List of top Questions asked in JEE Main

The ratio x/y on completion of the above reaction is _____

In an electrochemical reaction of lead, at standard temperature, if \( E^{\circ}(\text{Pb}^{2+}/\text{Pb}) = m \) volt and \( E^{\circ}(\text{Pb}^{4+}/\text{Pb}^{2+}) = n \) volt, then the value of \( E^{\circ}(\text{Pb}^{4+}/\text{Pb}) \) is given by \( m - xn \). The value of \( x \) is ____

A solution of sugar is obtained by mixing 200g of its 25% solution and 500g of its 40% solution (both by mass). The mass percentage of the resulting sugar solution is ______ (Nearest integer)

0.004 M K₂SO₄ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K₂SO₄ is______ (Nearest integer)

The number of hyperconjugation structures involved to stabilize carbocation formed in the below reaction is _______

The above reaction was studied at 300 K by monitoring the concentration of FeSO₄, in which initial concentration was 10 M and after half an hour became 8.8 M. The rate of production of Fe₂(SO₄)₃ is _____ × 10⁻⁶ mol L⁻¹ s⁻¹

For \( m, n>0 \), let \( \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt \). If \( \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt \) and \( \alpha(11,5) = p(14)^{5} \), then \( p \) is equal to:

Let \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} \), where \( a, c \in \mathbb{R} \). If \( A^n = A \) and the positive value of \( a \) belongs to the interval \( (n-1, n] \), where \( n \in \mathbb{N} \), then \( n \) is equal to:

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

The number of integral terms in the expansion of (3^1/2 + 5^1/4)⁶⁸⁰ is equal to:

Let f(x) = [x² - x] + [x], where x ∈ R and [t] denotes the greatest integer less than or equal to t. Then, f is:

Let (α, β, γ) be the image of the point P(3, 3, 5) in the plane 2x + y - 3z = 6. Then α + β + γ is equal to:

Let $y = y(x)$ be a solution curve of the differential equation $$(1 - x^2 y)\,dx = y\,dx + x\,dy.$$ If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$, then a value of $\alpha$ is:

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \( 2x + 4y + 5z = 8 \) and \( 3x - 2y + 3z = 5 \), is \( \alpha x + \beta y + \gamma z = 97 \), then \( \alpha + \beta + \gamma \) is:

Consider ellipse \( E_k : \frac{x^2}{k} + \frac{y^2}{k} = 1 \), for \( k = 1, 2, \dots, 20 \). Let \( C_k \) be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse \( E_k \). If \( r_k \) is the radius of the circle \( C_k \), then the value of \( \sum_{k=1}^{20} r_k^2 \) is:

Let \( w_1 \) be the point obtained by the rotation of \( z_1 = 5 + 4i \) about the origin through a right angle in the anticlockwise direction, and \( w_2 \) be the point obtained by the rotation of \( z_2 = 3 + 5i \) about the origin through a right angle in the clockwise direction. Then the principal argument of \( w_1 - w_2 \) is equal to:

Let \( \mathbf{a} \) be a non-zero vector parallel to the line of intersection of the two planes described by \( i + j + k \) and \( -i - j - k \). If \( \theta \) is the angle between the vector \( \mathbf{a} \) and the vector \( \mathbf{b} = -2i - 2j + 2k \), and \( \left| \mathbf{a} \right| = 6 \), then ordered pair \( (\mathbf{a} \cdot \mathbf{b}) \) is equal to:

Area of the region \((x, y) : x^2 + (y - 2)^2 \leq 4, \, x^2 \geq 2y\) is:

Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

The number of triplets \( (x, y, z) \), where \( x, y, z \) are distinct non-negative integers satisfying \( x + y + z = 15 \), is:

For any vector \( \mathbf{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \), with \( 10 | \mathbf{a} |<1 \), \( i = 1, 2, 3 \), consider the following statements:

The number of integral solutions of \( \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 \) is:

Let A be a \( 2 \times 2 \) matrix with real entries such that \( A^T = \alpha A + I \), where \( \alpha \in \mathbb{R} \setminus \{-1, 1\} \). If \( \text{det}(A^2 - A) = 4 \), then the sum of all possible values of \( \alpha \) is equal to:

Let \( f: [2, 4] \to \mathbb{R} \) be a differentiable function such that \( (x \log x) f'(x) + (\log x) f(x) \geq 1 \), \( x \in [2, 4] \) with \( f(2) = \frac{1}{2} \) and \( f(4) = \frac{1}{4} \). Consider the following two statements:
\( (A) \quad f(x) \geq 1 \quad \text{for all} \quad x \in [2, 4] \)
\( (B) \quad f(x) \leq \frac{1}{8} \quad \text{for all} \quad x \in [2, 4] \) Then,