List of top Questions asked in JEE Main

Consider the reaction: CH$\equiv$CH $\xrightarrow{\text{Red hot Fe}}$ (1) $\xrightarrow{CO, HCl, AlCl_3}$ (2). The number of sp$^2$ hybridized carbon atom(s) in the product is __________.

Using the provided information in paper chromatography

The calculated $R_f$ value of A is __________ $\times 10^{-1}$.

Let f,g : ℕ → ℕ such that f(n+1) = f(n) + f(1) ∀ n ∈ ℕ and g be any arbitrary function. Which of the following statements is NOT true?
Let the lines \( (2 - i)z = (2 + i)\bar{z} \) and \( (2 + i)z + (i - 2)\bar{z} - 4i = 0 \), (here \( i^2 = -1 \)) be normal to a circle \( C \). If the line \( iz + \bar{z} + 1 + i = 0 \) is tangent to this circle \( C \), then its radius is :
If Rolle's theorem holds for the function f(x) = x³ - ax² + bx - 4, x ∈ [1, 2] with f'(4/3) = 0, then ordered pair (a, b) is equal to :

\( \displaystyle \lim_{n \to \infty} \frac{1 + \frac{1}{2} + \cdots + \frac{1}{n}}{n} \) is equal to :

The value of \( \displaystyle \int_{-1}^{1} x^2 e^{x^3} \, dx \), where \( [t] \) denotes the greatest integer \( \leq t \), is :
If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x² - 4x + y + 8)/(x - 2), then this curve also passes through the point :
The image of the point (3, 5) in the line x - y + 1 = 0, lies on :
If the curves, x²/a + y²/b = 1 and x²/c + y²/d = 1 intersect each other at an angle of 90°, then which of the following relations is TRUE?
When a missile is fired from a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given that it is not intercepted, is 3/4. If three missiles are fired independently from the ship, then the probability that all three hit the target, is :
The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :
All possible values of θ ∈ [0, 2π] for which sin 2θ + tan 2θ>0 lie in :
The total number of positive integral solutions (x, y, z) such that xyz=24 is :
The statement A → (B → A) is equivalent to :
If \( A = \begin{bmatrix} 0 & -\tan\left(\frac{\theta}{2}\right) \\ \tan\left(\frac{\theta}{2}\right) & 0 \end{bmatrix} \) and \( (I_2 + A)(I_2 - A)^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix} \), then \( 13(a^2 + b^2) \) is equal to __________.
Let \( A = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix} \), where \( x, y \) and \( z \) are real numbers such that \( x + y + z > 0 \) and \( xyz = 2 \). If \( A^2 = I_3 \), then the value of \( x^3 + y^3 + z^3 \) is __________.
If the system of equations $kx + y + 2z = 1$, $3x - y - 2z = 2$, $-2x - 2y - 4z = 3$ has infinitely many solutions, then k is equal to ________
The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is _________
Let A₁, A₂, A₃, … be squares such that for each n ≥ 1, the length of the side of $A_n$ equals the length of diagonal of $A_{n+1}$. If the length of $A_1$ is 12 cm, then the smallest value of n for which area of $A_n$ is less than one, is __________.
The number of points, at which the function f(x) = |2x + 1| - 3|x + 2| + |x² + x - 2|, x ∈ ℝ is not differentiable, is ________
Let \( f(x) \) be a polynomial of degree 6 in \( x \), in which the coefficient of \( x^6 \) is unity and it has extrema at \( x = -1 \) and \( x = 1 \). If \( \displaystyle \lim_{x \to 0} \frac{f(x)}{x^3} = 1 \), then \( 5 \cdot f(2) \) is equal to __________.
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A⁴ is equal to __________
The locus of the point of intersection of the lines (√3)kx + ky - 4√3 = 0 and √3 x - y - 4(√3)k = 0 is a conic, whose eccentricity is _________
Let $\vec{a} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a} = \vec{c} \times \vec{a}$ and $\vec{r} \cdot \vec{b} = 0$, then $\vec{r} \cdot \vec{a}$ is equal to __________.