List of top Questions asked in WBJEE

Directions: The following question has four choices, out of which one or more are correct.Let $\alpha =a\hat{i}+b\hat{j}+c\hat{k},\beta =b\hat{i}+c\hat{j}+a\hat{k}$ and $y=c\hat{i}+a\hat{j}+b\hat{k}$ be three co-planar vectors with $a\ne b$ and$v=\hat{i}+\hat{j}+\hat{k},$ Then $v$ is perpendicular to

Directions: The following question has four choices, out of which one or more are correct.The internal bisector of $\mathrm{\angle }A$ of a triangle $ABC$ meets side $BC$ at $D$. A line drawn through $D$ perpendicular to $AD$ intersects the side $AC$ at $E$ and side $AB$ at $F$. If $a,b$ and $c$ represent the sides of $\mathrm{\Delta }ABC$, then

Complexes formed in the cyanide process are:

A solution of colourless unknown salt (X) on boiling with excess of NaOH produces non-flammable gas. The gas evolution ceases after some time. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt (X) is (are)

The longest wavelength in A^o in the Balmer series of singly ionised helium ion, He⁺ is

${\int }_0^2\left[x^2\right]dx\mid$ is equal to

Consider the following reaction in aqueous medium at 25^oC.

The equilibrium of above reaction shifts towards left in the presence of

3-tert-butylphenol reacts with different halogens by electrophillic substitution under appropriate conditions that are given below:

The observed pattern of electrophillic substitution can be explained by

Which of the following is the most suitable reagent used to distinguish compound (3) from rest of the compounds? 1. ${\mathrm{CH}}_3-\mathrm{C}\equiv \mathrm{C}-{\mathrm{CH}}_3$2. ${\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_3$3. ${\mathrm{CH}}_3-{\mathrm{CH}}_2\mathrm{C}$ : $\mathrm{CH}$4. ${\mathrm{CH}}_3-\mathrm{CH}={\mathrm{CH}}_2$

Sulphuric acid reacts with sodium hydroxide as follows.H2SO4 + 2NaOH ⇒ Na2SO4 + 2H2Ohen 1L of 0.1 M sulphuric acid solution is allowed to react with 1 L of 0.1 M sodium hydroxide solution, the amount of sodium sulphate formed and its molarity in the solution obtained is

Select the option(s) in which rate of SN1 is faster in II than I?

The two structures written below represent 

Directions: The following question has four choices, out of which one or more are correct. Assume that the nuclear binding energy per nucleon $\left(\frac{B}{A}\right)$ versus mass number (A) is as shown in the figure. Use this plot to choose the correct answer(s) from the choices given below.

The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is

Directions: The following question has four choices, out of which one or more are correct. The potential energy function of a particle moving in one dimension is $U=k[x-\frac{x^3}{3a^2}],$ where $a$ and $k$ areconstants. Then,

Directions: The following question has four choices, out of which one or more are correct.In a triangle $\mathrm{\Delta }PQR,\cos (P-R)\cos (Q)+\cos (2Q)=0$Which of the following options is/are correct?

$\int e^{x\log a}\cdot e^{x}dx$ is equal to

The cubic equation whose roots are the AM, GM and HM of the roots of x² - 2px + q² = 0 is

If n = 1, 2, 3 ..., then cos cos2∝ cos4∝… cos ^{2n - 1} ∝is equal to

A plane x + 2y + 2z – 15 = 0 cuts a sphere x² + y² + z² – 2y – 4z – 11 = 0 in a circular section. What is the radius of the cut section?

If the coordinates of one end of a diameter of the circle  x²+y²+4x–8y+5=0, is (2,1), the coordinates of the other end is 

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume, when radius is 4 m and altitude is 6 m, is

 If ⁿC4, ⁿC5 and ⁿC6 are in A.P., then n is 

The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is