WB JEE 2018

Let P(at2, 2at), Q, R(ar2, 2ar) be three points on a parabola y2 = 4ax. If PQ is the focal chord and PK, QR are parallel where the co-ordinates of K is (2a, 0), then the value of r is

Let A, B the two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, \(-\) 4) and Q(9, 6). Let R be a point on the arc of the parabola between P and Q. Then, the area of \(\Delta\)PQR is largest when

The number of selection of n objects from 2n objects of which n are identical and the rest are different, is

If (2 \(\le\) r \(\le\) n), then \({}^n{C_r}\) + 2 . \({}^n{C_{r + 1}}\) + \({}^n{C_{r + 2}}\) is equal to

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are 20 students in the class, the number of cards sends by students is

In order to get a head at least once with probability \(\ge\) 0.9, the minimum number of times a unbiased coin needs to be tossed is

A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing in tests I, II and III are respectively p, q and 1/2. If the probability of the student to ...

If the equation \({x^2} - cx + d = 0\) has roots equal to the fourth powers of the roots of \({x^2} + ax + b = 0\), where \({a^2} > 4b\), then the roots of \({x^2} - 4bx + 2{b^2} - c = 0\) will be

If \({b_1}{b_2} = 2({c_1} + {c_2})\) and b1, b2, c1, c2 are all real numbers, then at least one of the equations \({x^2} + {b_1}x + {c_1} = 0\) and \({x^2} + {b_2}x + {c_2} = 0\) has

Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b \(\in\) R. Suppose further that the mth means between these sets of numbers are same, then the ratio a : b equals

On R, a relation \(\rho\) is defined by x\(\rho\)y if and only if x \(-\) y is zero or irrational. Then,

Let \(\rho\) be a relation defined on N, the set of natural numbers, as\(\rho\) = {(x, y) \(\in\) N \(\times\) N : 2x + y = 41}. Then

On the set R of real numbers, the relation \(\rho\) is defined by x\(\rho\)y, (x, y) \(\in\) R.

The angular points of a triangle are A(\(-\) 1, \(-\) 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle \(\angle\)ABC is

The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the lines y = x and x + y = 2 is h2. The locus of the point P is

The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = \(-\) X. The circumcentre of the \(\Delta\)PQR is

A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, \(-\)3). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P and the Y-axis at Q. If AQ and BP meet at R, then the locus of R is

The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, \(-\)11, 4) and (2, \(-\)3, 1) is

A point P lies on a line through Q(1, \(-\)2, 3) and is parallel to the line \({x \over 1} = {y \over 4} = {z \over 5}\). If P lies on the plane 2x + 3y \(-\) 4z + 22 = 0, then segment PQ equals

If sin6\(\theta\) + sin4\(\theta\) + sin2\(\theta\) = 0, then general value of \(\theta\) is

The approximate value of sin31\(^\circ\) is

Let \(\overrightarrow \alpha\), \({\overrightarrow \beta }\), \({\overrightarrow \gamma }\) be the three unit vectors such that \(\overrightarrow \alpha .\overrightarrow \beta = \overrightarrow \alpha .\overrightarrow \gamma = 0\)...

Let \(\overrightarrow \alpha\) = \(\widehat i + \widehat j + \widehat k\), \(\overrightarrow \beta\) = \(\widehat i - \widehat j - \widehat k\) and \({\overrightarrow \gamma }\) = \(- \widehat i - \widehat j - \widehat k\) be three ve...