Consider the following compounds: $K{O}_2$, $H_2{O}_2$ and $H_{2}S{O}_4$. The oxidation states of the underlined elements in them are, respectively:

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of $60^{\circ }$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $g=10{\text{m s}}^{-2}$).

A bob of heavy mass $m$ is suspended by a light string of length $l$. The bob is given a horizontal velocity $v_0$ as shown. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the speed $v$ of the bob at point $P$ to its initial speed $v_0$ is:

Find the statement that is NOT correct with regard to the structure of a monocot stem.

Consider a water tank shown in the figure. It has one wall at $x=L$ and is very wide in the $z$-direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes a small angle ${\theta }_0({\theta }_0\ll 1)$ with the $x$-axis at $x=L$. If $y(x)$ is the height of the surface, the equation for $y(x)$ is: (take $\theta (x)=\sin \theta (x)=\tan \theta (x)=\frac{dy}{dx}$, $g$ is the acceleration due to gravity)

For the reaction $\mathrm{A}(\mathrm{g})\rightleftharpoons 2\mathrm{B}(\mathrm{g})$, the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500 at $1000\mathrm{K}$. $K_p$ for the reaction at $1000\mathrm{K}$ is [Given: $R=0.0831\mathrm{L}\mathrm{atm}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$]

The electric field in a plane electromagnetic wave is given by $E_z=60\cos (5x+1.5\times 10^{9}t)\text{V/m}$. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):

If the rate constant of a reaction is $0.03{\mathrm{s}}^{-1}$, how much time does it take for $7.2\mathrm{mol}{\mathrm{L}}^{-1}$ concentration of the reactant to get reduced to $0.9\mathrm{mol}{\mathrm{L}}^{-1}$?
(Given: $\log 2=0.301$)

Which one of the following is the characteristic feature of gymnosperms?

The current passing through the battery in the given circuit is:

A wire of resistance $R$ is cut into $8$ equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

Identify the suitable reagent for the following conversion

A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius $r$ of the $n$th orbit and the particle's speed $v$ in the orbit depend on $n$ as

A ball of mass $0.5$ kg is dropped from a height of $40$ m. The ball hits the ground and rises to a height of $10$ m. The impulse imparted to the ball during its collision with the ground is (Take $g=9.8{\text{m/s}}^2$)

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is:

The kinetic energies of two similar cars A and B are $100\text{J}$ and $225\text{J}$ respectively. On applying brakes, car A stops after $1000\text{m}$ and car B stops after $1500\text{m}$. If $F_A$ and $F_B$ are the magnitudes of the braking forces on cars A and B, respectively, then the ratio $F_A/F_B$ is:

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

The plates of a parallel plate capacitor are separated by $d$. Two slabs of different dielectric constants $K_1$ and $K_2$ with thicknesses $\frac{3}{8}d$ and $\frac{d}{2}$, respectively, are inserted between the plates. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If $K_1=1.25K_2$, the value of $K_1$ is:

An electric dipole with dipole moment $5\times 10^{-6}\text{C m}$ is aligned with the direction of a uniform electric field of magnitude $4\times 10^5\text{N/C}$. The dipole is then rotated through an angle of $60^{\circ }$ with respect to the electric field. The change in the potential energy of the dipole is: