List of top Mathematics Questions asked in JEE Main

Two sides of a parallelogram are along the lines $4x+5y=0$ and $7x+2y=0$. If the equation of one of the diagonals of the parallelogram is $11x+7y=9$, then other diagonal passes through the point :

Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x+y) + f(x-y) = 2f(x)f(y)$, $f(\frac{1}{2}) = -1$. Then, the value of $\sum_{k=1}^{20} \frac{1}{\sin(k) \sin(k+f(k))}$ is equal to :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $6\sqrt{5}$ on the x-axis. Then the radius of the circle C is equal to :

Let P be a plane containing the line (x-1)/3 = (y+6)/4 = (z+5)/2 and parallel to the line (x-3)/4 = (y-2)/(-3) = (z+5)/7. If the point (1, -1, α) lies on the plane P, then the value of |α| is equal to ________.

Let \( f : \mathbb{R} \to \mathbb{R} \) be a function defined as \[ f(x) = \begin{cases} \dfrac{\sin\!\big((a+1)x\big) + \sin 2x}{2x}, & \text{if } x < 0, \\[6pt] b, & \text{if } x = 0, \\[6pt] \dfrac{\sqrt{x + b x^3} - \sqrt{x}}{b\, x^{5/2}}, & \text{if } x > 0. \end{cases} \] If \( f \) is continuous at \( x = 0 \), then the value of \( a + b \) is equal to :

Let f: R → R satisfy the equation f(x + y) = f(x) · f(y) for all x, y ∈ R and f(x) ≠ 0 for any x ∈ R. If the function f is differentiable at x=0 and f'(0)=3, then lim_{h → 0} (1/h) (f(h) - 1) is equal to ________.

Let y=y(x) be the solution of the differential equation x dy - y dx = √(x² - y²) dx, x ≥ 1, with y(1) = 0. If the area bounded by the line x=1, x=e^{π}, y=0 and y=y(x) is α e^{2π} + β, then the value of 10(α + β) is equal to ________.

Let P(x) be a real polynomial of degree 3 which vanishes at x = -3. Let P(x) have local minima at x = 1, local maxima at x = -1 and ∫_{-1}^{1} P(x) dx = 18, then the sum of all the coefficients of the polynomial P(x) is equal to ________.

Let I be an identity matrix of order 2 × 2 and P = [2 -1; 5 -3]. Then the value of n ∈ N for which Pⁿ = 5I - 8P is equal to ________.

The term independent of x in the expansion of [ (x + 1)/(x^{2/3} - x^{1/3} + 1) - (x - 1)/(x - x^{1/2}) ]¹⁰, x ≠ 1, is equal to ________.

Let n C_r denote the binomial coefficient of x^r in the expansion of (1 + x)^n. If ∑_{k=0}^{10} (2² + 3k) n C_k = α 3^{10} + β 2^{10}, α, β ∈ R, then α + β is equal to ________.

If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x · g(x³) is divisible by x² + x + 1, then P(1) is equal to ________.

If ∑_{r=1}^{10} r! (r³ + 6r² + 2r + 5) = α (11!), then the value of α is equal to ________.

Let the mirror image of the point (1, 3, a) with respect to the plane r · (2 i - j + k) - b = 0 be (-3, 5, 2). Then, the value of |a + b| is equal to ________.