If y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
If A(1,2,3) B(3,7,-2) and D(-1,0,-1) are points in a plane, then the vector equation of the line passing through the centroids of △ABD and △ACD 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
The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =
If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
If the roots of the equation z2 - i = 0 are α and β, then | Arg β - Arg α | =
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
The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
The locus of z such that \(\frac{|z-i|}{|z+i|}\)= 2, where z = x+iy. is
In a triangle BC, if the mid points of sides AB, BC, CA are (3,0,0), (0,4,0),(0,0,5) respectively, then AB2 + BC2 + CA2 =
For l ∈ R, the equation (2l - 3) x2 + 2lxy - y2 = 0 represents a pair of distinct lines
There are 10 points in a plane, of which no three points are colinear expect 4. Then the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 colinear points is
A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =
If \(\int_{0}^{3} (3x^2-4x+2) \,dx = k,\) then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is
If the points of intersection of the parabola y2 = 5x and x2 = 5y lie on the line L, then the area of the triangle formed by the directrix of one parabola, latus rectum of another parabola and the line L is
If f(x) = ex, h(x) = (fof) (x), then \(\frac{h'(x)}{h'(x)}\) =
if |a| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =