List of top Mathematics Questions asked in JEE Main

If the Rolle's theorem holds for the function \(f(x) = 2x^3 + ax^2 + bx\) in the interval \([-1, 1]\) for the point \(c = \frac12\), then the value of \(2a + b\) is:

If \(y = e^{nx}\), then \(\frac{d^2y}{dx^2} \cdot \frac{d^2x}{dy^2}\) is equal to :

If \(B\) is a \(3 \times 3\) matrix such that \(B^2 = 0\), then \(\det.\left[(I + B)^{50} - 50B\right]\) is equal to :

The contrapositive of the statement "I go to school if it does not rain" is

In a set of \(2n\) distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then, the mean of the new set of observations :

Let \(P\) be the relation defined on the set of all real numbers such that \(P = \{(a, b) : \sec^2 a - \tan^2 b = 1\}\). Then, \(P\) is

If the point \((1,\ 4)\) lies inside the circle \(x^2+y^2-6x+10y+p=0\) and the circle does not touch or intersect the coordinate axes, then the set of all possible values of \(p\) is the interval

Let \(a\) and \(b\) be any two numbers satisfying \(\frac1{a^2}+\frac1{b^2}=\frac14\). Then, the foot of perpendicular from the origin on the variable line \(\frac xa+\frac yb=1\) lies on :

If \(OB\) is the semi-minor axis of an ellipse, \(F_1\) and \(F_2\) are its focii and the angle between \(F_1B\) and \(F_2B\) is a right angle, then the square of the eccentricity of the ellipse is

If \(f(x)\) is continuous and \(f\left(\frac92\right)=\frac29\), then \(\lim_{x\to0}f\left(\frac{1-\cos3x}{x^2}\right)\) equals to

The number of terms in the expansion of \((1+x)^{101}(1-x+x^2)^{100}\) in powers of \(x\) is

Given three points \(P,Q,R\) with \(P(5,3)\) and \(R\) lies on the \(x\)-axis. If the equation of \(RQ\) is \(x-2y=2\) and \(PQ\) is parallel to the \(x\)-axis, then the centroid of \(\Delta PQR\) lies on the line

If \(\operatorname{cosec}\theta=\frac{p+q}{p-q}\ (p\ne q,\ p\ne 0)\), then \(\left|\cot\left(\frac{\pi}{4}+\frac{\theta}{2}\right)\right|\) is equals to:

The number of values of \(\alpha\) in \([0,\ 2\pi]\) for which \(2\sin^3\alpha-7\sin^2\alpha+7\sin\alpha=2\), is :

The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is :

Let \(w\ (\mathrm{Im}\,w\ne 0)\) be a complex number. Then, the set of all complex numbers \(z\) satisfying the equation \(w-\overline{w}z=k(1-z)\), for some real number \(k\), is

If the sum \(\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+\ldots\) up to 20 terms is equal to \(\frac{k}{21}\), then \(k\) is equal to

If equations \(ax^2+bx+c=0\), \((a,\ b,\ c\in R,\ a\ne 0)\) and \(2x^2+3x+4=0\) have a common root, then \(a:b:c\) equals :

The statement \(\sim(p\leftrightarrow\sim q)\) is :

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is \(45^\circ\). It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to \(30^\circ\). Then the speed (in m/s) of the bird is :

If \(\left[\vec{a}\times\vec{b}\ \ \vec{b}\times\vec{c}\ \ \vec{c}\times\vec{a}\right]=\lambda\left[\vec{a}\ \ \vec{b}\ \ \vec{c}\right]^2\) then \(\lambda\) is equal to :

Let \(f_k(x)=\frac{1}{k}\left(\sin^k x+\cos^k x\right)\) where \(x\in\mathbf{R}\) and \(k\ge1\). Then \(f_4(x)-f_6(x)\) equals :

The locus of the foot of perpendicular drawn from the centre of the ellipse \(x^2+3y^2=6\) on any tangent to it is :

The integral \(\displaystyle\int\left(1+x-\frac1x\right)e^{x+\frac1x}\,dx\) is equal to :

Let \(PS\) be the median of the triangle with vertices \(P(2,2)\), \(Q(6,-1)\) and \(R(7,3)\). The equation of the line passing through \((1,-1)\) and parallel to \(PS\) is :