List of top Mathematics Questions asked in JEE Main

If the four points, whose position vectors are \(3 \hat{i}-4 j+2 \hat{k}, l+2 j-\hat{k}_4-2 \hat{k}-j+3 \hat{k}\) and \(5 \hat{i}-2 \alpha \hat{j}+4 \hat{k}\) are coplanar, then a is equal to

Let \( f(x) = 2x^n + \lambda \), where \( \lambda \in \mathbb{R} \) and \( n \in \mathbb{N} \) . Given that \( f(4) = 133 \) and \( f(5) = 255 \), What is the sum of all the positive integer divisors of \( f(3) - f(2) \)?

Let \(z\) be a complex number such that \(\left|\frac{z-2 i}{z+i}\right|=2 z \neq-i\) Then \(z\) lies on the circle of radius 2 and centre

Let \(f: R \rightarrow R\) be a function defined by\(f(x)=\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}\), for some \(m\), such that the range of \(f\) is \([0,2]\) Then the value of \(m\) is_____

Let \(N\) be the sum of the numbers appeared when two fair dice are rolled and let the probability that \(N-2, \sqrt{3 N}, N+2\) are in geometric progression be \(\frac{k}{48}\), Then the value of \(k\) is

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event .
Given below are two statements : 
(S1): If $P ( A )=0$, then $A =\emptyset$ 
(S2): If $P(A)=1$, then $A=\Omega$
Then

The distance of the point $(-1,9,-16)$ from the plane $2 x+3 y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is

Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$ x+y+z=1 $ $ 2 x + Ny +2 z=2 $ $ 3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is

If $y=y(x)$ is the solution curve of the differential equation $\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1$ then $y\left(\frac{\pi}{6}\right)$ is equal to

In a binomial distribution $B(n, p)$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to

The negation of the statement
(p v q) ∧ (q v(∼r)) is

For three positive integers $p , q , r , x^{p q^2}=y^{y r}=z^{p^2 r }$ and $r = pq +1$ such that $3,3 \log _y x, 3 \log _z y$ $7 \log _x z$ are in AP with common difference $\frac{1}{2}$ Then $r-p-q$ is equal to

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has :

Let $p , q \in R$ and $(1-\sqrt{3})^{200}=2^{199}(p+i q), t=\sqrt{-1}$ Then $p + q + q ^2$ and $p - q + q ^2$ are roots of the equation

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then

Let a tangent to the curve $y^2=24 x$ meet the curve $x y=2$ at the points $A$ and $B$ Then the mid points of such line segments $A B$ lie on a parabola with the

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to

The relation $R =\{(a, b)$ : $\operatorname{gcd}(a, b)=1,2 a \neq b, a, b \in Z\}$ is :

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively Later, the marks of one of the students is increased from 8 to 12 If the new mean of the marks is $10.2$, then their new variance is equal to :

Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :

Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$Then,