\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
If ∫(log x)3 x5 dx = \(\frac{x^6}{A}\) [B(log x)3 + C(logx)2 + D(log x) - 1] + k and A,B,C,D are integers, then A - (B+C+D) =
If ∫ \(\frac{x^{49} Tan^{-1} (x^{50})}{(1+x^{100})}\)dx = k(Tan-1 (x50))2 + c, then k =
If the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
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 sin y = sin 3t and x = sin t, then \(\frac{dy}{dx}\) =
If f(x) = ex, h(x) = (fof) (x), then \(\frac{h'(x)}{h'(x)}\) =
On differentiation if we get f (x,y)dy - g(x,y)dx = 0 from 2x2-3xy+y2+x+2y-8 = 0 then g(2,2)/f(1,1) =
The quadratic equation whose roots are
\(l = \lim_{\theta\to0} \frac{3sin\theta - 4sin^3\theta}{\theta}\)
m = \(\lim_{\theta\to0} \frac{2tan\theta}{\theta(1-tan^2\theta)}\) is
lim n→∞ \(\frac{1}{n^3}\) \(\sum_{k=1}^{n} k^{2} =\)
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 l,m,n and a,b,c are direction cosines of two lines then
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 =
If the angle between the asymptotes of a hyperbola is 30° then its eccentricity is
If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
If the line x cos α + y sin α = 2√3 is tangent to the ellipse \(\frac{x^2}{16} + \frac{y^2}{8} = 1\) and α is an acute angle then α =