Let f: [1, ∞) → [2, ∞) be a differentiable function such that f (1) = 2. If  for all x ≥ 1 then the value of f (2) is

Let f be a real valued differentiable function on ℝ (the set of all real numbers) such that f (1) = 1. If the Y–intercept of the tangent at any point P (x, y) on the curve y = f (x) is equal to the cube of the abscissa at P then the value of f (−3) is equal to

Let f be a real-valued function defined on the interval (-1, 1) such that f(x) = 2 +  dt for all x ε (-1, 1) and let  be the inverse of f. Then  is equal to

a) 1

b)

c)

d)

If a polynomial of degree 3, then  equals

a)

b)

c)

d) a constant

The order of the differential equation whose general solution is given by  is

a) 5

b) 4

c) 3

d) 2

A solution of the differential equation  is

a)  y = 2

b)  y = 2x

c)  

d)  2

If  is a solution of  and  then  is equal to

a)

b)

c) 1

d)

If  then

a)

b)

c)

d)

If  and  then  equals

a)

b)

c)

d) 1

A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .

Solve the differential equation
(12x + 5y – 9) dx + (5x + 2y – 1) dy = 0

a)

b)  = 2 [ln (x + 13) – ln (y – 33)] + c

c)  = ln (x + 13) + ln (y – 33) + c

d)

Solve the differential equation
(secx tanx tany – e^x) dx + secx sec²y dy = 0

a) secx tany = c

b) secx tany = e^x + c

c) secx + e^y = c

d) tany + e^x = c

Solve the differential equation
(x + y) (dx – dy) = dx + dy

a) y + ln (x + y) = c

b) x = ln (x + y) + c

c)

d) y – x + ln (x + y) = c

Solve the differential equation
ydx – xdy = 0

a) x = cy

b) xy = c

c) x = cy²

d) x²y = c

Solve the differential equation
 

a)

b)

c)

d)

Solve the differential equation
ydx – xdy = xydx

Solve the differential equation
tanx dy = coty dx

Solve the differential equation
 

Solve the differential equation
 

Solve the differential equation
 

Solve the differential equation
 

Solve  

Solve (x + 2y) (dx – dy) = dx + dy