The differential equation for the family of curve x² + y² - 2ay = 0, where a is an arbitrary constant, is

• 2(x² - y²)y' = xy

• 2(x² + y²)y' = xy

• (x² - y²)y' = 2xy

• (x² + y²)y' = 2xy

42.

Solution of the differential equation $\cos \left(\mathrm{x}\right)\frac{d\mathrm{y}}{d\mathrm{x}} + \mathrm{ysin}\left(\mathrm{x}\right) = 1$ is

• $\mathrm{ysec}\left(\mathrm{x}\right) + \tan \left(\mathrm{x}\right) = \mathrm{c}$

• $\mathrm{ysec}\left(\mathrm{x}\right) = \tan \left(\mathrm{x}\right) + \mathrm{c}$

• $\mathrm{ytan}\left(\mathrm{x}\right) = \sec \left(\mathrm{x}\right) + \mathrm{c}$

• $\mathrm{ytan}\left(\mathrm{x}\right) = \sec \left(\mathrm{x}\right)\tan \left(\mathrm{x}\right) + \mathrm{c}$

The solution of the differential equation ydx + (x + x²y)dy = 0 is

• $\frac{- 1}{\mathrm{xy}} = \mathrm{c}$

• $\frac{- 1}{\mathrm{xy}} + \log \left(\mathrm{y}\right) = \mathrm{c}$

• $\frac{1}{\mathrm{xy}} = \log \left(\mathrm{y}\right) + \mathrm{c}$

• $\log \left(\mathrm{y}\right) = \mathrm{cx}$

The mean and variance ofa random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

• $\frac{1}{32}$

• $\frac{1}{16}$

• $\frac{1}{8}$

• $\frac{1}{4}$

The value of f(x) is given only at x = 0, $\frac{1}{3}, \frac{2}{3}$ wich of the following can be used to evaluate ${\int }_0^1\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$ approximately

• Trapezoidal rule

• Simpson's rule

• Trapezoidal as well as Simpson's rule

• None of the above