$A$ line cuts off equal intercepts on the coordinate axes. The angle made by this line with the positive direction of the $X$-axis is: (in $^{\circ}$)

If the slope of the line $ax + (3 - a)y + 7 = 0$ is $7$,then the value of the integral part of '$a$' is

The point $P(a, b)$ lies on the straight line $3x + 2y = 13$ and the point $Q(b, a)$ lies on the straight line $4x - y = 5$. Then the equation of the line $PQ$ is

The equation of a given straight line is $\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}=\gamma$. If the equation of the line perpendicular to the given line and passing through $(\alpha, \beta)$ is $\frac{x}{a}+\frac{y}{b}=1$,then $\frac{b}{a}$ is equal to

In the figure,a time-distance graph of a linear motion is given. Two positions of time and distance are recorded as: when $T = 0, D = 2$ and when $T = 3, D = 8$. Using the concept of slope,find the law of motion,i.e.,how distance depends upon time.

If $p = a_1 x + b_1 y + k_1 = 0$,$q = a_2 x + b_2 y + k_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{k_1}{k_2}$,then the curve $p + c q = 0$ is