Let y=y(x) be the solution of the differential equation (1+y^2)e^tan x dx + cos^2 x (1+e^2tan x)dy=0

A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured

Lim n tends to ♾️ [(1^2-1)(n-1)+(2^2-2)(n-2)+…+((n-1)^2-(n-1)).1]/[(1^3+2^3+…+n^3)-(1^2+2^2+…+n^2)]

The value of k€N for which integral In=Integral of (1-x^k)^n dx from 0 to 1, n € N, satisfies 147

Let y=y(x) be the solution of the differential equation (1+y^2)e^tan x dx + cos^2 x (1+e^2tan x)dy=0

The number of Integers, between 100 and 1000 having the sum of their digits equals to 14, is ____

Let the sum of two positive integers be 24. If the probability, that their product is not less

Let Integral of 2-tan x/3+tan x dx=1/2(ax+log |b sin x+ y cos x| )+C, where C is constant of Integra

Suppose for a differentiable function h, h(0)=0, h(1)=1 and h’(0)=h’(1)=2. If g(x)=h(e^x)e^(h(x))

Let P be a point on the ellipse x^2/9+y^2/4=1. Let the line passing through P and parallel to y-axis

For a,b greater than 0, let f(x) = tan((a+1)x)+b tan x /x, x less than 0

Let the maximum and minimum values of (sq.rt.(8x-x^2-12)-4)^2+(x-7)^2, x€R be M and m respectively.

Let Integral of dx/sq.rt.(e^x-1) from a to log4=pi/6. Then e^a and e^-a are the roots of equation