WB JEE 2022

A line passes through the point \(( - 1,1)\) and makes an angle \({\sin ^{ - 1}}\left( {{3 \over 5}} \right)\) in the positive direction of x-axis. If this line meets the curve \({x^2} = 4y - 9\) at A and B, then |AB| is equal to

Let P be a point on (2, 0) and Q be a variable point on (y \(-\) 6)2 = 2(x \(-\) 4). Then the locus of mid-point of PQ is

AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

From the point (\(-\)1, \(-\)6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is

Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is

If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the

There are n white and n black balls marked 1, 2, 3, ...... n. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

A, B, C are mutually exclusive events such that \(P(A) = {{3x + 1} \over 3}\), \(P(B) = {{1 - x} \over 4}\) and \(P(C) = {{1 - 2x} \over 2}\). Then the set of possible values of x are in

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is

If a, b are odd integers, then the roots of the equation \(2a{x^2} + (2a + b)x + b = 0\), \(a \ne 0\) are

The value of a for which the sum of the squares of the roots of the equation \({x^2} - (a - 2)x - a - 1 = 0\) assumes the least value is

If a, b, c are in G.P. and log a \(-\) log 2b, log 2b \(-\) log 3c, log 3c \(-\) log a are in A.P., then a, b, c are the lengths of the sides of a triangle which is

Let \({a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}\) and \({b_n} = {n^n}(n!)\). Then

A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P \(\cap\) Q = \(\varphi\) is

Let S, T, U be three non-void sets and f : S \(\to\) T, g : T \(\to\) U and composed mapping g . f : S \(\to\) U be defined. Let g . f be injective mapping. Then

For the mapping \(f:R - \{ 1\} \to R - \{ 2\}\), given by \(f(x) = {{2x} \over {x - 1}}\), which of the following is correct?

Let R and S be two equivalence relations on a non-void set A. Then

If the algebraic sum of the distances from the points (2, 0), (0, 2) and (1, 1) to a variable straight line be zero, then the line passes through the fixed point

If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is

Consider the equation \(y - {y_1} = m(x - {x_1})\). If m and x1 are fixed and different lines are drawn for different values of y1, then

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y \(-\) z + 4 = 0 and parallel to the x-axis is

The line \(x - 2y + 4z + 4 = 0\), \(x + y + z - 8 = 0\) intersect the plane \(x - y + 2z + 1 = 0\) at the point

If \((\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2\), then the maximum value of \((\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})\) is given by

If \(\overrightarrow a = \widehat i + \widehat j - \widehat k\), \(\overrightarrow b = \widehat i - \widehat j + \widehat k\) and \(\overrightarrow c\) is unit vector perpendicular to \(\overrightarrow a\) and coplanar with $$\overright...

If \({\overrightarrow \alpha }\) is a unit vector, \(\overrightarrow \beta = \widehat i + \widehat j - \widehat k\), \(\overrightarrow \gamma = \widehat i + \widehat k\) then the maximum value of $$\left[ {\overrightarrow \alpha \over...