List of top Questions asked in WBJEE- 2024

Which of the following ion/ions is/are diamagnetic?

Consider an electron moving in the first Bohr orbit of a He$^+$ ion with velocity $v_1$. If it is allowed to move in the third Bohr orbit with velocity $v_3$, determine the correct $v_3 : v_1$ ratio.\\

The major product of the following reaction is:

In a single-slit diffraction experiment, the slit is illuminated by light of two wavelengths $\lambda_1$ and $\lambda_2$. It is observed that the 2nd order diffraction minimum for $\lambda_1$ coincides with the 3rd diffraction minimum for $\lambda_2$. Then:

For a first-order reaction with rate constant k, the slope of the plot of log(reactant concentration) against time is:

Q and R in the reaction sequences are respectively:

The elastic potential energy of a strained body is:

In the following sequence of reactions, compound 'M' is:

$ \text{M} \xrightarrow{\text{CH}_3\text{MgBr}} \text{N} + \text{CH}_4 \uparrow \xrightarrow{\text{H}^+} \text{CH}_3\text{COCH}_2\text{COCH}_3 $

A metal plate of area 10^-2m² rests on a layer of castor oil, 2 × 10^-3m thick, whose viscosity coefficient is 1.55 Ns/m². The approximate horizontal force required to move the plate with a uniform speed of 3 × 10^-2ms^-1 is:

Which of the following statements is correct for a spontaneous polymerization reaction?

Which hydrogen-like species will have the same radius as the 1st Bohr orbit of a hydrogen atom?

Which of the following statements about the S_N2 reaction mechanism is/are true?

The acceleration-time graph of a particle moving in a straight line is shown in the f igure. If the initial velocity of the particle is zero, then the velocity-time graph of the particle will be:

Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:

If two circles which pass through the points $ (0, a) $ and $ (0, -a) $ and touch the line $ y = mx + c $ cut orthogonally, then:

Let $y = f(x)$ be any curve on the X-Y plane and $P$ be a point on the curve. Let $C$ be a fixed point not on the curve. The length $PC$ is either a maximum or a minimum. Then:

Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = |x^2 - 1|$, then:

Let \[ f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2 \sin x & x^3 & 2x \\ \tan x & x & 1 \end{vmatrix}, \] then \[ \lim_{x \to 0} \frac{f(x)}{x^2} = ? \]

Consider the function
\[ f(x) = x(x - 1)(x - 2) \cdots (x - 100). \]
Which one of the following is correct?

Evaluate: $$ \lim_{n \to \infty} \frac{1}{n^{k+1}} \left[ 2^k + 4^k + 6^k + \dots + (2n)^k \right]. $$

Let $ \Gamma $ be the curve $ y = b e^{-x/a} $ and $ L $ be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If $a_n$ and $b_n$ be the $n$-th term of A.P. and G.P. respectively, then:

If for the series $a_1, a_2, a_3, \ldots$, etc., $a_{n+1} - a_n$ bears a constant ratio with $a_n + a_{n+1}$, then $a_1, a_2, a_3, \ldots$ are in:

If $ a_1, a_2, \dots, a_n $ are in A.P. with common difference $ \theta $, then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where $ k = ? $

If $(1 + x + x^2 + x^3)^5 = \sum_{k=0}^{15} a_k x^k$, then $\sum_{k=0}^{7} (-1)^k \cdot a_{2k}$ is equal to: