List of top Mathematics Questions asked in JEE Main

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

Equation of the line of the shortest distance between the lines $\frac{x}{1} = \frac{y}{-1} = \frac{z}{1}$ and $\frac{x-1}{0} = \frac{y+1}{-2} = \frac{z}{1}$ is :

For all complex numbers z of the form 1 + i$\alpha$, $\alpha$ $\epsilon$ R, if z = x + iy, then :

Given an $A.P$. whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is :

If $\frac{1}{\sqrt{\alpha}}$ and $\frac{1}{\sqrt{\beta}}$ are the roots of the equation, $ax^{2} + bx +1 = 0 \left(a ^{ }\ne 0, a, b \in R\right)$, then the equation, $x\left(x + b^{3}\right) + \left(a^{3} ? 3abx\right)$ = 0 has roots :

If $ 1 + x^4 + x^5 = \sum\limits^{5}_{i =0} a_i$ $(1 + x)^i$ , for all $x$ in $R$, then $a_2$ is:

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :

Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :

The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :

The number of terms in an $A.P$. is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10 \frac{1}{2},$ then the number of terms in the $A.P$. is :

The variance of first $50$ even natural numbers is

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$, (where n $\le$ 22 is any positive integer), is :-

The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x (1 + x)^{999} + x^2(1 + x)^{998} + .... + x^{1000}$ is:

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x - y + z+ 3 = 0$ is the line.

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :

The least positive integer n such that $1-\frac{2}{3}-\frac{2}{3^{2}}-.......-\frac{2}{3^{n-1}} < \frac{1}{100},$ is :

If the lines \(\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}\) and \(\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}\) are coplanar, then \(k\) can have :

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers \(x\) is given by \(\frac{dP}{dx} = 100 - 12\sqrt{x}\). If the firm employs 25 more workers, then the new level of production of items is

Consider :
Statement - I : \((p\wedge\sim q)\wedge(\sim p\wedge q)\) is a fallacy.
Statement - II : \((p\to q)\leftrightarrow(\sim q\to\sim p)\) is a tautology.

If \(P=\begin{bmatrix}1&\alpha&3\\1&3&3\\2&4&4\end{bmatrix}\) is the adjoint of a \(3\times3\) matrix \(A\) and \(|A|=4\), then \(\alpha\) is equal to :

Given : A circle, \(2x^2 + 2y^2 = 5\) and a parabola, \(y^2 = 4\sqrt{5}\,x\).
Statement-1 : An equation of a common tangent to these curves is \(y = x + \sqrt{5}\).
Statement-2 : If the line, \(y = mx + \frac{\sqrt{5}}{m}\;(m \ne 0)\) is their common tangent, then \(m\) satisfies \(m^4 - 3m^2 + 2 = 0\).