If `t(1+x^2)=x and x^2+t^2=y,` then at `x=2` the value of `(d y)/(d x)` is equal to Option 1. 24/5 Option 2: 101/125 Option 3: 488/155 Option 4: 358/125

If g(x)=(4cos^4x-2cos2x-1/2cos4x-x^7)^(1/7) then the value of g(g(100)) is equal to Option 1: -1 Option 2: 0 Option 3: 1 Option 4: 100

If x = 3 tant and y = 3 sec t, then the value of (d^2y)/(dx^2)" at" t=pi/4 is

If f(x)=(x-1)^(100)(x-2)^(2(99))(x-3)^(3(98))…(x-100)^(100), then the value of (f'(101))/(f(101)) is Option 1: 5050 Option 2: 2575 Option 3: 3030 Option 4: 1250

Consider the equaiton 2 + |x^(2) + 4x + 3|= m , m in R Set of all real values of m so that the given equation has three solution is Option 1: 3 Option 2: 2 Option 3: 1 Option 4: 0

If g(x,y) = 3x^(2) - 5y + 2y^(2), x(t) =e^(t) and y(t) = cos t , then (dg)/(dt) is equal to

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

Consider the equaiton 2 + |x^(2) + 4x + 3| = m , m in R Set of all real values of m so that given equation have four distinct solutions, is Option 1: (0,1) Option 2: (1,2) Option 3: (1,3) Option 4: (2,3)

If f (x,y) =x ^(2) + xy+y ^(2),x =t ,y=t ^(2) then (df )/(dt)=

The number of points on the real line where the function f(x) = log_(|x^2-1|)|x-3| is not defined is Option 1: 4 Option 2: 5 Option 3: 6 Option 4: 7