List of top Questions asked in JEE Main

Let \( H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} \). Let \( k \) be the smallest even value of \( n \) such that the eccentricity of \( H_n \) is a rational number. If \( l \) is the length of the latus rectum of \( H_k \), then 21 \( l \) is equal to:
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:
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:
Let (\alpha, \beta, \gamma) \text{ be the image of the point } P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6. \text{ Then } \alpha + \beta + \gamma \text{ is equal to:}
\( Let f(x) = | x^2 - x | + |x|, \text{ where } x \in \mathbb{R} \text{ and } | t | \text{ denotes the greatest integer less than or equal to } t. \text{ Then, } f \text{ is:} \)
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 triplets \( (x, y, z) \), where \( x, y, z \) are distinct non-negative integers satisfying \( x + y + z = 15 \), 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:
Area of the region \((x, y) : x^2 + (y - 2)^2 \leq 4, \, x^2 \geq 2y\) is:
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:
The number of elements in the set \(S = \{ \theta \in [0, 2\pi] : 3 \cos^4 \theta - 5 \cos^2 \theta - 2 \sin^2 \theta + 2 = 0 \}\) is:
The value of the integral \[ \int_{\log_2}^{-\log_2} e^x \left( \log \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx \] 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,
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:
The number of integral solutions of \( \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 \) is:
Let \(x_1, x_2, \dots, x_{100}\) be in an arithmetic progression, with \(x_1 = 2\) and their mean equal to 200. If \(y_i = (i \cdot x_i)\), then the mean of \(y_1, y_2, \dots, y_{100}\) is:
The value of x compound ‘D’ is
The value of x compound ‘D’ is  H5C2OCHNH4CLKCNH2SO4H
Three organic compounds A, B and C were allowed to run in thin layer chromatography using hexane and gave the following result (see figure). The Rf value of the most polar compound is ____ x 10-2.
The reaction 2NO + Br2 → 2NOBr 
takes places through the mechanism given below : 
NO + Br2 ⇔ NOBr2 (fast)  
NOBr2 + NO → 2NOBr (slow) 
The overall order of the reaction is_____.
pH of 1 litre of HCL solution is 1. How much water (in litres) is added to make pH=2?
80 mole percent of MgCl2 is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of MgCl2 at 38°C is ____mm Hg. (Nearest integer)
Given : Vapour pressure of water at 38°C is 50 mm Hg.
Match the terms in Column-I with their description in Column-II and choose the correct option:
 Column I Column II
(A).Biodegradable(P).Polyacrylonitrie
(B).Synthetic(Q).PHBV
(C).Natural(R).Dacron
(D).Polyester(S).Rubber
The incorrect statement regarding the reaction given below is
NaNO2 +HX-'B'

Let [t] denote the greatest integer function. If \(\int\limits_0^{2.4}[x^2]dx=α+β√2+γ√3+δ√5,\) then α+β+γ +δ is equal to _____.

Let \( k \) and \( m \) be positive real numbers such that the function} \[ f(x) = \begin{cases} 3x^2 + \frac{k}{\sqrt{x} + 1}, & 0 < x < 1, \\ mx^2 + k^2, & x \geq 1 \end{cases} \] is differentiable for all \( x > 0 \). Then \( 8f'(8) \left(\frac{1}{f(8)}\right) \) is equal to __________