SPSC Lecture Mathematics Past Paper

The set of limit points of ] 0, 1 [ in real line R is?

1. [ 0,1 ]
2. ] 0,1 [
3. [0,1 [
4. ] 0,1]

A subset F of a metric space X is closed if and only if?

1. F = F°
2. F ∪ F = X
3. F ∩ F´ = ∅
4. F = F´

The solution of differential equation. day/dx = 1/√1+x^2 is y =?

1. sinh^-1 x+c
2. sech^-1x+c
3. tanh^-1x+c
4. cotx+c

If f(x,y) is a homogeneous function of degree zero in x and y, then f(x,y) is a function of ___ alone.

1. y^2/x
2. y/x^2
3. y/x
4. xy

In the first-order linear differential equation dy/dx + P(x)y = Q(x), the integrating factor is?

1. exp (∫P(x)dx)
2. exp (∫P(y)dy)
3. ∫P(x)dx
4. ∫P(y)dy

The equation of the form y'+P(x)y+Q(x)y² - R(x) is called the ____ equation.

1. Bernoulli
2. Ricatti
3. Clairaut
4. None

The differential form xdy + ydx/xy is equivalent to?

1. d(y²/x)
2. d(tan⁻¹(y/x))
3. d(ln(xy))
4. d(x^m/y^n)

The differential equation of the form y=x dy/dx +f (dy/dx) is known as ___ equation.

1. Bernoulli
2. Ricatti
3. Clairaut
4. None

The general solution of the differential equation d^2y/dx^2 - 4 dy/dx + 4y = 0 is?

1. (c1 + c2x)e^2x
2. c1e^2x + c2e^-2x
3. c1e^3x + c2e^-3x
4. c1e^4x + c2e^-4x

The solution of the differential equation ydx-2xdy=0 represents?

1. A family of straight lines
2. A family of parabolas
3. A family of hyperbolas
4. A family of circles