List of top Questions asked in WBJEE

For the mapping $f: \mathbb{R} \setminus \{1\} \to \mathbb{R} \setminus \{2\}$ given by $f(x) = \frac{2x}{x - 1}$, which of the following is correct?
If the algebraic sum of the distances from the points $(2, 0)$, $(0, 2)$, and $(1, 1)$ to a variable straight line is zero, then the line passes through the fixed point.
A line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1} \left( \frac{3}{5} \right)$ with the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at $A$ and $B$, then $|AB|$ is equal to
Let $S$, $T$, $U$ be three non-void sets, where $f: S \to T$, $g: T \to U$, and the composed mapping $g \circ f: S \to U$ is defined. If $g \circ f$ is an injective mapping, then
A, B, C are mutually exclusive events such that $P(A) = \frac{3x + 1}{3}$, $P(B) = \frac{1 - x}{4}$, and $P(C) = \frac{1 - 2x}{2}$. Then the set of possible values of $x$ are in
If $\Delta(x)= \begin{vmatrix} x - 2 & (x - 1)^2 & x^3 \\ x - 1 & x^2 & (x + 1)^3 \\ x & (x + 1)^2 & (x + 2)^3 \end{vmatrix}$, then coefficient of $x$ in $\Delta(x)$ is
If $p = \begin{bmatrix} 1 & a & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of the $3 \times 3$ matrix $A$ and $\det A = 4$, then $A$ is equal to
If $A= \begin{bmatrix} 1 & 1 \\ 0 & i \end{bmatrix}$ and $A^{2018} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$, then $(a + d)$ equals
Under which of the following condition(s) does(do) the system of equations $\begin{bmatrix} 1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & a-4 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ a \end{bmatrix}$ possess(possess) a unique solution?
The Respiratory Quotient (RQ) of glucose is
A capacitor of capacitance $'C'$, is connected across an ac source of voltage $V$, given by $V = V _{0} \sin \omega t$ The displacement current between the plates of the capacitor, would then be given by:
The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is $x$. When both the current and radius is doubled the ratio will be
Compounds with spin-only magnetic moment equivalent to five unpaired electrons are
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement S is given as a function of time (t) as
The three sides of a right-angled triangle are in G.P (geometric progression). If the two acute angles be $\alpha$ and $\beta$, then tan $\alpha$ and tan $\beta$ are
The general value of the real angle $\theta$, which satisfies the equation, (cos$\theta$ + i sin$\theta$) (cos2$\theta$ + i sin2$\theta$)........ (cosn$\theta$ + i sinn$\theta$) = 1 is given by, (assuming k is an integer)
General solution of $\left(x+y\right)^{2} \frac{dy}{dx} = a^{2}, a \ne 0$ is (c is an arbitrary constant)
Let P (4, 3) be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1.$ If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is
A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions ?
An electric current ?I? enters and leaves a uniform circular wire of radius r through dfiametrically opposite points. A particle carrying a charge q moves along the axis of the circular wire with speed v. What is the magnetic force experienced by the particle when it passes through the centre of the circle ?
The kinetic study of a reaction like vA $\to$ P at 300 K provides the following curve, where concentration is taken in mol dm$^-3$ and time in min. Identify the correct order(n) and rate constant(k) :
A projectile thrown with an initial velocity of 10 ms$^-1$ at an angle $\alpha$ with the horizontal, has a range of 5 m. Taking g = 10 ms$^-2 $and neglecting air resistance, what will be the estimated value of $\alpha$ ?
In the Bayer�s process, the leaching of alumina is done by using
A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson?s ratio for the material of the rod be 0.2, which of the following statements is correct ? "The volume approximately ....."