The number of natural numbers less than $1000$,in which no two digits are repeated,is:

If the angle of intersection at a point where the two circles with radii $5 \ cm$ and $12 \ cm$ intersect is $90^{\circ}$,then the length (in $cm$) of their common chord is

If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

Two rods of different materials having coefficients of linear expansion $\alpha_1$ and $\alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,the thermal stress developed in the two rods is equal provided $Y_1 : Y_2$ is equal to:

If one of the lines $2x^2 - xy + by^2 = 0$ passes through the point $(-4, -2)$,then $b^2 =$

Which of the following phases is not a part of interphase?