List of top Mathematics Questions asked in JEE Main

Let \( A_1, A_2, A_3, \dots, A_9 \) be 9 AM’s between 49 and 149. Then the mean of \( A_1, A_2, A_3 \) and \( A_9 \) is:

Consider a parabola \( y^2 = 8x \). The directrix of parabola cuts x-axis at A and PQ is a focal chord of parabola. If slope of PA = 3/5 and abscissa of P is greater than 1, then the area of \(\Delta AQP\) is:

A bag contains 5 red balls, 6 blue balls and 4 black balls (balls of same colour are considered to be distinct). The number of ways in which 8 balls can be selected if at least two balls of each colour is there, is:

Consider the differential equation \[ \sin\left(\frac{y}{x}\right)\frac{dy}{dx} + 1 = \frac{y}{x}\sin\left(\frac{y}{x}\right) \] with \( y(1) = \frac{\pi}{2} \). Let \[ \alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right). \] If \( r \) is the radius of the circle \[ x^2 + y^2 - 2px + 2py + \alpha + 2 = 0, \] then the number of integral values of \( p \) is:

Sum of \( 1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \dots \) up to 10 terms is

The sum of all possible values of \( \theta \in [0, 2\pi] \), for which the system of equations:
\( x \cos 3\theta - 8y - 12z = 0 \)
\( x \cos 2\theta + 3y + 3z = 0 \)
\( x \sin \theta + y + 3z = 0 \)
has a non-trivial solution, is equal to:

\[ \int_{-1}^{1} \frac{x^3 + |x| + 1}{x^2 + |x| + 1} \, dx \]

The area (in square units) of the region \(\{(x,y): x^2 - 8x \leq y \leq -x\}\) is:

If the percentage change in the radius of a sphere is \(2\%\), then find the percentage change in the volume of the sphere.

If \(\left(2\alpha+1,\;\alpha^2-3\alpha,\;\frac{\alpha-1}{2}\right)\) is the image of \((\alpha,2\alpha,1)\) in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then the value of \(\alpha\) is:

P is a point on \[ \frac{x^2}{9}+\frac{y^2}{4}=1 \] as \(P(3\cos\alpha,2\sin\alpha)\). Q is a point on \[ x^2+y^2-14x+14y+82=0 \] R is a point on line \[ x+y=5 \] If the centroid of triangle \(PQR\) is \[ \left(\cos\alpha+2,\;\frac{2\sin\alpha}{3}+3\right) \] find the sum of possible ordinates of \(R\).

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

If \( \lim_{x \to 0} \frac{1 - \cos(\alpha x)\cos((\alpha + 1)x)\cos((\alpha + 2)x)}{\sin^2((\alpha + 1)x)} = 2 \), then the product of all possible values of \( \alpha \) is:

If \( f(x) \) satisfies the relation \( f\left(\frac{x+y}{3}\right) = \frac{f(x) + f(y)}{3} \) and \( f(0) = 3 \), then the minimum value of \( g(x) = 3 + e^x f(x) \) is:

Find the square of the distance of the point \( (5, 6, 7) \) from the line \( \frac{x-2}{2} = \frac{y-5}{3} = \frac{z-2}{4} \):

In the expansion of \( \left( \frac{1}{x^3} - x^4 \right)^n \), if the sum of the coefficients of \( x^7 \) and \( x^{14} \) is zero, then find \( n \):

If \( 3\sin t - 12\cos t - 3 = p \), then the sum of all integral values of 'p' such that the equation has at least one real root, is:

Let \( p(x, y) \) be a variable point on the circle \( x^2 + y^2 - 6x - 8y + 21 = 0 \). Then the maximum possible distance from the vertex of \( y^2 + 6y + x + 13 = 0 \) is:

The value of \( \int_{0}^{\pi/3} \frac{4 - \cos x \sec^3 x}{\cos^3 x} \, dx \) (or equivalent form) is:

Let \( f: A \to A \) be a function, where \( A = \{1, 2, 3, 4, 5, 6\} \). The number of one-one functions such that \( f(1) \le 3 \), \( f(3) \le 4 \) and \( f(2) + f(3) = 5 \), is:

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

If the system of equations (in variables \(x, y, z\)): \(x - 2y + tz = 0\), \(3x + 5y + t^2 z = 0\), and \(6x + ty + f(t)z = 0\) has infinitely many solutions (where \(f(t)\) represents a real function), then:

If \( \vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0} \), \( \vec{a} = \sqrt{7}\hat{i} + \hat{j} + \hat{k} \), \( \vec{b} = \hat{j} - 2\hat{k} \) and \( \vec{r} \cdot \vec{a} = 0 \), then the value of \( |3\vec{r}|^2 \) is:

If \( \tan A \) and \( \tan B \) are roots of the equation \( x^2 - 2x - 5 = 0 \), then the value of \( 10\left(\sin^2\left(\frac{A+B}{2}\right)\right) \) is: