WB JEE 2016

The line through the points (a, b) and (\(-\)a, \(-\)b), passes through the point

The cosine of the angle between any two diagonals of a cube is

Angle between the planes x + y + 2z = 6 and 2x \(-\) y + z = 9 is

If x is a positive real number different from 1 such that logax, logbx, logcx are in AP, then

\(1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta\) equals

Let \(Q = \left[ {\matrix{ {\cos {\pi \over 4}} & { - \sin {\pi \over 4}} \cr {\sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr } } \right]\) and $$x = \left[ {\matrix{
{{1 \over {\sqrt 2 }}} \cr
{{1 \over {\sqrt 2 }}}...

The area enclosed by \(y = \sqrt {5 - {x^2}}\) and \(y = |x - 1|\) is

The equation x3 \(-\) yx2 + x \(-\) y = 0 represents

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at

If z1, z2, z3 are imaginary numbers such that \(|{z_1}|\, = \,|{z_2}|\, = \,|{z_3}|\, = \,\left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right|\, = \,1\), then \(|{z_1} + {z_2} + {z_3}|\) is

Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P \(\in\) S, such that the sum of the distance of P from (8, 0) and (0, 12) is minimum among all elements in S. Then, the number of such points P and S is

The smallest positive root of the equation tan x \(-\) x = 0 lies in

If the parabola x2 = ay makes an intercept of length \(\sqrt {40}\) units on the line y \(-\) 2x = 1, then, a is equal to

The points (\(-\)a, \(-\)b), (a, b), (0, 0) and (a2, ab), a \(\ne\) 0, b \(\ne\) 0 are always

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

The locus of the point of intersection of the straight lines \({x \over a} + {y \over b} = K\) and \({x \over a} - {y \over b} = {1 \over K}\), where K is a non-zero real variable, is given by

The number of points at which the function f(x) = max {a \(-\) x, a + x, b}, \(-\) \(\infty\) < x < \(\infty\), 0 < a < b cannot be differentiable, is

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

\(\int {{{\log \sqrt x } \over {3x}}} dx\) is equal to

If the function f : R \(\to\) R is defined by f(x) = (x2 + 1)35, \(\forall\) x\(\in\)R, then f is

If f(x) is an odd differentiable function defined on (\(-\)\(\infty\), \(\infty\)) such that f'(3) = 2, then f'(\(-\)3) is equal to

The value of \(\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}\) is

For non-zero vectors a and b, if | a + b | < | a \(-\) b |, then a and b are

If the first and (2n \(-\) 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then always

If the matrix \(A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr } } \right]\), then \({A^n} = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr b & 0 & a \cr } } \right],n \in N\), where