( x ) = \left\{ \begin{array} { l } { x , \text { when } x \text { is rational } } \\ { 0 , \text { when } x \text { is irrational } } \end{array} ;
g ( x ) = \left\{ \begin{array} { l } { 0 , \text { when } x \text { is rational } } \\ { x , \text { when } x \text { is irrational } } \end{array} \right. \right. {/tex}<br>then {tex} ( f - g ) {/tex} is<br>
Question 5 :
The function {tex} f ( x ) = \log ( x + \sqrt { x ^ { 2 } + 1 } ) , {/tex} is
Question 6 :
If the function {tex} f : [ 2 , \infty ) \rightarrow [ 1 , \infty ) {/tex} is defined by {tex} f ( x ) = 3 ^ { x ( x - 2 ) } , {/tex} then what is {tex} f ^ { - 1 } ( x ) ? {/tex}
Question 7 :
The domain of {tex}f ( x ) = \frac { 1 } { \sqrt { 2 x - 1 } } - \sqrt { 1 - x ^ { 2 } } {/tex}
Question 8 :
Letf {tex} ( x ) = \sin x + \cos x , g ( x ) = x ^ { 2 } - 1 . {/tex} Thus, {tex} g [ f ( x ) ] {/tex} is invertible for {tex} x \in R {/tex}
Question 9 :
Let {tex} f : ( - 1,1 ) \rightarrow R {/tex} be a continuous function. If {tex} \int _ { 0 } ^ { \sin x } f ( t ) d t = \frac { \sqrt { 3 } } { 2 } x {/tex} then {tex} f \left( \frac { \sqrt { 3 } } { 2 } \right) {/tex} is equal to<br>
Question 10 :
If {tex} f ( x ) {/tex} is an even function and satisfies the relation {tex} x ^ { 2 } f ( x ) - 2 f {/tex} {tex} ( 1 / x ) = g ( x ) , x \neq 0 , {/tex} where {tex} g ( x ) {/tex} is an odd function, then the value of {tex} f ( 2 ) {/tex} is<br>
Question 11 :
Consider the following relations:<br> {tex} R = \{ ( x , y ) | x , y {/tex}are real numbers and {tex}x = w y{/tex} for some rational number {tex}w\}{/tex}<br> {tex}S = \left\{ \begin{array} { l } { \left( \frac { m } { n } , \frac { p } { q } \right) | m , n , p \text { and } q } \ \end{array} \right\}{/tex} are integers such that {tex}n , q \neq 0{/tex} and {tex}q m = p n{/tex}. Then
Question 12 :
If A = {1, 2, 3, 4}, then the number of subsets of A that contain the element 2 but not 3, is
Question 13 :
The solution set of the equation sin<sup>-1</sup> x = 2 tan<sup>-1</sup> x is-
Question 14 :
If circum-radius and in-radius of a triangle be 10 and 3 respectively then value of a cot A + b cot B + c cot C is equal to-
Question 15 :
If in a {tex} \triangle A B C ,\, \sin ^ { 2 } A + \sin ^ { 2 } B + \sin ^ { 2 } C = 2 , {/tex} then the triangle is always
Question 17 :
If {tex} \sin \alpha , \sin \beta {/tex} and {tex} \cos \alpha {/tex} are in {tex} \mathrm {GP} {/tex}, then roots of the equation {tex} x ^ { 2 } + 2 x \cot \beta + 1 = 0 {/tex} are always
Question 18 :
If the sine of the angles of a triangle {tex} A B C {/tex} satisfy the equation {tex} c ^ { 3 } x ^ { 3 } - c ^ { 2 } ( a + b + c ) x ^ { 2 } + \lambda x + \mu = 0 {/tex} (where {tex} a , b , c {/tex} are the sides of {tex} \Delta A B C {/tex} , then triangle {tex} A B C {/tex} is
Question 19 : In the det. <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9b419f8d44d3a17ee3d' height='63' width='77' >the value of C<sub>23</sub> is-
Question 20 : If the matrix A= <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa0b19f8d44d3a17eea0' height='63' width='91' > is singular, then λ equal to -
Question 21 : If a, b, & c are sides of a ΔABC and <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f84fe6d3604eaa92de57' height='71' width='168' >, then
Question 22 :
If A is a singular matrix, then adj A is :
Question 23 : If X = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f8c819f8d44d3a17ecec' height='41' width='37' >, then X<sup>n</sup>, for n ∈ N, is equal to -
Question 24 : If A is a 3 x 3 matrix and det <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9c775ed294f2c7c34fb' height='20' width='119' >
Question 25 :
In a symmetric matrix of order '12' maximum number of different elements are -
Question 26 :
The value of a for which the system of equations x + y + z = 0 ax + (a + 1)y + (a + 2)z = 0 a<sup>3</sup>x + (a + 1)<sup>3</sup>y + (a + 2)<sup>3</sup>z = 0 has a non-zero solution is -
Question 27 :
The system of equations x + 2y + 3z = 4, 2x + 3y + 4z = 5, 3x + 4y + 5z = 6 has
Question 28 : If a, b, c be positive and not all equal, then the value of the determinant <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f866e6d3604eaa92de7b' height='63' width='60' > is -
Question 29 :
The number of values of k for which the system of equations (k + 1) x + 8y = 4k, kx + (k + 3) y = 3k - 1 has no solution is-
Question 30 : If x is real number such that <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f98375ed294f2c7c3493' height='63' width='120' > = 0 . Then α, β, γ are in
Question 31 : <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f995e6d3604eaa92e035' height='63' width='131' > = mb<sup>n</sup>(a + b) Then :
Question 32 : If A, B, C are angles of a triangle and <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f884e6d3604eaa92dea8' height='63' width='252' > = 0 then triangle ABC is
Question 33 : If <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9bb19f8d44d3a17ee47' height='68' width='132' > = ax<sup>5</sup> + bx<sup>4</sup> + cx<sup>3</sup> + dx<sup>2</sup> + ex + f be an identity in x, where a, b, c, d, e, f are independent of x, then the value of f is -
Question 34 :
$\left| \begin{matrix} \alpha & - \beta & 0 \\ 0 & \alpha & \beta \\ \beta & 0 & \alpha \\ \end{matrix} \right|$ =0, then
Question 35 :
The determinant $\mathrm{\Delta} = \left| \begin{matrix} a^{2} + x^{2} & \text{ab} & \text{ac} \\ \text{ab} & b^{2} + x^{2} & \text{bc} \\ \text{ac} & \text{bc} & c^{2} + x^{2} \\ \end{matrix} \right|$ is divisible by
