In a $∆ABC, 2x+3y+1=0, x+2y-12=0$ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively and if $A$ is $(3, 2),$ then the slope of the side $BC$ is

If \(y=\sin x+A \cos x\) is the general solution of \(\frac{d y}{d x}+f(x) y=\sec x\), then an integrating factor of the differential equation is

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be \(30^{\circ}\). After walking 120 metres towards it on level ground the elevation is found to be \(60^{\circ}\). Then the height of the object (in metres) is :

In a quadrilateral \(P Q R S, A\) divides \(S R\) in the ratio \(1: 3\) and \(B\) is the mid-point of \(P R\). If \(3 \mathbf{S R}-\mathbf{Q R}-3 \mathbf{P S}-\mathbf{P Q}=k \mathbf{A B}\), then \(k=\)

If \(\frac{3 x}{(x-a)(x-b)}=\frac{2}{x-a}+\frac{1}{x-b}\), then \(a: b\) is equal to

The solution set of the inequation \(\sqrt{x^2+x-2}\gt(1-x)\) is

If \(|x| < 1\) and \(y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots\), then \(x\) is equal to :

Observe the following reactions

The correct order of reactivity of \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\) towards \(\mathrm{S}_{\mathrm{N}} 1\) reaction is

If a triangle \(A B C\) with two vertices \(A(5,4,6)\) and \(B(1,-1,3)\) has its centroid at \(\left(\frac{10}{3}, 2, \frac{11}{3}\right)\), then the third vertex \(C\) is

Two trains \(A\) and \(B\) travel in two parallel rail tracks in opposite direction with speed \(v_1\) and \(v_2\), respectively. They talse \(4 \mathrm{~s}\) to pass each other at this speed. If the speed of \(\operatorname{train} A\) is increased by \(50 \%\), then they talse \(3 \mathrm{~s}\) to pass each other. The ratio of \(v_1 / v_2\) is

If \(A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 3 & 2 \\ 3 & 4 & 5\end{array}\right]\) then \(\left(A+A^T\right)\left(A-A^T\right)=\)

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?

Which of the following compounds has the highest dipole moment \((D)\) ?