$1\,kg$ of ice at $-10\,^{\circ}C$ is mixed with $4.4\,kg$ of water at $30\,^{\circ}C$. The final temperature of the mixture is ........ $^{\circ}C$ (specific heat of ice is $2100\,J/kg\cdot K$,latent heat of fusion of ice is $336000\,J/kg$,and specific heat of water is $4200\,J/kg\cdot K$).

An electron initially present in an excited state of $H$ atom is further excited to another energy level by an incident photon. It releases $10$ photons while coming back to the ground state,out of which $7$ have higher energy than the incident photon. The electron was initially present in

$A$ thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. The maximum value of $\lambda$ to produce a maxima at $D$ is given by

Which of the following is least likely to behave as a Lewis base?

If $e$ and $e^{\prime}$ are the eccentricities of the ellipse $5x^2 + 9y^2 = 45$ and the hyperbola $5x^2 - 4y^2 = 45$ respectively,then $ee^{\prime}$ is equal to