List of top Mathematics Questions asked in JEE Main

Consider the observations: 2, 4, \(\alpha\), \(\beta\), 6, 12, 14. If their mean is 8 and variance = 16, then the quadratic equation whose roots are \(3\alpha + 2\) and \(2\beta + 1\), is

A bag contains 6 Red and 6 black balls. 6 pair of balls are selected one by one without replacement then the probability that each of the 6 pairs contains 1 red and 1 black ball.

The shortest distance between the lines \(\frac{x-3}{-1} = \frac{y-2}{4} = \frac{z-1}{2}\) and \(\frac{x-1}{2} = \frac{y-1}{1} = \frac{z-2}{5}\) is:

An ellipse has directrix \(x = 9\) & eccentricity \(= \frac{1}{3}\). If one of its focus is \((\alpha,0)\), \(\alpha<0\), then locus of the mid-point of the chord passing through \(P(\alpha,0)\) is

Let \(x = 9\) be a directrix of an ellipse centred at \((0, 0)\) and having eccentricity \(\frac{1}{3}\). If focus at \((\alpha, 0)\) (\(\alpha<0\)), then locus of the mid-point of the chord passing through the focus \((\alpha, 0)\) is

A lift of a 10 floor building contains 9 persons and group of 4 and 5 leave the lift on different floor and there is no stoppage of lift at 1st and 2nd floor, then find number of ways this can be done.

A 3rd order square matrix M satisfies \( M \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 2 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 2 & 1 \end{pmatrix} \) and \( M \begin{pmatrix} 0 & -1 \\ 1 & 2 \\ 2 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 2 & 1 \end{pmatrix} \). If \( M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \\ 7 \end{pmatrix} \), then \( x + y + z \) is:

Let \( A = \{1, 4, 7\} \), \( B = \{2, 3, 8\} \). Let \( R \) be a relation defined as \[ \{((a_1, b_1), (a_2, b_2)) \in (A \times B) \times (A \times B) : (a_2 + b_1) \text{ divides } (a_1 + b_2)\} \], then find the number of such relations.

Let \( f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix} \). If \( \sum_{n=1}^{k} f(n) = 98 \), then find \( k \).

Let \( f(x) + 3f\left(\frac{\pi}{2} - x\right) = \sin x \) & maximum value of f is \( \alpha \). If area bounded between \( g(x) = x^2 \) & \( h(x) = \beta x^3 \) (\( \beta >" 0 \)) is \( \alpha^2 \), then \( 30\beta^3 \) is equal to:

If distance of point (a, 2, 5) from image of point (1, 2, 7) in the line \( \frac{x}{1} = \frac{y-1}{1} = \frac{z-2}{2} \) is 4, then sum of all possible values of a is:

Let \( A = \{2, 3\} \) and \( B = \{5, 6\} \), then the number of relations from \( A \times B \) to \( A \times B \) are:

Let foci of a hyperbola be (3, 5) and (3, -4). If eccentricity ‘e’ of the hyperbola satisfies the equation \( 3e^2 - 11e + 6 = 0 \), then the length of the latus rectum of the hyperbola is:

If the sum of the first 10 terms of the series \( \frac{1}{1 + 4 \cdot 1^4} + \frac{2}{1 + 4 \cdot 2^4} + \frac{3}{1 + 4 \cdot 3^4} + \dots \) is \( \frac{m}{n} \) (where m, n are coprime), then (m + n) is:

The coefficient of \( x^2 \) in the binomial expansion of \( (2x^2 + \frac{1}{x})^{10 \) is:

A line \( L : x + y = 0 \) is given. Two lines \( L_1 \) & \( L_2 \) are passing through (-1, -1) inclined at an angle of 45° from line L. Reflection of lines \( L_1 \) and \( L_2 \) in line \( 2y + x = 1 \) is \( ax + by = 9 \) and \( cx + dy = 1 \) then the value of \( |ad + bc| \) is equal to:

If \( \alpha, \beta \) are the roots of the equation \( x^2 - 4x + p = 0 \) and \( \gamma, \delta \) are the roots of the equation \( x^2 - x + q = 0 \). When \( \alpha, \beta, \gamma, \delta \) form a G.P. with positive common ratio, then the value of \( (p + q) \) equals:

If \( f(x) \) satisfies the equation \( f(x) = \int_1^x f(t) \, dt + (1-x)(\log_e x - 1) + e \), then \( f(f(1)) \) is equal to:

Let \[ f(x) = \lim_{y \to 0} \frac{(1 - \cos(xy)) \tan(xy)}{y^3} \] then the number of points of intersection of \( f(x) = \sin x \) is:

If \( Z_1 \) and \( Z_2 \) are roots of equation \( Z^2 + 4Z - (1 + 12i) = 0 \), where \( Z \) is complex number, then the value of \( |Z_1|^2 + |Z_2|^2 \) is:

Let \( y(x) \) be the solution of the differential equation \[ \sqrt{\tan x}\, dy = \left(\sec^3 x - y (\tan x)^{3/2} \right)\, dx \] and \( y\left(\frac{\pi}{4}\right) = \frac{6\sqrt{2}}{5} \), then the value of \( y\left(\frac{\pi}{3}\right) \) is:

In a cricket team A and B can be chosen as captain, probability of A to be chosen as captain is 0.6, and that of B is 0.4. If A is chosen as captain then probability of winning is 0.8 and if B is chosen then it is 0.7. Then total probability of winning of the team is:

If \( S = \{\theta : \theta \in [-\pi, \pi], \cos\theta \cos(50^\circ/2) - \cos 70^\circ \cos(70^\circ/2) = 0\ \), then \( n(S) \) is equal to:

Let \( \vec{OP} = \vec{a} \), \( \vec{OQ} = \vec{b} \). If \( R \) be a point on \( OP \) such that \( \vec{OR} = \vec{OP}/5 \) and \( M \) be a point on \( OQ \) such that \( \vec{RM} = \vec{OQ}/5 \), then \( \vec{PM} \) is equal to (where O is origin):

If \( 3^a + 3^{-a} \), \( f(a) \) and \( 2^a + 2^{-a} \) are in A.P. If \( a \) is the minimum value of \( f(x) \), then the value of \( \int_{\ln 2}^{\ln 3} \frac{dx}{e^{2x} - e^{-2x}} \) is: