List of top Mathematics Questions asked in JEE Main

The intercepts on \(x\)-axis made by tangents to the curve,
\(y = \int_0^x |t|\,dt,\; x \in R,\)
which are parallel to the line \(y = 2x\), are equal to :

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :

The circle passing through \((1, -2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point :

If the vectors \(\overrightarrow{AB} = 3\hat{i} + 4\hat{k}\) and \(\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}\) are the sides of a triangle \(ABC\), then the length of the median through \(A\) is :

The number of values of \(k\), for which the system of equations :
\((k + 1)x + 8y = 4k\)
\(kx + (k + 3)y = 3k - 1\)
has no solution, is

A ray of light along \(x + \sqrt{3}\,y = \sqrt{3}\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :

If \(\displaystyle\int f(x)\,dx=\psi(x)\), then \(\displaystyle\int x^5 f(x^3)\,dx\) is equal to

If \(y=\sec\left(\tan^{-1}x\right)\), then \(\dfrac{dy}{dx}\) at \(x=1\) is equal to :

If \(x,y,z\) are in A.P. and \(\tan^{-1}x,\tan^{-1}y\) and \(\tan^{-1}z\) are also in A.P., then :

The area (in square units) bounded by the curves \(y=\sqrt{x}\), \(2y-x+3=0\), \(x\)-axis, and lying in the first quadrant is :

Statement-1 : The value of the integral \(\displaystyle\int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}\) is equal to \(\pi/6\)
Statement-2 : \(\displaystyle\int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx\).

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of \(A \times B\) having 3 or more elements is :

\(\displaystyle\lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\) is equal to

If the events A and B are mutually exclusive events such that \(P(A)=\frac{3x+1}{3}\) and \(P(B)=\frac{1-x}{4}\), then the set of possible values of \(x\) lies in the interval :

Let \(\vec a=2\hat i+\hat j-2\hat k,\ \vec b=\hat i+\hat j\). If \(\vec c\) is a vector such that \(\vec a\cdot\vec c=|\vec c|,\ |\vec c-\vec a|=2\sqrt2\) and the angle between \(\vec a\times\vec b\) and \(\vec c\) is \(30^\circ\), then \(|(\vec a\times\vec b)\times\vec c|\) equals:

The equation of the curve passing through the origin and satisfying the differential equation \((1+x^2)\frac{dy}{dx}+2xy=4x^2\) is

Let ABC be a triangle with vertices at points \(A(2,3,5),\ B(-1,3,2)\) and \(C(\lambda,5,\mu)\) in three dimensional space. If the median through A is equally inclined with the axes, then \((\lambda,\mu)\) is equal to:

The equation of a plane through the line of intersection of the planes \(x+2y=3,\ y-2z+1=0\), and perpendicular to the first plane is :

Let \(f:[-2,3]\to[0,\infty)\) be a continuous function such that \(f(1-x)=f(x)\) for all \(x\in[-2,3]\). If \(R_1\) is the numerical value of the area of the region bounded by \(y=f(x),\ x=-2,\ x=3\) and the axis of \(x\) and \(R_2=\int_{-2}^{3}xf(x)\,dx\), then :

Let \(f(1) = -2\) and \(f'(x) \ge 4.2\) for \(1 \le x \le 6\). The possible value of \(f(6)\) lies in the interval :

A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in \(\mathrm{cm^2}\)/min.) of the balloon when its diameter is 14 cm, is :

If an equation of a tangent to the curve, \(y - \cos(x + y) = 0,\ -1 \le x \le 1 + \pi\), is \(x + 2y = k\) then \(k\) is equal to :

For \(0 \le x \le \frac{\pi}{2}\), the value of \(\displaystyle\int_0^{\sin^2 x}\sin^{-1}(\sqrt{t})\,dt+\int_0^{\cos^2 x}\cos^{-1}(\sqrt{t})\,dt\) equals :

Let \(p\) and \(q\) be any two logical statements and \(r : p \rightarrow (\sim p \vee q)\). If \(r\) has a truth value \(F\), then the truth values of \(p\) and \(q\) are respectively:

In a set of \(2n\) observations, half of them are equal to 'a' and the remaining half are equal to '\(-a\)'. If the standard deviation of all the observations is 2 ; then the value of \(|a|\) is :