If the plane \(3 x-2 y-z-18=0\) meets the coordinate axes in \(A, B, C\) then the centroid of \(\triangle A B C\) is

If the slopes of the lines represented by the equation \(6 x^2+2 h x y+4 y^2=0\) are in the ratio \(2: 3\), then the value of h such that both the lines make acute angles with the positive X -axis measured in positive direction is

If \((-1,-1)\) is the focus and \(x+y+4=0\) is the directrix of a parabola, then its vertex is

If a line having slope 2 is a tangent to the curve \(y=x^4-6 x^3+13 x^2-12 x+5\) at points \(P\left(x_1, y_1\right)\) and \(Q\) \(\left(\mathrm{x}_2, \mathrm{y}_2\right), \mathrm{x}_1, \mathrm{x}_2 \in \mathrm{N}\) then \(\mathrm{x}_1 \mathrm{x}_2-\mathrm{y}_1 \mathrm{y}_2=\)

In a $\mathrm{\Delta }ABC,\frac{{\cos }^2\left(\frac{B-C}{2}\right)}{(b+c{)}^2}+\frac{{\sin }^2\left(\frac{B-C}{2}\right)}{(b-c{)}^2}=$

If the circle \(x^2+y^2=a^2\) intersects the hyperbola \(x y=c^2\) in four points \(\left(x_i, y_i\right)\), for \(i=1,2,3\) and 4 , then \(y_1+y_2+y_3+y_4\) equals

If the focal distance of a point \(\mathrm{P}\left(2, \mathrm{y}_1\right)\) on the parabola \(\mathrm{y}^2=\mathrm{kx}\) is 3 , then the equation of the tangent drawn at \(\mathrm{P}\) to the given parabola is

An air bubble of radius \(1 \mathrm{~cm}\) rises from the bottom portion through a liquid of density \(1.5 \mathrm{~g} / \mathrm{cc}\) at a constant speed of \(0.25 \mathrm{~cm} \mathrm{~s}^{-1}\). If the density of air is neglected, the coefficient of viscosity of the liquid is approximately, (In Pas) :

Arrange the following compounds in the correct order of their acid strength.

Which of the following has the least electron gain enthalpy?

Which of the following wave has the largest wave speed?

Which one of the following statements is correct for the reaction?

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?