WB JEE 2017

The axis of the parabola \({x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0\) is

The focus of the conic x2 \(-\) 6x + 4y + 1 = 0 is

The number of all numbers having 5 digits, with distinct digits is

Out of 7 consonants and 4 vowels, words are formed each having 3 consonants and 2 vowels. The number of such words that can be formed is

The probability that a non-leap year selected at random will have 53 Sunday is

For real x, the greatest value of \({{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}\) is

The greatest integer which divides \((p + 1)(p + 2)(p + 3)...(p + q)\) for all \(p \in N\) and fixed \(q \in N\) is

Let \(\alpha\) and \(\beta\) be the roots of \({x^2} + x + 1 = 0\). If n be a positive integer, then \(\alpha\)n + \(\beta\)n is

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

If a, b\(\in\) {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then

In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is

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

On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,

On the set R of real numbers we define xPy if and only if xy \(\ge\) 0. Then, the relation P is

On R, the set of real numbers, a relation \(\rho\) is defined as 'a\(\rho\)b if and only if 1 + ab > 0'. Then,

Mean of n observations x1, x2, ...., xn is \(\overline x\). If an observation xq is replaced by xq' then the new mean is

The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = \(-\) x to get the image point Q'. Then, the circumcentre of the \(\Delta\)PQQ' is

Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line \(7x - 9y + 10 = 0\) upon the lines 3x + 4y = 5 and 12x + 5y = 7, respectively. Then,

Let A(2, \(-\)3) and B(\(-\) 2, 1) be two angular points of \(\Delta\)ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by

Transforming to parallel axes through a point (p, q), the equation \(2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0\) becomes \(2{x^2} + 3xy + 4{y^2} = 1\). Then,

Three lines are drawn from the origin O with direction cosines proportional to (1, \(-\)1, 1), (2, \(-\)3, 0) and (1, 0, 3). The three lines are

The equation of the plane through (1, 2, \(-\)3) and (2, \(-\)2, 1) and parallel to X-axis is

The equation \(\sin x(\sin x + \cos x) = k\) has real solutions, where k is a real number. Then,

For any vector x, where \(\widehat i\), \(\widehat j\), \(\widehat k\) have their usual meanings the value of \({(x \times \widehat i)^2} + {(x \times \widehat j)^2} + {(x \times \widehat k)^2}\) where \(\widehat i\), \(\widehat j\), $$\wid...

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is