List of top Mathematics Questions asked in JEE Main

Let \(A=\{x_1, x_2, \ldots, x_7\}\) and \(B=\{y_1, y_2, y_3\}\) be two sets containing seven and three distinct elements respectively. Then the total number of functions \(f: A \to B\) that are onto, if there exist exactly three elements \(x\) in \(A\) such that \(f(x)=y_2\), is equal to :

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements is:

If the points \((1, 1, \lambda)\) & \((-3, 0, 1)\), are equidistant from the plane, \(3x + 4y - 12z + 13 = 0\), then \(\lambda\) satisfies the equation:

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that \(|\vec{a} + \vec{b}| = \sqrt{3}\). If \(\vec{c} = \vec{a} + 2\vec{b} + (\vec{a} \times \vec{b})\), then \(2|\vec{c}|\) is equal to:

If the shortest distance between the line \(\frac{x-1}{\alpha}=\frac{y+1}{-1}=\frac{z}{1}\), \((\alpha \neq -1)\), and \(x+y+z+1=0=2x-y+z+3\) is \(\frac{1}{\sqrt{3}}\), then value of \(\alpha\) is :

The integral \(\int \frac{dx}{(x+1)^{\frac{3}{4}}(x-2)^{\frac{5}{4}}}\), is equal to

If Rolle's theorem holds for the function \(f(x) = 2x^3 + bx^2 + cx\), \(x \in [-1, 1]\) at the point \(x = \frac{1}{2}\), then \(2b + c\) is equal to

If \(y(x)\) is the solution of the differential equation \((x+2)\frac{dy}{dx} = x^2 + 4x - 9\), \(x \neq -2\) and \(y(0) = 0\), then \(y(-4)\) is equal to

The distance from the origin, of the normal to the curve, \(x = 2\cos t + 2t\sin t\), \(y = 2\sin t - 2t\cos t\) at \(t = \frac{\pi}{4}\), is :

The area (in square units) of the region bounded by the curves \(y + 2x^2 = 0\) and \(y + 3x^2 = 1\), is equal to

For \(x \gt 0\), let \(f(x) = \int_1^x \frac{\log t}{1+t}\,dt\). Then \(f(x) + f\left(\frac{1}{x}\right)\) is equal to

If \(A = \begin{bmatrix} 0\;\;-1\\1\;\;0 \end{bmatrix}\), then which one of the following statements is not correct?

The contrapositive of the statement "If it is raining, then I will not come", is

A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively. If per day mean wage of the day shift workers is, ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹) is :

The least value of the product \(xyz\) (such that \(x\), \(y\) and \(z\) are positive real numbers) for which the determinant \(\begin{vmatrix} x\;\;1\;\;1\\1\;\;y\;\;1\\1\;\;1\;\;z \end{vmatrix}\) is non-negative is

\(\lim_{x\to0}\frac{e^{x^2}-\cos x}{\sin^2x}\) is equal to

The points \(\left(0,\frac{8}{3}\right)\), \((1,3)\) and \((82,30)\)

Let the tangents drawn to the circle, \(x^2+y^2=16\) from the point \(P(0,h)\) meet the \(x\)-axis at points \(A\) and \(B\). If the area of \(\Delta APB\) is minimum, then positive value of \(h\) is:

Let \(L\) be the line passing through the point \(P(1,2)\) such that its intercepted segment between the co-ordinate axes is bisected at \(P\). If \(L_1\) is the line perpendicular to \(L\) and passing through the point \((-2,\,1)\), then the point of intersection of \(L\) and \(L_1\) is

In a \(\Delta ABC\), \(\frac{a}{b}=2+\sqrt{3}\), and \(\angle C=60^\circ\). Then the ordered pair \((\angle A,\angle B)\) is equal to:

If the tangent to the conic, \(y-6=x^2\) at \((2,10)\) touches the circle, \(x^2+y^2+8x-2y=k\) (for some fixed \(k\)) at a point \((\alpha,\,\beta)\); then \((\alpha,\,\beta)\) is

If the coefficient of the three successive terms in the binomial expansion of \((1+x)^n\) are in the ratio \(1:7:42\), then the first of these terms in the expansion is

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman is

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

If \(2+3i\) is one of the roots of the equation \(2x^3-9x^2+kx-13=0\), \(k\in R\), then the real root of this equation (where \(i^2=-1\)) :