List of top Mathematics Questions asked in JEE Main

Let $f : R \rightarrow R$ be a continuous function such that $f (3x)- f(x)= x$. If $f(8)=7$, then $f (14)$ is equal to :

The ordered pair (a, b), for which the system of linear equations
3x – 2y + z = b
5x – 8y + 9z = 3
2x + y + az = –1
has no solution, is :

If \(\displaystyle\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0 \) then \(8(\alpha+\beta)\) is equal to :

The area of the region given by \(A =\left\{( x , y ): x ^2 \leq y \leq \min \{ x +2,4-3 x \}\right\}\) is :

The total number of functions, \(f :\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}\) such that \(f (1)+ f (2)= f (3)\), is equal to :

A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B If the length of the line segment AB is \(\frac{\sqrt{29}}{3},\) then B also lies on the line :

Let the locus of the centre \((\alpha, \beta), \) \(\beta>0\), of the circle which touches the circle \(x ^2+( y -1)^2=1\) externally and also touches the x-axis be L Then the area bounded by L and the line y=4 is :

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

If the numbers appeared on the two throws of a fair six faced die are \(\alpha\) and \(\beta\), then the probability that \(x^2+\alpha x+\beta>0\), for all \(x \in R\), is :

The number of solutions of $|\cos x |=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is :

Which of the following statements is a tautology?

The minimum value of the twice differentiable function \(f(x)=\int\limits_0^x e^{x-1} f^{\prime}(t) d t-\left(x^2-x+1\right) e^x, x \in R\), is :

Let $O$ be the origin and $A$ be the point $z _1=1+2 i$. If $B$ is the point $z _2, \operatorname{Re}\left( z _2\right)<0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true ?

Consider the sequence \(a_1, a_2, a_3, \ldots \ldots\) such that \(a_1=1, a_2=2\) and \(a_{n+2}=\frac{2}{a_{n+1}}+a_n\) for \(n =1,2,3, \ldots\) If \(\left(\frac{a_1+\frac{1}{a_2}}{a_3}\right) \cdot\left(\frac{a_2+\frac{1}{a_3}}{a_4}\right) \cdot\left(\frac{a_3+\frac{1}{a_4}}{a_5}\right) ... \left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^a\left({ }^{61} C_{31}\right)\), then \(\alpha\) is equal to :

Let A be a $2 \times 2$ matrix with det $( A )=-1$ and $\operatorname{det}(( A + I )(\operatorname{Adj}( A )+ I ))=4$. Then the sum of the diagonal elements of A can be:

Consider two GPs $2,2^2, 2^3, \ldots$ and $4,4^2$, $4^3, \ldots$ of 60 and $n$ terms respectively. If the geometric mean of all the $60+ n$ terms is $(2)^{\frac{225}{8}}$, then $\displaystyle\sum_{ k =1}^{ n } k ( n - k )$ is equal to :

Let \(\alpha, \beta\) and \(\gamma\) be three positive real numbers Let \(f ( x )=\alpha x ^5+\beta x ^3+\gamma x , x \in R\) and \(g: R \rightarrow R\) be such that \(g(f(x))=x\) for all \(x \in R\) If \(a_1, a_2, a_3, \ldots, a_n\) be in arithmetic progression with mean zero, then the value of \(f\left(g\left(\frac{1}{n} \displaystyle\sum_{i=1}^n f\left(a_i\right)\right)\right)\)is equal to :

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and 
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$ 
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

Let \(S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}\) and \(S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}\) Then, for \(z_1 \in S_1\) and \(z_2 \in S_2\), the least value of \(\left|z_2-z_1\right|\) is :

Let the matrix \(A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}\) and the matrix \(B_0=A^{49}+2 A^{98}\) If \(B_n=\text{Adj}\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\text{det}\left( B _4\right)\) is equal to :

The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y$-axis at the point $C, D$. Then the area of the quadrilateral $ACBD$ is equal to