WB JEE 2020

The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola is

If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through (\(-\)1, 0), then

The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. Then, the length of the latusrectum is

In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

If the total number of m-element subsets of the set A = {a1, a2, ..., an} is k times the number of m element subsets containing a4, then n is

A and B are independent events. The probability that both A and B occur is \({1 \over {20}}\) and the probability that neither of them occurs is \({3 \over {5}}\). The probability of occurrence of A is

A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire to have more than 50% chance of hitting it at least once, is

Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins if A begins?

The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if

Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an equilateral triangle if

If P(x) = ax2 + bx + c and Q(x) = \(-\)ax2 + dx + c, where ac \(\ne\) 0 [a, b, c, d are all real], then P(x).Q(x) = 0 has

In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i = 1, 2, ..., n. If the total number of wrong answers given is 2047, then n is equal to

If a and b are arbitrary positive real numbers, then the least possible value of \({{6a} \over {5b}} + {{10b} \over {3a}}\) is

Let I(n) = nn, J(n) = 13.5 ......... (2n \(-\) 1) for all (n > 1), n \(\in\) N, then

Let the relation p be defined on R by a p b holds if and only if a \(-\) b is zero or irrational, then

Let p1 and p2 be two equivalence relations defined on a non-void set S. Then

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment PQ in the ratio

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

Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, \(-\)5). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P(a, 0) and the Y-axis at Q(0, b). If AQ and BP intersect at R, the locus of R is

The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is \(- 1\) is

The sine of the angle between the straight line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) and the plane \(2x - 2y + z = 5\) is

The equation of the plane through the point \((2, - 1, - 3)\) and parallel to the lines\({{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}\) and \({x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}\) is

Let f(x) = sin x + cos ax be periodic function. Then,

\(\cos (2x + 7) = a(2 - \sin x)\) can have a real solution for

The unit vector in ZOX plane, making angles \(45^\circ\) and \(60^\circ\) respectively with \(\alpha = 2\widehat i + 2\widehat j - \widehat k\) and \(\beta = \widehat j - \widehat k\) is