List of top Questions asked in WBJEE

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 $

Which of the following species exhibits both LMCT and paramagnetism?

The number(s) of -OH group(s) present in H₃PO₃ and H₃PO₄ is/are:

The compressibility factor for a van der Waals gas at high pressure is

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

The internal energy of a thermodynamic system is given by $ U = a s^{4/3} v^\alpha $, where $ s $ is entropy, $ v $ is volume, and $ a $ and $ \alpha $ are constants. The value of $ \alpha $ is:

The equivalent weight of $\text{Na}_2\text{S}_2\text{O}_3$ (Gram molecular weight = $M$) in the given reaction is:
\[\text{I}_2 + 2 \text{Na}_2\text{S}_2\text{O}_3 \rightarrow 2 \text{NaI} + \text{Na}_2\text{S}_4\text{O}_6\]

How many P–O–Plinkages are there in P₄O₁₀?

The elastic potential energy of a strained body is:

Longitudinal waves cannot:

The compounds A and B are respectively:

The equivalent capacitance of a combination of connected capacitors shown in the figure between the points P and N is:

Two convex lenses ($L_1$ and $L_2$) of equal focal length $f$ are placed at a distance $\frac{f}{2}$ apart. An object is placed at a distance $4f$ to the left of $L_1$ as shown in the figure. The final image is at:

The reactivity order of the following molecules towards SN1 reaction is:
Allyl chloride (I), Chlorobenzene (II), Ethyl chloride (III)

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 true about the equilibrium constant and rate constant of a single-step chemical reaction?

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

Toluene reacts with mixed acid at 25°C to produce:

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:

If \[ A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] and $\theta = \frac{2\pi}{7}$, then $A^{100} = A \times A \times \ldots$ (100 times) is equal to:

A unit vector in XY-plane making an angle $45^\circ$ with $\hat{i} + \hat{j}$ and an angle $60^\circ$ with $3\hat{i} - 4\hat{j}$ is:

If $a_i, b_i, c_i \in \mathbb{R}$ ($i = 1, 2, 3$) and $x \in \mathbb{R}$, and
$\begin{vmatrix} a_1 + b_1x & a_1x + b_1 & c_1 \\ a_2 + b_2x & a_2x + b_2 & c_2 \\ a_3 + b_3x & a_3x + b_3 & c_3 \end{vmatrix} = 0$,
then:

The plane $2x - y + 3z + 5 = 0$ is rotated through $90^\circ$ about its line of intersection with the plane $x + y + z = 1$. The equation of the plane in the new position is:

The equation $r \cos \theta = 2a \sin^2 \theta$ represents the curve:

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