List of top Mathematics Questions asked in JEE Main

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:

Let the plane $P : 8 x+\alpha_1 y+\alpha_2 z+12=0$ be parallel to the line $L : \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $P$ on the $y$-axis is 1 , then the distance between $P$ and $L$ is :

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1, a_2, a_3, \ldots , a_{100}$ is $25$ Then $S$ is
If $P ( h , k )$ be a point on the parabola $x=4 y^2$, which is nearest to the point $Q (0,33)$, then the distance of $P$ from the directrix of the parabola $y^2=4(x+y)$ is equal to :
The coefficient of $x^{301}$ in $(1+x)^{500}+x(1+x)^{499}+x^2(1+x)^{498}+\ldots \ldots +x^{500}$ is :
Consider the following statements: 
P : I have fever 
Q: I will not take medicine 
R : I will take rest 
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

The sum\(\displaystyle\sum_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}\) is equal to:

Let \(f: R -\{0,1\} \rightarrow R\)be a function such that \(f(x)+f\left(\frac{1}{1-x}\right)=1+x\) Then \(f(2)\) 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

Two dice are thrown independently Let\(A\) be the event that the number appeared on the \(1^{\text {st }}\) die is less than the number appeared on the \(2^{\text {nd }}\) die, \(B\) be the event that the number appeared on the \(1^{\text {st }}\) die is even and that on the second die is odd, and \(C\) be the event that the number appeared on the \(1^{\text {st }}\) die is odd and that on the \(2^{\text {nd }}\) is even Then :

The number of values of $r \in\{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is :

Let\( S={x∈R:0<x<1 and\ 2 tan−1\frac{(1+x)}{(1−x​)}=cos^{−1}\frac{(1-x^2)}{(1+x^2​)}}\). If n(S) denotes the number of elements in S then :

Let \(9 =\) \(x_1​<x_2​<…<x_7​\) be in an A.P. with common difference d. If the standard deviation of \(x_1​,x_2​ …,x_7\)​ is 4 and the mean is \(\bar x\), then \(\bar x+x_6\)​ is equal to :

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

Which of the following statements is a tautology?
The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to
Let for x∈R, S0(x)=x,Sk(x)=Ckx+k\(∫^x_0S_{k−1}\)(t)dt, where C0=1,Ck≡1−\(∫^1_0S_{k−1}\)(x)dx,k==1,2,3,..... Then s2(3)+6c3 is equal to___.
Let the image of the point \(\left(\frac{5}{3},\frac{5}{3},\frac{8}{3}\right)\) in the plane x - 2y + z - 2 = 0 be P. If the distance of the point Q(6,-2,α), α > 0, from P is 13, then α is equal to___.
Let \(\overrightarrow{a}=3\^i+\^j −\^k\)  and \(\overrightarrow{c}=2\^i+3\^j −3\^k\)  if \(\overrightarrow{b}\) is a vector such that  \(\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}\) and \(|\overrightarrow{b}|=50\) , then \(|72|\overrightarrow{b}+\overrightarrow{c}|^2|\)| |  is equal to _______. 
If S={ x ∈ R : sin−1\(( \frac{x + 1}{ √ x^ 2 + 2 x + 2} ) \)−-sin−1\((\frac{x}{√x ^2+1 }) = \frac{π}{ 4} \)}
then \(∑_{x∈R }(sin( (x^2+x+5)\frac{π}{2})−cos( ( x^2+x+5)π ) ) \)is equal to ____.
Find area bounded by the curves \(y\) = \(max\{sin x, cos x\}\) and \(x-axis\) between \(x = -  \pi  \)and \(x =   \pi\)
Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : \(\frac{y^2}{25} − \frac{x^2}{16 }\)= 1. If Q is the point from which the tangents drawn to H have slopes |m1| and |m2| and they make positive intercepts α and β on the x-axis, then  \(\frac{( P Q ) ^2}{ α β}\) α β is equal to _____.
Let α be the constant term in the binomial expansion of \( (√x−\frac{6}{x^{\frac{3}{2}}} )^n ,n≤15.\)  If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of x-n is λα, then λ is equal to _______.