KCET 2022

If \(|\mathbf{a}|=2\) and \(|\mathbf{b}|=3\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then the length of the vector \(\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|\) is

If voltage across a bulb rated \(220 \mathrm{~V}, 100 \mathrm{~W}\) drops by \(2.5 \%\) of its rated value, then the percentage of the rated value by which the power would decrease is

Vacant space in body centered cubic lattice unit cell is about

If \(3 x+i(4 x-y)=6-i\) where \(x\) and \(y\) are real numbers, then the values of \(x\) and \(y\) are respectively,

The Vernier scale of a travelling microscope has 50 divisions which coincides with 49 main scale divisions. If each main scale division is \(0.5 \mathrm{~mm}\), then the least count of the microscope is

The volume of \(2.8 \mathrm{~g}\) of \(\mathrm{CO}\) at \(27^{\circ} \mathrm{C}\) and 0.821 atm pressure is (\(R=0.08210 \text { L. atm K} \mathrm{~mol}^{-1}\))