The area (in sq units) of the region bounded by $x=-1, x=2, y=x^2+1$ and $y=2x-2$ is

$15 \text{ mL}$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20 \text{ mL}$ of $0.03 \text{ M}$ aqueous $Cr_2O_7^{2-}$. The molarity of the $Fe^{2+}$ solution is $.......... \times 10^{-2} \text{ M}$ (Round off to the Nearest Integer).

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant,the springs are relaxed. The left mass is displaced to the left and the right mass is displaced to the right by the same distance and released. The resulting collision is elastic. The time period of the oscillations of the system is

If $a, b, c$ are unit vectors and the maximum value of $|a-b|^2+|b-c|^2+|c-a|^2$ is $k$,then $k(2|a|^2+3|b|^2-4|c|^2)=$

If $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$,then $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$ is equal to

Initially a photon of wavelength $\lambda_1$ falls on a photocathode and emits an electron of maximum energy $E_1$. If the wavelength of the incident photon is changed to $\lambda_2$,the maximum energy of the electron emitted becomes $E_2$. Then the value of $hc$ ($h=$ Planck's constant,$c=$ velocity of light) is