The differential equation of family of circles whose centre lies on x-axis, is

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 + 1 = 0$

• $\mathrm{y}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 - 1 = 0$

• $\mathrm{y}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} - {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 - 1 = 0$

• $\mathrm{y}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 + 1 = 0$

The solution of the differential equation $\mathrm{y}\left(1 + \log \left(\mathrm{x}\right)\right)\frac{d\mathrm{y}}{d\mathrm{x}} - \mathrm{xlog}\left(\mathrm{x}\right) = 0$ is

• x log(x) = y + c

• x log(x) = yc

• y(1 + log(x) = c

• log(x) - y = c

The order of the differential equation whose solution is ae^x + be^2x + ce^3x + d = 0, is

• 1

• 2

• 3

• 4

The maximum value of the objective function Z = 3x + 2y for linear constraints x + y $\le$ 7, 2x + 3y $\le$ 16, x² $\ge$ 0, y² $\ge$ 0 is

• 16

• 21

• 25

• 28

25.

The position vectors of vertices of a $∆$ABC are $4\hat{\mathrm{i}} - 2\hat{\mathrm{j}}$, $\hat{\mathrm{i}} + 4\hat{\mathrm{j}} - 3\hat{\mathrm{k}}$ and $- \hat{\mathrm{i}} + 5\hat{\mathrm{j}}+ \hat{\mathrm{k}}$ respectively, then $\angle$ABC is equal to

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

A four digit number is to be formed using the digits 1, 2, 3 4, 5 6, 7 (no digit is being repeated in any number). Then, the probability that it is > 4000, is

• 3/2

• 1/2

• 4/7

• 3/7

The equation of the plane which passes through (2, - 3, 1) and is normal to the line joining the points (3, 4, - 1) and (2, - 1, 5), is given by

• x + 5y - 6z + 19 = 0

• x - 5y + 6z - 19 = 0

• x + 5y + 6z + 19 = 0

• x - 5y - 6z - 19 = 0

The angle between the lines x² - xy - 6y² - 7x + 31y - 18 = 0 is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

The equation of the lines passing through the origin and having slopes 3 and - $\frac{1}{3}$, is

• 3y² + 8xy - 3x² = 0

• 3x² + 8xy + 3y² = 0

• 3y² - 8xy - 3x² = 0

• 3x² + 8xy - 3y² = 0

The point where the line $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} - 2}{- 3} = \frac{\mathrm{z} + 3}{4}$ meets the plane 2x + 4y - z = 1, is

• (3, - 1, 1)

• (3, 1, 1)

• (1, 1, 3)

• (1, 3, 1)