List of top Mathematics Questions asked in JEE Main

The coefficient of \(x^2\) in the expansion of the product
\((2-x^2)\cdot\left((1+2x+3x^2)^6+(1-4x^2)^6\right)\) is :

The sum of the first 20 terms of the series
\(1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+\ldots,\)
is :

Let P be a point on the parabola, \(x^2=4y\). If the distance of P from the center of the circle, \(x^2+y^2+6x+8=0\) is minimum, then the equation of the tangent to the parabola at P, is :

If the angle between the lines, \(\frac{x}{2} = \frac{y}{2} = \frac{z}{1}\) and \(\frac{5-x}{-2} = \frac{7y-14}{p} = \frac{z-3}{4}\) is \(\cos^{-1}\left(\frac{2}{3}\right)\), then p is equal to :

Let \(A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}\) and \(B = A^{20}\). Then the sum of the elements of the first column of B is :

Let p, q and r be real numbers (\(p \neq q,\ r \neq 0\)), such that the roots of the equation \(\frac{1}{x+p} + \frac{1}{x+q} = \frac{1}{r}\) are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

The sum of the intercepts on the coordinate axes of the plane passing through the point \((-2,-2,2)\) and containing the line joining the points \((1,-1,2)\) and \((1,1,1)\) is :

If the area of the region bounded by the curves, \(y = x^2,\ y = \frac{1}{x}\) and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then t is equal to :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is \(\frac{1}{12}\), then the number of children in each family is :

The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

If a circle C, whose radius is 3, touches externally the circle, \(x^2 + y^2 + 2x - 4y - 4 = 0\) at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

If \(\int \frac{\tan x}{1 + \tan x + \tan^2 x}\,dx = x - \frac{K}{\sqrt{A}}\tan^{-1}\left(\frac{K\tan x + 1}{\sqrt{A}}\right) + C\), (C is a constant of integration) then the ordered pair (K, A) is equal to :

If an angle A of a \(\Delta\)ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, \(9x^2 + 27x + 20 = 0\) are :

Let A, B and C be three events, which are pair-wise independent and \(\overline{E}\) denotes the completement of an event E. If \(P(A \cap B \cap C) = 0\) and \(P(C) \gt 0\), then \(P\left[(\overline{A} \cap \overline{B}) \mid C\right]\) is equal to :

The number of values of k for which the system of linear equations,
\((k+2)x + 10y = k\)
\(kx + (k+3)y = k-1\)
has no solution, is :

Let \(\vec{a} = \hat{i} + \hat{j} + \hat{k},\ \vec{c} = \hat{j} - \hat{k}\) and a vector \(\vec{b}\) be such that \(\vec{a} \times \vec{b} = \vec{c}\) and \(\vec{a} \cdot \vec{b} = 3\). Then \(|\vec{b}|\) equals :

\(\lim_{x \to 0} \frac{(27+x)^{\frac{1}{3}} - 3}{9 - (27+x)^{\frac{2}{3}}}\) equals.

If the function f defined as
\(f(x) = \frac{1}{x} - \frac{k-1}{e^{2x}-1},\ x \neq 0,\)
is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :

The Boolean expression \(\sim(p \vee q) \vee (\sim p \wedge q)\) is equivalent to :

The sum of the co-efficients of all odd degree terms in the expansion of \((x+\sqrt{x^3-1})^5+(x-\sqrt{x^3-1})^5\), \((x \gt 1)\) is

Tangents are drawn to the hyperbola \(4x^2 - y^2 = 36\) at the points P and Q. If these tangents intersect at the point \(T(0, 3)\) then the area (in sq. units) of \(\triangle PTQ\) is :

If the curves \(y^2=6x\), \(9x^2+by^2=16\) intersect each other at right angles, then the value of \(b\) is :

Tangent and normal are drawn at \(P(16, 16)\) on the parabola \(y^2 = 16x\), which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and \(\angle CPB = \theta\), then a value of \(\tan\theta\) is :

Let \(S=\{x\in R: x\ge0\) and \(2\left|\sqrt{x}-3\right|+\sqrt{x}\left(\sqrt{x}-6\right)+6=0\}\). Then \(S\)

If \(\sum_{i=1}^{9}(x_i-5)=9\) and \(\sum_{i=1}^{9}(x_i-5)^2=45\), then the standard deviation of the 9 items \(x_1,x_2,\ldots,x_9\) is