वैश्वीकरण और स्वास्थ्य पर इसके प्रभावों का विवरण लिखिए।

भारत में विभिन्न स्वास्थ्य देखभाल सेवाओं की संक्षेप में चर्चा कीजिए।

सार्वजनिक (जन) स्वास्थ्य क्या है? भारत में सार्वजनिक स्वास्थ्य का विवरण लिखिए।

Show that the following function is not continuous at (0,0):

The population of a town grows at a rate proportional to the population at any time. Its initial population of 500 increases by 15% in 10 years. What will be the population in 30 years?

State Euler’s theorem for homogeneous functions and verify it for the function:

Find partial derivatives  f_x and  f_y for the function:

f(x,y) = 5x⁴y² + 6x² y³ 

at the point ,(1,-1)

Using Charpit’s method, find the complete integral of the differential equation:

p²x + q²y = z 

Find the complete solution of the equation px + qy = pq.

Show that the following function f is differentiable at (0,0):

Show that for the function f given by:

Find the general solution of the equation:

x(y²-z²)u_x + y(z²-x²)u_y +z(x²- y²)u₂ = 0

Solve:

Verify that the differential equation:

z(x²-y²-z^²)dx+(x+z)xzdy

                                  + x(z²-x2-xy)dz = 0

is integrable and find its integral.

If:

Z= x²y+2xy²

where x = sin zt

and

y = cost

find dz/dt  when t=0by (i) chain rule and by (ii) the direct substitution. 

By using the method of variation of parameter, find the general solution of the differential equation:

Solve the simultaneous equations:

Solve the differential equations:

Verigy Lagrange's mean value theorem for the function f defined by

f(x) = 2x²-7x-10over [2, 5].

a) If , show that:

(m+1)I_^m,n = x^m+l (log x)" -nI_m, n-1.

Hence find the value of fx²(logx)³dx.