List of top Mathematics Questions asked in JEE Main

The least positive integer n for which $\left( \frac{1 + i \sqrt{3}}{1 - i \sqrt{3}} \right)^n = 1 $, is :

The length of the projection of the line segment joining the points $ (5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x + y + z = 7$ is:

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

Two sets $A$ and $B$ are as under: $A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $; $B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then

The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, is :

The two adjacent sides of a cyclic quadrilateral are \(2\) and \(5\) and the angle between them is \(60^\circ\). If the area of the quadrilateral is \(4\sqrt3\), then the perimeter of the quadrilateral is :

From a group of \(10\) men and \(5\) women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

Let \(E\) and \(F\) be two independent events. The probability that both \(E\) and \(F\) happen is \(\dfrac1{12}\) and the probability that neither \(E\) nor \(F\) happens is \(\dfrac12\), then a value of \(\dfrac{P(E)}{P(F)}\) is :

The sum of \(100\) observations and the sum of their squares are \(400\) and \(2475\), respectively. Later on, three observations, \(3\), \(4\) and \(5\), were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :

If the vector \(\vec b=3\hat j+4\hat k\) is written as the sum of a vector \(\vec b_1\), parallel to \(\vec a=\hat i+\hat j\) and a vector \(\vec b_2\), perpendicular to \(\vec a\), then \(\vec b_1\times\vec b_2\) is equal to :

If the line, \(\dfrac{x-3}{1}=\dfrac{y+2}{-1}=\dfrac{z+\lambda}{-2}\) lies in the plane, \(2x-4y+3z=2\), then the shortest distance between this line and the line, \(\dfrac{x-1}{12}=\dfrac y9=\dfrac z4\) is :

A value of \(x\) satisfying the equation \(\sin\left[\cot^{-1}(1+x)\right]=\cos\left[\tan^{-1}x\right]\), is :

A square, of each side \(2\), lies above the \(x\)-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle \(30^\circ\) with the positive direction of the \(x\)-axis, then the sum of the \(x\)-coordinates of the vertices of the square is :

A line drawn through the point \(P(4,7)\) cuts the circle \(x^2+y^2=9\) at the points \(A\) and \(B\). Then \(PA\cdot PB\) is equal to :

If a variable plane, at a distance of \(3\) units from the origin, intersects the coordinate axes at \(A\), \(B\) and \(C\), then the locus of the centroid of \(\Delta ABC\) is :

A tangent to the curve, \(y=f(x)\) at \(P(x,y)\) meets \(x\)-axis at \(A\) and \(y\)-axis at \(B\). If \(AP:BP=1:3\) and \(f(1)=1\), then the curve also passes through the point :

If \(y=mx+c\) is the normal at a point on the parabola \(y^2=8x\) whose focal distance is \(8\) units, then \(|c|\) is equal to :

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points \((4,-1)\) and \((-2,2)\) is :

If \(f\left(\frac{3x - 4}{3x + 4}\right) = x + 2,\ x \neq -\frac43\), and \(\int f(x)\,dx = A\log|1 - x| + Bx + C\), then the ordered pair \((A, B)\) is equal to :
(where C is a constant of integration)

If \(\int_1^2 \frac{dx}{(x^2 - 2x + 4)^{3/2}} = \frac{k}{k + 5}\), then k is equal to :

The function f defined by \(f(x) = x^3 - 3x^2 + 5x + 7\), is :

Let f be a polynomial function such that \(f(3x) = f'(x)\cdot f''(x)\), for all \(x \in \mathbf{R}\). Then :

If \(\lim_{n\to\infty}\dfrac{1^a+2^a+\cdots+n^a}{(n+1)^{a-1}\left[(na+1)+(na+2)+\cdots+(na+n)\right]}=\dfrac{1}{60}\) for some positive real number \(a\), then \(a\) is equal to :

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy \(B_1\) and a particular girl \(G_1\) never sit adjacent to each other, is :

The coefficient of \(x^{-5}\) in the binomial expansion of \(\left(\frac{x+1}{x^{2/3} - x^{1/3} + 1} - \frac{x-1}{x - x^{1/2}}\right)^{10}\), where \(x \neq 0, 1\), is :