List of top Questions asked in JEE Main

If in a G.P. of64terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to:

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

If the function \(f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, \, a>0\) has a local maximum at \(x = \alpha\) and a local minimum at \(x = \alpha^2\), then \(\alpha\) and \(\alpha^2\) are the roots of the equation:

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ______ m.

The number of electrons present in all the completely filled subshells having n=4 and s=+½​ is _____. (Where n = principal quantum number and s = spin quantum number).

If \(f(x)=\begin{vmatrix} x^3 & 2x^2+1 & 1+3x \\[0.3em] 3x^2+2 & 2x & x^3+6 \\[0.3em] x^3-x & 4 & x^2-2 \end{vmatrix}\)  for all \(x∈R\), then \(2f(0) + f'(0)\) is equal to

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \( R_1 = 2\pi \, m \) and \( R_2 = 4\pi \, m \) carrying current \( I = 4A \) as per figure given below is \( \alpha \times 10^{-7} \, T \). The value of \( \alpha \) is ______. (Centre O is common for all segments)

A sample of \( \text{CaCO}_3 \) and \( \text{MgCO}_3 \) weighed 2.21 g is ignited to constant weight of 1.152 g. The composition of the mixture is:
(Given molar mass in g mol\(^{-1}\))

Position of an ant \( S \) (in meters) moving in the Y-Z plane is given by \( S = 2t \hat{j} + 5t \hat{k} \) (where \( t \) is in seconds). The magnitude and direction of velocity of the ant at \( t = 1 \, s \) will be:

Consider the two different first-order reactions given below: \[\text{A + B} \rightarrow \text{C (Reaction 1)} \\\text{P} \rightarrow \text{Q (Reaction 2)}\]The ratio of the half-life of Reaction 1 : Reaction 2 is $5 : 2$. If $t_1$ and $t_2$ represent the time taken to complete $\frac{2}{3}^\text{rd}$ and $\frac{4}{5}^\text{th}$ of Reaction 1 and Reaction 2, respectively, then the value of the ratio $t_1 : t_2$ is ____ $\times 10^{-1}$ (nearest integer).[Given: $\log_{10}(3) = 0.477$ and $\log_{10}(5) = 0.699$]

Two vertices of a triangle \( \triangle ABC \) are \( A(3, -1) \) and \( B(-2, 3) \), and its orthocentre is \( P(1, 1) \). If the coordinates of the point \( C \) are \( (\alpha, \beta) \) and the centre of the circle circumscribing the triangle \( \triangle PAB \) is \( (h, k) \), then the value of \[ (\alpha + \beta) + 2(h + k) \] equals:

1 mole of PbS is oxidised by “X” moles of O₃>to get “Y” moles of O2. X + Y = __________

A clock has a 75 cm long second hand and a 60 cm long minute hand, respectively. In 30 minutes duration, the tip of the second hand will travel \(x\) distance more than the tip of the minute hand. The value of \(x\) in meters is nearly (Take \(\pi = 3.14\)):

Ail organic compound has 42.1% carbon, 6.4% hydrogen and remainder is oxygen. If its molecular weight is 342, then its molecular formula is :

Let 2nd, 8th, and 44th terms of a non-constant A.P. be respectively the 1st, 2nd, and 3rd terms of a G.P. If the first term of A.P. is 1, then the sum of the first 20 terms is equal to

In the given circuit, the current in resistance R3 is :

Let \( A = \{2, 3, 6, 7\} \) and \( B = \{4, 5, 6, 8\} \). Let \( R \) be a relation defined on \( A \times B \) by \((a_1, b_1) R (a_2, b_2)\) if and only if \(a_1 + a_2 = b_1 + b_2\). Then the number of elements in \( R \) is __________.

Let a circle passing through (2, 0) have its centre at the point \( (h, k) \). Let \( (x_c, y_c) \) be the point of intersection of the lines \( 3x + 5y = 1 \) and \( (2 + c)x + 5c^2y = 1 \). If \( h = \lim_{c \to 1} x_c \) and \( k = \lim_{c \to 1} y_c \), then the equation of the circle is:

Let \( S_n \) denote the sum of the first \( n \) terms of an arithmetic progression. If \( S_{20} = 790 \) and \( S_{10} = 145 \), then \( S_{15} - S_5 \) is:

Let \( A, B, \) and \( C \) be three points on the parabola \( y^2 = 6x \), and let the line segment \( AB \) meet the line \( L \) through \( C \) parallel to the \( x \)-axis at the point \( D \). Let \( M \) and \( N \) respectively be the feet of the perpendiculars from \( A \) and \( B \) on \( L \). Then \[ \left( \frac{\text{AM} \cdot \text{BN}}{\text{CD}} \right)^2 \] is equal to ______ .

Which of the following compounds has the highest boiling point?

Given below are two statements :
Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford’s model.
Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford’s model.
In the light of the above statements, choose the most appropriate from the options given below.

Let \( f : \mathbb{R} \to \mathbb{R} \) be a thrice differentiable function such that \[ f(0) = 0, \, f(1) = 1, \, f(2) = -1, \, f(3) = 2, \, \text{and} \, f(4) = -2. \] Then, the minimum number of zeros of \( (3f' f' + f'') (x) \) is:

To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is :

If \( S = \{ a \in \mathbb{R} : |2a - 1| = 3[a] + 2\{a\} \} \), where \([t]\) denotes the greatest integer less than or equal to \(t\) and \(\{t\}\) represents the fractional part of \(t\), then \( 72 \sum_{a \in S} a \) is equal to _________.