List of top Mathematics Questions asked in JEE Main

If the equation of a line which divides the line segment joining the points \((1,0)\) and \((3,0)\) in the ratio \(2:1\) and is also perpendicular to it, is \(ax=7\), then the value of \(a\) is equal to :

Equations of the common tangent of the ellipse \(\frac{(x+1)^{2}}{2^{2}}+\frac{(y-1)^{2}}{3^{2}}=1\) and the circle \((x+1)^{2}+(y-1)^{2}=4\) are :

Equation of the circle, which is the mirror image of the circle \(x^{2}+y^{2}-2x=0\) with respect to the line \(x+y=2\), is :

Derivative of \(\tan^{-1}\left(\frac{2x}{1-x^{2}}\right)\) with respect to \(\sin^{-1}\left(\frac{2x}{1+x^{2}}\right)\) in \((1, \infty)\), is :

The values of \(s\) and \(t\), for which the system of equations
\(x_{1}+x_{2}+x_{3}=5\)
\(x_{1}+2x_{2}+3x_{3}=9\)
\(x_{1}+3x_{2}+sx_{3}=t\)
has no solution, are :

The probability of solving a problem in Mathematics by two students X and Y are \(\frac{1}{4}\) and \(\frac{1}{5}\) respectively. If both of them try to solve the problem independently, then the probability that the problem will be solved by exactly one of them is equal to :

The distance between the planes \(\vec{r}\cdot(2\hat{i}+\hat{j}-2\hat{k})+5=0\) and \(\vec{r}\cdot(6\hat{i}+3\hat{j}-6\hat{k})+2=0\) is :

The polar form of the complex number \(\frac{1+i}{1-i}\) is equal to :

If \( y=\frac{ax-b}{(x-1)(x-4)} \) has an extremum at the point \( (2,-1) \), then the values of \( a \) and \( b \) are :

There are 4, 5 and 6 points on the three parallel and co-planar lines. If no set of four or more points is cyclic and no set of three points lying on distinct lines is collinear, then the number of circles passing through exactly three points is :

The sum of infinite number of terms of a Geometric Progression is 3 and the sum of the squares of its terms is \( \frac{9}{2} \). The sum of the cubes of its terms is :

The least positive integral value of \( \lambda \) such that \( 10^{50}+(3 \times(4)^{52})+\lambda \) is divisible by 9 is :

\( \sum_{n=1}^{\infty} \frac{2n^{2}+7n+5}{n!} \) is equal to :

Which of the following Boolean expression is a tautology ?

Let \( |a|<1,|b|<1,|c|<1 \) and \( x=\sum_{n=0}^{\infty} a^{n}, y=\sum_{n=0}^{\infty} b^{n}, z=\sum_{n=0}^{\infty} c^{n} \). If \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in Arithmetic Progression, then :

The value of the integral \( \int_{-4}^{4}\left|9-x^{2}\right| \mathrm{d}x \) is :

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is ___________.

If the sum of the coefficients in the expansion of \((x+y)^n\) is 4096, then the greatest coefficient in the expansion is _____________.

Let \(\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\) and \(\vec{b}=\hat{i}+2\hat{j}-\hat{k}\). Let a vector \(\vec{v}\) be in the plane containing \(\vec{a}\) and \(\vec{b}\). If \(\vec{v}\) is perpendicular to the vector \(3\hat{i}+2\hat{j}-\hat{k}\) and its projection on \(\vec{a}\) is 19 units, then \(\left|2\vec{v}\right|^2\) is equal to ______________.

A man starts walking from the point P(\(-3\), 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then \(50\left((PR)^2+(RQ)^2\right)\) is equal to ____________.

Let [t] denote the greatest integer \(\le t\). The number of points where the function \(f(x)=[x]\left|x^2-1\right|+\sin\left(\frac{\pi}{[x]+3}\right)-[x+1],\ x\in(-2,2)\) is not continuous is _____________.

Let X be a random variable with distribution.

x	\(-2\)	\(-1\)	3	4	6
P(X = x)	\(\frac15\)	a	\(\frac13\)	\(\frac15\)	b

If the mean of X is 2.3 and variance of X is \(\sigma^2\), then \(100\sigma^2\) is equal to :

Let the points of intersections of the lines \(x-y+1=0\), \(x-2y+3=0\) and \(2x-5y+11=0\) are the mid points of the sides of a triangle \(\Delta ABC\). Then, the area of the \(\Delta ABC\) is ______________.

If for the complex numbers z satisfying \(|z-2-2i|\le1\), the maximum value of \(|3iz+6|\) is attained at \(a+ib\), then \(a+b\) is equal to ______________.

Let f(x) be a polynomial of degree 3 such that \(f(k)=-\frac{2}{k}\) for k = 2, 3, 4, 5. Then the value of \(52-10f(10)\) is equal to :