A bisector of the angle between the normals of the planes \(4 x+3 y=5\) and \(x+2 y+2 z=4\) is along the vector

Consider the following statements: Assertion (A): The direction ratios of a line \(\mathrm{L}_1\) are \(2,5,7\) and the direction ratios of another line \(\mathrm{L}_2\) are \(\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}\). Then the lines \(\mathrm{L}_1, \mathrm{~L}_2\) are parallel Reason (R): If the direction ratios of a line \(L_1\) are \(a_1, b_1, c_1\), the direction ratios of a line \(\mathrm{L}_2\) are \(\mathrm{a}_2, \mathrm{~b}_2, \mathrm{c}_2\) and \(\mathrm{a}_1 \mathrm{a}_2+\mathrm{b}_1 \mathrm{~b}_2\) \(+c_1 c_2=0\), then the lines of \(L_1, L_2\) are parallel Which one of the following is True?

Let \(3 x^2+8 x y-3 y^2=\) are present the lines \(L_1\), \(L_2\) and \(3 x^2+8 x y-3 y^2+2 x-4 y-1=0\) represent the lines \(L_3, L_4\). Let \(L\) be the line joining the points of intersection of \(L_1, L_3\) and \(L_2, L_4\). Then, the area (in sq units) of the triangle formed by \(L\) with the coordinate axes is

If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-6 x^2+11 x+6=0\), then \(\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2\) is equal to :

If $x=\alpha , y=\beta , z=y$ is the unique solution of the system of equations $5x-7y+3z=0,$ $7x+10y-8z=3$ and $2x+3y-4z+4=0,$ then $\beta =$

The slope of a line $L$ is $2.$ If $m_1, m_2$ are slopes of two lines which are inclined at an angle of $\frac{\pi }{6}$ with $L,$ then $m_1+m_2=$

If \(A\) and \(B\) are two events of a random experiment such that \(P(\bar{A})=\frac{2}{3}, P(B)=\frac{4}{15}\) and \(\mathrm{P}(\mathrm{A} \cap \bar{B})=\frac{1}{5}\), then \[ \sqrt{195[P(B \mid(A \cup \bar{B}))+P(A \cup B)]}= \]

If \(\theta\) is the angle between the circles \(x^2+y^2-4 x+2 y-4=0\) and \(x^2+y^2-2 x+4 y-11=0\), then \(\sin \theta=\)

A constant force of $5 \mathrm{N}$ accelerates a stationary particle of mass $500 \mathrm{gm}$ through a displacement of $5\mathrm{m}.$The average power delivered is

\(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

\(A^{2+}, B^{2+}\) and \(C^{-}\)form an ionic complex like \(A_{x-2}\left[B(C)_x\right]_2\). If the complex is \(75 \%\) dissociated in a solvent with \(i=4\), the coordination number of \(B\) is

$\mathrm{NaCl}$ is a $\mathrm{FCC}$ lattice where ${\mathrm{Na}}^{+}$ ions are at corner and face centre positions. Chloride ions are at edge centres and body centre positions. How many $\mathrm{NaCl}$ formula units will be in an unit cell