The number of diagonals of a polygon is 35. If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having AB as one of its sides is:
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 (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
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 y = \(\frac{3}{4} + \frac{3.5}{4.8}+\frac{5.5.7}{4.8.12}+ \).... to ∞, then
If \(\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}\), then A - B + C=
The period of function f(x) = \(e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)\)is
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If x = log (y +√y2 + 1 ) then y =
Let d be the distance between the parallel lines 3x - 2y + 5 = 0 and 3x - 2y + 5 + 2√13 = 0. Let L1 = 3x - 2y + k1 = 0 (k1 > 0) and L2 = 3x - 2y + k2 = 0 (k2 > 0) be two lines that are at the distance of \(\frac{4d}{√13}\) and \(\frac{3d}{√13}\) from the line 3x - 2y + 5y = 0. Then the combined equation of the lines L1 = 0 and L2 = 0 is:
5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of the independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is
If the parametric equations of the circle passing through the points (3,4), (3,2) and (1,4) is x = a + r cosθ, y = b + r sinθ then ba ra =
A tangent PT is drawn to the circle x2 + y2 = 4 at the point P(√3, 1). If a straight line L which is perpendicular to PT is a tangent to the circle (x- 3)2 + y2 = 1, then a possible equation of L is
If the angle between the pair of tangents drawn to the circle $ x^2 + y^2 - 2x + 4y + 3 = 0 $ from the point $(6, -5)$ is \(\theta\) than \(\cot \theta\) =
The angle between the circles \(x^2+y^2−4x−6y−3=0\), \(x^2+y^2+8x−4y+11=0\) is \(\frac{\pi}{2}\), then the value of K is?
The radius of a circle touching all the four circles (x ± λ)2 + (y ± λ)2 = λ2 is
If the radical center of the given three circles x2 + y2 = 1, x2 + y2 -2x - 3 =0 and x2 + y2 -2y - 3 = 0 is C(α,β) and r is the sum of the radii of the given circles, then the circle with C(α,β) as center and r as radius is
A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white 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
Let a = i + 2j -2k and b = 2i - j - 2k be two vectors. If the orthogonal projection vector of a on b is x and orthogonal projection vector of b on a is y then |x - y| =
If a + b + c = 0. |a| = 3, |b| = 5, |c| = 7, then the angle between a and b is
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