List of top Mathematics Questions asked in JEE Main

The coefficient of x² in the binomial expansion of (2x² + 1/x)¹⁰ is:

Let A1, A2, A3, ..., A49 be 49 arithmetic means between 49 and 149. Then the mean of A1, A25, A47 and A49 is:

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

If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of \(\alpha\).

Let \(x_1, x_2, x_3, \ldots, x_n\) be ‘\(n\)’ observations such that \( \sum_{i=1}^{n-1} x_i = 48 \) and \( \sum_{i=1}^{n-1} x_i^2 = 496 \). If mean and variance of the distribution are 8 and 16 respectively then value of \(n\) is:

The sum of value \( \sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)} \) is equal to:

The value of \( \int_{0}^{\infty} \frac{\ln x}{x^2 + 4} \, dx \) is equal to:

Consider an equilateral triangle PQR, where P(3, 5) and QR is \( x + y = 4 \). The orthocentre of \( \Delta PQR \) is \( (\alpha, \beta) \), then \( 9(\alpha + \beta) \) is equal to:

Consider a set \( A = \{1, 2, 3, 5, 6\ \). The number of one-one functions \( f: A \to A \) such that \( f(1) \geq 3 \), \( f(3) \leq 4 \), and \( f(2) + f(3) = 5 \) is equal to:}

Let \( S_n \) be the sum of the first \( n \) terms of an A.P. If \( S_n = 3n^2 + 5n \), then the sum of the squares of the first ten terms of the given A.P. is:

If the quadratic expression \[ (\lambda+2)x^2 - 3\lambda x + 4\lambda = 0, \qquad \lambda \ne -2 \] has two positive roots, then the number of possible integral values of \(\lambda\) is:

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is picked from B and put in A. Then a ball is drawn from A. Probability it is white is $p/q$. Find $p+q$.

If the domain of the function $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha)\cup[\beta,\gamma]\cup[\delta,\infty)$, then $\alpha+\beta+\gamma+\delta$ is equal to

The domain of the function $\cos^{-1} \left\{ \frac{4x + 2[x]}{3} \right\}$, where $[\cdot]$ is greatest integer function, is

$y = \tan^{-1} \left( \frac{3 \cos x - 4 \sin x}{4 \cos x + 3 \sin x} \right) + \tan^{-1} \left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$, then find $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$

The number of ways 4 boys and 3 girls are to be arranged in a row so that all 3 girls are not together, is equal to:

Let \( A \) be a matrix of order 3 such that \( |A| = -4 \). Then, the value of \( |adj(adj(2adj(A)))^{-1}| \) is:

If \( z \) is a complex number such that \( |z + 2| = |z - 2| \) and \( \arg\left( \frac{z-3}{z+i} \right) = \frac{\pi}{4} \), then the value of \( z \) is:

If \( I(x) = \int \frac{16x+24}{x^2+2x-15}\,dx \), \( I(1) = 14\ln 3 \) and \( I(7) = \ln\left(2^\alpha \cdot 3^\beta\right) \), then \( (\alpha+\beta) \) is equal to

If foot of the perpendicular from a point \( P(a,b,0) \) on the line \( \dfrac{x-1}{2}=\dfrac{y-2}{1}=\dfrac{z-\alpha}{3} \) is \( A \) and mid-point of \( AP \) is \( \left(0,\dfrac{3}{4},-\dfrac{1}{4}\right) \), then the value of \( \left(a^2+b^2+\alpha^2\right) \) is -

If \( {}^{30}C_{30-r} + 3 \cdot {}^{30}C_{31-r} + 3 \cdot {}^{30}C_{32-r} + {}^{30}C_{33-r} = {}^{n}C_{r} \), then value of \( n \) is

If the lines \( x + (k - 1)y + 3 = 0 \) \& \( 2x + k^2y - 4 = 0 \) are perpendicular and their point of intersection is the centre of a circle which passes through origin. If chord \( x - y + 2 = 0 \) intersects this circle at \( A \) \& \( B \) then \( (AB)^2 = ? \)

Let \( x(y) \) be the solution of the given differential equation \( 2y^2 \dfrac{dx}{dy} - 2xy + x^2 = 0 \). If \( x(e) = e \), then \( \dfrac{3x(e^2)}{e^2} \) equals.

Find number of points of discontinuity of the function \( f(x) = [x^2 - x + 2] \) in \( x \in [2,4] \) (where \( [\ ] \) denotes greatest integer function).

If \( z_1 \) lies on curve \( |z| = r \) and \( z_2 \) lies on curve \( |z - 3 - 4i| = 5 \), if minimum of \( |z_1 - z_2| = 2 \), then the maximum of \( |z_1 - z_2| \) is