List of top Questions asked in WBJEE

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, Then 

If R and R₁ are equivalence relations on a set A, then so are the relations

An electron in the 5d orbital can be represented by the following(n,1,mr) values

The correct set(s) of reactions to synthesize benzoic acid starting from benzene is/are

The conversion(s) that can be carried out by bromine in carbon tetrachloride solvent is/are

If all the nucleophilic substitution reactions at saturated carbon atoms in the above sequence of reactions follow Sn₂ mechanism, then E and F will be respectively,

Which of the following mixtures act(s) as a buffer solution?

For the reaction A+B\(\rightarrow\)C, we have the following data:

Initial concentration of A(in molarity)	Initial concentration of B (in molarity)	Rate(initial)(Relevant unit)
1	10	100
1	1	1
10	1	10

The order of the reaction with respect to A and B are:

The tangent at point(a cosθ, b sinθ), 0<θ<\(\frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the x-axis at T and y-axis at T₁, Then the value of \(\min_{\,\,\,0<\theta<\frac{\pi}{2}}\)(OT)(OT₁) is

A, B are fixed points with coordinates (0,a) and (0,b) (a>0,b>0). P is a variable point (x,0) referred to as the rectangular axis. If the angle \(\angle\)APB is maximum, then

63g of a compound (Mol.Wt.=126) was dissolved in 500g of distilled water.The density of the resultant solution is 1.126g/ml. The molarity of the solution is

\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) is equal to

Let A be the point (0,4) in the xy-plane and B be the point (2t,0). Let L be AB's midpoint and let AB's perpendicular bisector meet the y-axis M. Let N be the midpoint of LM. The locus of N is

The equation \(r^2=cos^2(\theta-\frac{\pi}{3})=2\) represents

The average length of all vertical chords of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\),  \(a \leq x\leq 2a\), is

Let A be a set containing n elements, A subset P of A is chosen and set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

Let a₁, a₂, a₃,.....,a_n be positive real numbers.Then the minimum value of \(\frac{a_1}{a_2}+\frac{a_2}{a_3}+....+\frac{a_n}{a_1}\) is

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and E_k={(a,b)∈S:ab=k}. If P_k=P(E_k), then the correct among the following is 

Which statement(s) is/are applicable above critical temperature?

Let A and B be orthogonal and det A+det B=0. Then

Which of the following statements is incorrect? 

The expression \(\frac{\int_{0}^{n}[x]dx}{\int_{0}^{n}\left \{ x\right \}dx}\), where [x] and {x} are respectively integral and fractional part of x and n∈N, is equal to

Reflection of the line \(\bar{a}z\)+\(a\bar{z}\)=0 in the real axis is given by

If the volume of the parallelopiped with \(\vec a\times \vec b\), \(\vec b\times \vec c\)  and  \(\vec c\times \vec a\) as coterminous edges is 9 cu. units,then the volume of the parallelopiped with (\(\vec a\times \vec b\))×(\(\vec b\times \vec c\)), (\(\vec b\times \vec c\))×(\(\vec c\times \vec a\)) and (\(\vec c\times \vec a\))×(\(\vec a\times \vec b\)) as coterminous edges is

If the distance between the plane αx-2y+z=k and the plane containing the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) is \(\sqrt{6}\), then|k| is :