Glucose and mannose are

$A$ body of mass $m_1 = 4 \ kg$ moves at $5 \hat{i} \ m/s$ and another body of mass $m_2 = 2 \ kg$ moves at $10 \hat{i} \ m/s$. The kinetic energy of the centre of mass is

The cathode of a photoelectric cell is changed such that the work function changes from $W_1$ to $W_2$ $(W_2 > W_1)$. If the current before and after the change are $I_1$ and $I_2$ respectively,with all other conditions remaining unchanged,then (assuming $h\nu > W_2$):

Find the length of the intercept cut by the pair of lines $2x^2+4xy-4y^2-6x-8y+7=0$ on the $Y$-axis.

The concentration of an organic compound in chloroform is $6.15 \ g$ per $100 \ mL$ of solution. $A$ portion of this solution in a $5 \ cm$ polarimeter tube causes an observed rotation of $-1.2^{\circ}$. What is the specific rotation of the compound?

High purity copper metal is obtained by