If cosθ = \(\frac{-3}{5}\)- and π < θ < \(\frac{3π}{2}\), then tan \(\frac{ θ}{2}\) + sin \(\frac{ θ}{2}\)+ 2cos \(\frac{ θ}{2}\) =
A straight line parallel to the line y = √3 x passes through Q(2,3) and cuts the line 2x + 4y - 27 = 0 at P. Then the length of the line segment PQ is
A random variable X has the following probability distribution
For the events E = {x/x is a prime number} and F = {x/x <4} then P(E ∪ F)
If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.
If a point P moves so that the distance from (0,2) to P is \(\frac{1}{√2 }\) times the distance of P from (-1,0), then the locus of the point P is
The orthocenter of the triangle whose sides are given by x + y + 10 = 0, x - y - 2 = 0 and 2x + y - 7 = 0 is
If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is
If R -(α,β) is the range of \(\frac{x+3}{(x-1)(x+2)}\) then the sum of the intercepts of the line ax + βy + 1 = 0 on the coordinate axes is:
Let $ X = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \middle| a, b, c, d \in \mathbb{R} \right\} $. If $ f: X \to \mathbb{R} $ is defined by $ f(A) = \det(A) $ for all $ A \in X $, then $ f $ is
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1) is
If the roots of the equation z2 - i = 0 are α and β, then | Arg β - Arg α | =
For l ∈ R, the equation (2l - 3) x2 + 2lxy - y2 = 0 represents a pair of distinct lines
The locus of z such that \(\frac{|z-i|}{|z+i|}\)= 2, where z = x+iy. is
If \(\int_{0}^{3} (3x^2-4x+2) \,dx = k,\) then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is