List of top Mathematics Questions asked in JEE Main

If the point \((p,5)\) lies on the line parallel to the \(y\)-axis and passing through the intersection of the lines \(2\left(a^{2}+1\right)x+by+4\left(a^{3}+a\right)=0\) and \(\left(a^{2}+1\right)x-3by+2\left(a^{3}+a\right)=0\), then \(p\) is equal to :

The locus of the mid points of the chords of the parabola \(x^{2}=4py\) having slope \(m\) is a :

The area bounded by the curves \(y^{2}=12x\) and \(x^{2}=12y\) is divided by the line \(x=3\) in two parts. The area (in square units) of the larger part is :

If \(f(x)=\frac{e^{x}}{1+e^{x}}\),
\(I_{1}=\int_{f(-a)}^{f(a)} x\, g\{x(1-x)\}\, d x\) and
\(I_{2}=\int_{f(-a)}^{f(a)} g\{x(1-x)\}\, d x\),
where \(g\) is not an identity function. Then the value of \(\frac{I_{2}}{I_{1}}\) is :

If \(\int \frac{1-5 \sin ^{2} x}{\cos ^{5} x \sin ^{2} x}\, d x=\frac{f(x)}{\cos ^{5} x}+C\), then \(f(x)\) is :

\(f(x)=\left|x \log_{e} x\right|\), \(x>0\), is monotonically decreasing in :

If \(f(x)=(x-p)(x-q)(x-r)\), where \(p<q<r\), are real numbers, then the application of Rolle's theorem on \(f\) leads to :

Let \(f(x)=\left|x-x_{1}\right|+\left|x-x_{2}\right|\), where \(x_{1}\) and \(x_{2}\) are distinct real numbers. Then the number of points at which \(f(x)\) is minimum, is :

Let \(f(x)=\begin{cases}\frac{1}{|x|} & \text{if } |x|>2 \\ a+b x^{2} & \text{if } |x| \leq 2\end{cases}\),
then \(f(x)\) is differentiable at \(x=-2\) for :

\(\log_{10} 2\), \(\log_{10}\left(2^{x}-1\right)\) and \(\log_{10}\left(2^{x}+3\right)\) are three consecutive terms of an A. P. for :

Let \(f(x)=(x+1)^{2}-1\), \(x \geq -1\), then the set \(\left\{x : f(x)=f^{-1}(x)\right\}\) :

Sum of the last 30 coefficients of powers of \(x\) in the binomial expansion of \((1+x)^{59}\) is :

If
\(\dfrac{48}{2.3}+\dfrac{47}{3.4}+\dfrac{46}{4.5}+\cdots+\dfrac{2}{48.49}+\dfrac{1}{49.50}\)
\(=\dfrac{51}{2}+\mathrm{K}\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\cdots+\dfrac{1}{50}\right)\), then
\(\mathrm{K}\) equals :

If \(S_{k}=\begin{pmatrix}1 & k \\ 0 & 1\end{pmatrix}\), \(k \in \mathrm{N}\), where \(\mathrm{N}\) is the set of natural numbers, then \((\mathrm{S}_{2})^{\mathrm{n}}(\mathrm{S}_{\mathrm{k}})^{-1}\), for \(\mathrm{n} \in \mathrm{N}\), is :

Suppose that six students, including Madhu and Puja, are having six beds arranged in a row. Further, suppose that Madhu does not want a bed adjacent to Puja. Then the number of ways, the beds can be allotted to students is :

In a \(\Delta \mathrm{ABC}\), if \(\begin{vmatrix}1 & a & b \\ 1 & c & a \\ 1 & b & c\end{vmatrix}=0\), then \(\sin ^{2} \mathrm{A}+\sin ^{2} \mathrm{B}+\sin ^{2} \mathrm{C}\) is :

If the roots of the equation
\(\dfrac{1}{x+\mathrm{p}}+\dfrac{1}{x+\mathrm{q}}=\dfrac{1}{\mathrm{r}}\) are equal in magnitude and opposite in sign, then the product of roots is :

Let \(\mathrm{N}\) be the set of natural numbers and for \(\mathrm{a} \in \mathrm{N}\), \(\mathrm{aN}\) denotes the set \(\{\mathrm{a}x : x \in \mathrm{N}\}\).
If \(\mathrm{bN} \cap \mathrm{cN} = \mathrm{dN}\), where \(\mathrm{b}, \mathrm{c}, \mathrm{d}\) are natural numbers greater than 1 and the greatest common divisor of \(\mathrm{b}\) and \(\mathrm{c}\) is 1, then \(\mathrm{d}\) equals :

If \(z\) is a complex number of unit modulus and argument \(\theta\), then the real part of \(\dfrac{z(1-\bar{z})}{\bar{z}(1+z)}\) is :

Let \(\bar x\), M and \(\sigma^2\) be respectively the mean, mode and variance of n observations \(x_1,x_2,\ldots,x_n\) and \(d_i=-x_i-a,\ i=1,2,\ldots,n\), where a is any number.
Statement I : Variance of \(d_1,d_2,\ldots,d_n\) is \(\sigma^2\).
Statement II : Mean and mode of \(d_1,d_2,\ldots,d_n\) are \(-\bar x-a\) and \(-M-a\), respectively.

The function \(f(x)=|\sin 4x|+|\cos 2x|\), is a periodic function with period :

The principal value of \(\tan^{-1}\left(\cot\frac{43\pi}{4}\right)\) is :

Let A and E be any two events with positive probabilities :
Statement - 1 : \(P(E/A)\ge P(A/E)P(E)\)
Statement - 2 : \(P(A/E)\ge P(A\cap E)\).

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{5}=1\), meets \(x\)-axis and \(y\)-axis at A and B respectively. Then \((OA)^2-(OB)^2\), where O is the origin, equals :

If \(\vec x=3\hat i-6\hat j-\hat k,\ \vec y=\hat i+4\hat j-3\hat k\) and \(\vec z=3\hat i-4\hat j-12\hat k\), then the magnitude of the projection of \(\vec x\times\vec y\) on \(\vec z\) is :