List of top Questions asked in WBJEE

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

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

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

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

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

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. ${\mathrm{CH}}_3-\mathrm{CH}={\mathrm{CH}}_2$

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.

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

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,

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?

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

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 

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?

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

The door of a running refrigerator inside a closed room was left open. Which of the following observations will be seen?

The value(s) of k for which the equations x² - kx - 21 = 0 and x² - 3kx + 35 = 0 will have a common root is/are

In a triangle ABC, tan C < 0. Then

If the ratio of the roots of the equation $p{x}^2+qx+r=0$ is $a:b,$ then $\frac{ab}{(a+b{)}^2}=$

The sum of n terms of an AP is n² + n; the common difference will be: