List of top Questions asked in WBJEE- 2019

If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by

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)

Compounds with spin-only magnetic moment equivalent to five unpaired electrons are

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 $\alpha$ ?

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 ?

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 ....."

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

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

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 $f(x) = x^{4} - 4x^{3} + 4x^{2} +c, c \in \mathbb{R}.$ Then

Let S, T, U be three non-void sets and f : S $\to$ T,g : T $\to$ U is surjective. Then

T$\displaystyle\lim_{x \to 0+}$ $\left(x^{n} \,ln\, x\right), n > 0$

Identify the correct statement(s):

A copper coin was electroplated with Zn and then heated at high temperature until there is a change in colour. What will be the resulting colour ?

The compound(s), capable of producing achiral compound on heating at 100°C is/are

Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3. Then the matrix $A - 3I_3$ is

$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3,.....,n$ and the probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$ .Now , the probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is

If $log_{2}\,6+\frac{1}{2x} = log_{2}\left(2^{\frac{1}{x}} + 8\right)$, then the values of x are

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

Two weights of the mass m$_1 $and m$_2$ (> m$_1$) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads 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 ?