Trajectory of particle in a projectile motion is given as y = x - $\frac{x^2}{80}$ .

Here , x and y are in meters. For this projectile motion match the following with g = 10 m / $s^2$

"$$\begin{array}{cc}coloumn1& coloumn2\\ \left(a\right)AngleofProjection& \left(p\right)20\\ \left(b\right)Angleofvelocitywithhorizontalafter4s& \left(q\right)80\\ \left(c\right)MaximumHieght& \left(r\right){45}^{\circ }\\ \left(d\right)HorizontalRange& \left(s\right){tan}^{-1}\frac{1}{2}\end{array}$$ "

Q. Trajectory of particle in a projectile motion is given as $y=x-\frac{x^2}{80}$. Here, $x$ and $y$ are in $\text{metre}$. For this projectile motion match the following and select proper option $(g=10{\text{m/s}}^2)$:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Angle of projection}& \text{(p)}& 20\text{m}\\ \text{(B)}& \text{Angle of velocity}& \text{(q)}& 80\text{m}\\ & \text{with horizontal}& & \\ & \text{after}4\text{s}& & \\ \text{(C)}& \text{Maximum height}& \text{(r)}& {45}^{\circ }\\ \text{(D)}& \text{Horizontal range}& \text{(s)}& {\tan }^{-1}\left(\frac{1}{2}\right)\end{array}$

Q.

Let B and C be points (12, 19) and (23, 20) respectively. Let A $(\alpha ,\beta )$ be a point such that area of triangle formed by the points A, B and C is 70. Also the slope of the median through A is – 5.

Match the following:
$\begin{array}{cccc}& ColumnI& & ColumnII\\ \left(a\right)& Apossiblevalue\alpha +\beta is& \left(p\right)& 2\\ \left(b\right)& Apossiblevalue\beta -2\alpha is& \left(q\right)& 27\\ \left(c\right)& Apossiblevalue3\alpha -\beta -11is& \left(r\right)& -33\\ \left(d\right)& Apossiblevalue\alpha -2\beta +16is& \left(s\right)& 47\\ & & \left(t\right)& 28\end{array}$

Q.

Three rods of material x and two rods of material y are connected as shown in figure. All the rods are of identical length and cross - sectional area. The end A is maintained at 100${}^{\circ }$C and the junction C at 0${}^{\circ }$C. It is given that resistance of rod of material x is R. Further, $K_x$ = ${2K}_y$ .

Match the entries of column I and column II

$$\begin{array}{cc}column1& column2\\ A.TemperatureofjunctionB& P.Doesnotbehavelikeabalancedwheatstone{s}^{\prime }sbridge\\ B.TemperatureofjunctionC& Q.Istwiceoftheother\\ C.Thisnetworkis& R.{\frac{400}{7}}^{\circ }C\\ D.Resistanceofrodofmaterialy& S.{\frac{300}{7}}^{\circ }C\end{array}$$

Q. A body of mass $m_1$ elastically collide with another stationary body of mass $m_2$
$\begin{array}{cc}\text{Column - I}& \text{Column -II}\\ \text{(a) After the collision, velocity of second}& \left(p\right)>1\\ \text{body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(b) After the collision, the momentum}& \left(q\right)<1\\ \text{of second body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(c) After the collision, K.E. of second}& \left(r\right)=1\\ \text{body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(D) For elastic collision, coefficient of}& \left(s\right)=0\\ \text{restitution is}& \end{array}$

Q. Trajectory of particle in a projectile motion is given as $y=x-\frac{x^2}{80}$. Here, $x$ and $y$ are in metre. For this projectile motion match the following and select proper option $(g=10{\text{m/s}}^2)$:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Angle of projection}& \text{(p)}& 20\text{m}\\ \text{(B)}& \text{Angle of velocity}& \text{(q)}& 80\text{m}\\ & \text{with horizontal}& & \\ & \text{after}4s& & \\ \text{(C)}& \text{Maximum height}& \text{(r)}& {45}^{\circ }\\ \text{(D)}& \text{Horizontal range}& \text{(s)}& {\tan }^{-1}\left(\frac{1}{2}\right)\end{array}$