Maths NCERT Exemplar Solutions Class 12th Chapter Twelve

The solution of differential equation $\frac{dy}{dx}-\frac{y+3x}{{\mathrm{l}\mathrm{o}\mathrm{g}}_e?(y+3x)}+3=0$ is:

(where $\mathrm{C}$ is a constant of integration.)

Suppose the vectors $x_1,x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax$ $=\mathrm{b}$ when the vector $\mathrm{b}$ on the right side is equal to ${\mathrm{b}}_1,{\mathrm{b}}_2$ and ${\mathrm{b}}_3$ respectively. If $x_1=\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right],x_2=\left[\begin{array}{l}0\\ 2\\ 1\end{array}\right],x_3=\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right],b_1=\left[\begin{array}{l}1\\ 0\\ 0\end{array}\right],b_2=\left[\begin{array}{l}0\\ 2\\ 0\end{array}\right]$ and $b_3=\left[\begin{array}{l}0\\ 0\\ 2\end{array}\right]$ , then the determinant of $A$ is equal of $A$ is equal to :

The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$ -axis and vertices $C$ and $D$ lie on the parabola, $y=x^2-1$ below the $x$ -axis, is:

The integral ${\int }_{\pi /6}^{\pi /3}?{\mathrm{t}\mathrm{a}\mathrm{n}}^3?x\cdot {\mathrm{s}\mathrm{i}\mathrm{n}}^2?3x\left(2{\mathrm{s}\mathrm{e}\mathrm{c}}^2?x\cdot {\mathrm{s}\mathrm{i}\mathrm{n}}^2?3x+3\mathrm{t}\mathrm{a}\mathrm{n}?x\cdot \mathrm{s}\mathrm{i}\mathrm{n}?6x\right)dx$ is

The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y$ $=0$ , having its centre on the line, $2x-3y+12=0$ , also passes through the point:

The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y$ $=0$ , having its centre on the line, $2x-3y+12=0$ , also passes through the point:

Let $\lambda \ne 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$ , then $\frac{\beta \gamma }{\lambda }$ is equal to:

Let $\lambda \ne 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$ , then $\frac{\beta \gamma }{\lambda }$ is equal to:

Let $\lambda \ne 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$ , then $\frac{\beta \gamma }{\lambda }$ is equal to:

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin, coincides with the positive direction of the axes through the origin?