if |a| = 4, |b| = 5, |a - b| = 3 and θ is the angle between the vectors a and b, then cot2 θ =
In △ABC, if a : b : c = 4 : 5 : 6, then the ratio of the circumference to its in radius 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 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
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 =
The area (in square units) of the region bounded by the curve y = |sin2x| and the X-axis in [0,2π] is
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} sin^2xcos^2x(sinx+cosx)dx=\)
\(∫\frac{dx}{(x-1)^{34} (x+2)^{\frac54}}=\)
\(∫\frac{dx}{(x2+1) (x2+4)} =\)
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