WB JEE 2023

Let A be a set containing n elements. A subset P of A is chosen, and the 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 mo...

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

Let A and B are two independent events. The probability that both A and B happen is \({1 \over {12}}\) and probability that neither A and B happen is \({1 \over 2}\). Then

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

ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC = 10, then OP equals

If one root of \({x^2} + px - {q^2} = 0,p\) and \(q\) are real, be less than 2 and other be greater than 2, then

If the n terms \({a_1},{a_2},\,......,\,{a_n}\) are in A.P. with increment r, then the difference between the mean of their squares & the square of their mean is

If \(1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)\) are in A.P., then x equals

Consider a quadratic equation \(a{x^2} + 2bx + c = 0\) where a, b, c are positive real numbers. If the equation has no real root, then which of the following is true?

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

Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:

Let X be a nonvoid set. If \(\rho_1\) and \(\rho_2\) be the transitive relations on X, then
(\(\circ\) denotes the composition of relations)

Let \(\rho\) be a relation defined on set of natural numbers N, as \(\rho = \{ (x,y) \in N \times N:2x + y = 4\}\). Then domain A and range B are

If R and R\(^1\) are equivalence relations on a set A, then so are the relations

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

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

If \(4{a^2} + 9{b^2} - {c^2} + 12ab = 0\), then the family of straight lines \(ax + by + c = 0\) is concurrent at

The straight lines \(x + 2y - 9 = 0,3x + 5y - 5 = 0\) and \(ax + by - 1 = 0\) are concurrent if the straight line \(35x - 22y + 1 = 0\) passes through the point

The locus of points (x, y) in the plane satisfying \({\sin ^2}x + {\sin ^2}y = 1\) consists of

A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = \(-\)1 respectively. The coordinate of C can be

If the distance between the plane \(\alpha x - 2y + z = k\) and the plane containing the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) is \(\sqrt 6\), ...

The angle between a normal to the plane \(2x - y + 2z - 1 = 0\) and the X-axis is

If \({1 \over 6}\sin \theta ,\cos \theta ,\tan \theta\) are in G.P, then the solution set of \(\theta\) is
(Here \(n \in N\))

The value of 'a' for which the scalar triple product formed by the vectors \(\overrightarrow \alpha = \widehat i + a\widehat j + \widehat k,\overrightarrow \beta = \widehat j + a\widehat k\) and $$\overrightarrow \gamma = a\widehat i ...

If the volume of the parallelopiped with \(\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overrightarrow c\) and \(\overrightarrow c \times \overrightarrow a\) as conterminous edges is 9 cu. units, then the volum...