List of top Questions asked in WBJEE

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
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
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 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)
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 ?
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
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
General solution of $\left(x+y\right)^{2} \frac{dy}{dx} = a^{2}, a \ne 0$ is (c is an arbitrary constant)
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
Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also moves around the sun in circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is
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 ....."
Let a, b, c be real numbers such that $a + b + c < 0$ and the quadratic equation $ax^2 + bx + c = 0$ has imaginary roots. Then
The initial pressure and volume of a given mass of an ideal gas $\left(with\frac{C_{p}}{C_{v}} =\gamma\right),$ taken in a cylinder fitted with a piston, are P$ _0$ and V$_0$ respectively. At this stage the gas has the same temperature as that of the surrounding medium which is T$_0$. It is adiabatically compressed to a volume equal to $\frac{v_{0}}{2}.$ Subsequently the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surroundings ?
Let S, T, U be three non-void sets and f : S $\to$ T,g : T $\to$ U is surjective. Then
Let $f(x) = x^{4} - 4x^{3} + 4x^{2} +c, c \in \mathbb{R}.$ Then
T$\displaystyle\lim_{x \to 0+}$ $\left(x^{n} \,ln\, x\right), n > 0$