Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

JEE Mathematics Solved Question Paper 2005

Multiple Choice Questions

41.
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

(x² - y²)y' = 2xy

The given equation is

x² + y² - 2ay = 0 ...(i)

On differentiating w.r.t. .x, we get

$2 x + 2 yy' = 2 ay [∵ \frac{dy}{dx} = y'] \Rightarrow a = \frac{x + yy'}{y'} On putting the value of a in Eq . (i), we get x^{2} + y^{2} - 2 (\frac{x + yy'}{y'}) y = 0 \Rightarrow (x^{2} + y^{2}) y' - 2 y (x + yy') = 0 \Rightarrow x^{2} y' + y^{2} y' - 2 xy - 2 y^{2} y' = 0 \Rightarrow (x^{2} + y^{2}) y' = 2 xy$

42.

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

$ysec (x) + \tan (x) = c$
$ysec (x) = \tan (x) + c$
$ytan (x) = \sec (x) + c$
$ytan (x) = \sec (x) \tan (x) + c$

43.

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

$\frac{- 1}{xy} = c$
$\frac{- 1}{xy} + \log (y) = c$
$\frac{1}{xy} = \log (y) + c$
$\log (y) = cx$

44.

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

$\frac{1}{32}$
$\frac{1}{16}$
$\frac{1}{8}$
$\frac{1}{4}$

45.

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 $\int_{0}^{1} f (x) dx$ approximately