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:
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
The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
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 the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
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
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 =
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
If ∫ \(\frac{x^{49} Tan^{-1} (x^{50})}{(1+x^{100})}\)dx = k(Tan-1 (x50))2 + c, then k =
If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
For l ∈ R, the equation (2l - 3) x2 + 2lxy - y2 = 0 represents a pair of distinct lines
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:
Let y = t2 - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =
If
then an integer root of 3x2-4x+2= \(\frac{3k}{5}\) is
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
If order and degree of the differential equation corresponding to the family of curves y2 = 4a(x+a)(a is parameter) are m and n respectively, then m+n2 =
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
If 2i - j + 3k, -12i - j - 3k, -i + 2j -4k and λi + 2j - k are the position vectors of four coplanar points, then λ =
If \(\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}\), then A - B + C=
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
if |a| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =