$A$ person walks along a straight road from his house to a market $2.5 \ km$ away with a speed of $5 \ km/h$ and instantly turns back and reaches his house with a speed of $7.5 \ km/h$. The average speed of the person during the time interval $0$ to $50 \ min$ is (in $m/s$):

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha$,and $\beta$ are positive constants. The velocity of the particle will:

Let $A = \{ (x, y) : y = e^x, x \in R \} $ and $B = \{ (x, y) : y = e^{-x}, x \in R \} $. Then

The line $\frac{x + 1}{2} = \frac{y + 1}{3} = \frac{z + 1}{4}$ meets the plane $x + 2y + 3z = 14$ at the point:

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially,the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$,the number of nuclei of both are equal. Then the ratio $\frac{N_A}{N_B}$ is

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):