If \(\vec{a}=2 \hat{i}-\hat{j}+3 \hat{k}, \vec{b}=-3 \hat{i}+5 \hat{j}-4 \hat{k}\) and \(\vec{c}=6 \hat{i}-4 \hat{j}+5 \hat{k}\), then \((\vec{a} \times \vec{b}) \cdot(\vec{b} \times \vec{c})=\)

The period of the function \(f(\theta)=\sin \frac{\theta}{3}+\cos \frac{\theta}{2}\) is

If the determinant of a \(3^{\text {rd }}\) order matrix A is K , then the sum of the determinants of the matrices \(\left(A A^T\right)\) and \(\left(A-A^T\right)\) is

If \(x\) is the number of ways in which six women and six men can be arranged to sit in a row such that no two women are together and if \(y\) is the number of ways they are seated around a table in the same manner, then \(x: y=\)

The acute angle between lines $6x^2+11xy-10y^2=0$ is

\(\sin A+\sin B=\sqrt{3}(\cos B-\cos A)\)
\(\Rightarrow \sin 3 A+\sin 3 B\) is equal to

The rank of the matrix \(\left[\begin{array}{ccc}1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8\end{array}\right]\) is

If a diagonal of a square is along the line \(8 x-15 y=0\) and one of its vertices is \((1,2)\), then the equations of the sides of the square passing through this vertex are

Which of the following molecules contain sulphur atom in their structures
I. Morphine
II. Heroin
III. Penicillin
IV. Terpineol
V. Cimetidine

At 240.55 K , for one mole of an ideal gas, a graph of P (on \(y\)-axis) and \(\mathrm{V}^{-1}\) (on \(x\)-axis) gave a straight line passing through origin. Its slope \((m)\) is \(2000 \mathrm{~J} \mathrm{~mol}^{-1}\). What is the kinetic energy (in \(\mathrm{J} \mathrm{mol}^{-1}\) ) of ideal gas?

When an inductor of inductance \(\frac{6}{\pi} \mathrm{H}\), a capacitor of capacitance \(\frac{50}{\pi} \mu \mathrm{F}\) and resistor of resistance \(R\) are connected in series with an AC supply of rms voltage \(220 \mathrm{~V}\) and frequency \(50 \mathrm{~Hz}\), the rms current through the circuit is \(440 \mathrm{~mA}\). Match the inductive reactance, \(X_L\) the capacitive reactance, \(X_C\) the resistance \(R\) and the impedance \(Z\) of the circuit given in List-I with the corresponding values given in List-II.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

Consider the following data:


The coefficient of variation of the above distribution of wages, if its standard deviation is 14.72 , is

Which of the following is an example of a multi molecular colloid?