The product formed in the reaction of SOCl2 with white phosphorous is
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
Let f:R→(0,∞) and g:R→R be twice differentiable functions such that f" and g" are continuous functions on R. suppose fprime(2)=g(2)=0,f(2)=0 and g′(2)=0, If x→2limf′(x)g′(x)f(x)g(x)=1 then
The function y=f(x) is the solution of the differential equation dxdy+x2−1xy=1−x2x4+2x in (−1,1) satisfying f(0)=0. Then ∫2323f(x)dx is
A vertical line passing through the point (h,0) intersects the ellipse 4x2+3y2=1 at the points P and Q.Let the tangents to the ellipse at P and Q meet at R. If δ(h) Area of triangle δPQR, and δ121≤h≤1maxδ(h) A further δ221≤h≤1minδ(h) Then 58δ1−8δ2
Late a∈Rand let f:Rbe given by f(x)=x5−5x+a,thenf(x)has three real roots if a>4f(x)has only one real roots if a>4f(x)has three real roots if a<−4f(x)has three real roots if −4<a<4
For each positive integer n, let yn=n1((n+1)(n+2)n+n˙)n1For x∈Rlet [x]be the greatest integer less than or equal to x. If (lim)n→∞yn=L, then the value of [L]is ______.
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.264 b. 265 c. 53 d. 67