Q.1
Differentiation of function f(x,y,z) = Sin(x)Sin(y)Sin(z)-Cos(x) Cos(y) Cos(z) w.r.t ‘y’ is?
  • a) f’(x,y,z) = Cos(x)Cos(y)Sin(z) + Sin(x)Sin(y)Cos(z)
  • b) f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z)
  • c) f’(x,y,z) = Cos(x)Cos(y)Cos(z) + Sin(x)Sin(y)Sin(z)
  • d) f’(x,y,z) = Sin(x)Sin(y)Sin(z) + Cos(x)Cos(y)Cos(z)
Q.2
In euler theorem x ∂z⁄∂x + y ∂z⁄∂y = nz, here ‘n’ indicates?
  • a) order of z
  • b) degree of z
  • c) neither order nor degree
  • d) constant of z
Q.3
If z = xn f(y⁄x) then?
  • a) y ∂z⁄∂x + x ∂z⁄∂y = nz
  • b) 1/y ∂z⁄∂x + 1/x ∂z⁄∂y = nz
  • c) x ∂z⁄∂x + y ∂z⁄∂y = nz
  • d) 1/x ∂z⁄∂x + 1/y ∂z⁄∂y = nz
Q.4
Necessary condition of euler’s theorem is _________
  • a) z should be homogeneous and of order n
  • b) z should not be homogeneous but of order n
  • c) z should be implicit
  • d) z should be the function of x and y only
Q.5
If f(x,y) = x+y⁄y , x ∂z⁄∂x + y ∂z⁄∂y = ?
  • a) 0
  • b) 1
  • c) 2
  • d) 3
Q.6
If u = xx + yy + zz , find du⁄dx + du⁄dy + du⁄dz at x = y = z = 1.
  • a) 1
  • b) 0
  • c) 2u
  • d) u
Q.7
Find the approximate value of [0.+ 2.+ 1.942](1⁄2).
  • a) 1.96
  • b) 2.96
  • c) 0.04
  • d) -0.04
Q.8
The happiness(H) of a person depends upon the money he earned(m) and the time spend by him with his family(h) and is given by equation H=f(m,h)=400mh2 whereas the money earned by him is also depends upon the time spend by him with his family and is given by m(h)=√(1-h2). Find the time spend by him with his family so that the happiness of a person is maximum.
  • a) √(1⁄3)
  • b) √(2⁄3)
  • c) √(4⁄3)
  • d) 0
0 h : 0 m : 1 s