An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ km/h$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ m/s^2$):

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $xy-x-y+1=0$ is

If $A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$,then the value of $\alpha$ for which $A^2 = B$ is

Which of the following is the most stable conformer of butane?

$A$ radioactive nucleus undergoes a series of decays according to the scheme:
$A \xrightarrow{\alpha} A_1 \xrightarrow{\beta} A_2 \xrightarrow{\alpha} A_3 \xrightarrow{\gamma} A_4$
If the mass number and atomic number of $A$ are $180$ and $72$ respectively,what are these numbers for $A_4$?

Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between them is $2 \lambda$ as shown in the figure. The first bright fringe is formed at $P$ due to interference on a screen placed at a distance $D$ from $S_1$ $(D >> \lambda)$. Then the distance $OP$ is: