n→∞limn7/3((na+a)21+(na+2)21+...+(na+n)21)31+32+…+3n=54 then possible values a is/zer
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 ______.
Let f:RRbe a differentiable function such that f(0),f(2π)=3andfprime(0)=1.If g(x)=∫x2π[fprime(t)cosect−cottcosectf(t)]dtforx(0,2π],then (lim)x0g(x)=
A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the parabola y2=16x 0≤y≤6 at the point art F(x0,y0). The tangent to the parabola at F(X0,Y0) intersects the y-axis at G(0,y). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum P) m= Q) = Maximum area of △EFG is (R) y0= (S) y1=
Let s, t, rbe non-zero complex numbers and Lbe the set of solutions z=x+iy (x, y∈R, i=−1)of the equation sz+tz+r=0, where z=x−iy. Then, which of the following statement(s) is (are) TRUE?If Lhas exactly one element, then ∣s∣=∣t∣(b) If ∣s∣=∣t∣, then Lhas infinitely many elements(c) The number of elements in
Let m be the smallest positive integer such that the coefficient of x2 in the expansion of (1+x)2+(1+x)3+(1+x)4+……..+(1+x)49+(1+mx)50 is (3n+1).51C3 for some positive integer n. Then the value of n is
Let f:R→Rand g:R→Rbe two non-constant differentiable functions. If fprime(x)=(e(f(x)−g(x)))gprime(x)for all x∈R, and f(1)=g(2)=1, then which of the following statement(s) is (are) TRUE?f(2)<1−(log)e2(b) f(2)>1−(log)e2(c) g(1)>1−(log)e2(d) g(1)<1−(log)e2