Relative permittivity and permeability of a material $${\epsilon }_r$$ and $${\mu }_r,$$ respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. Given that the escape velocity from the earth is $$11km{s}^{-1},$$ the escape velocity from the surface of the planet would be

This question contains Statement - $$1$$ and Statement - $$2$$. of the four choices given after the statements, choose the one that best describes the two statements. Statement - $$1$$: For a mass $$M$$ kept at the center of a cube of side $${}^{\prime }{a}^{\prime }$$, the flux of gravitational field passing through its sides $$4\pi GM.$$ Statement - 2: If the direction of a field due to a point source is radial and its dependence on the distance $${}^{\prime }{r}^{\prime }$$ from the source is given as {1 \over {{r^2}}}, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

A parallel plate capacitor with air between the plates has capacitance of $$9$$ $$pF.$$ The separation between its plates is $${}^{\prime }{d}^{\prime }.$$ The space between the plates has dielectric constant $$k_1$$ $$=3$$ and thickness {d \over 3} while the other one has dielectric constant $$k_2=6$$ and thickness {{2d} \over 3}. Capacitance of the capacitor is now

A wave travelling along the $$x$$-axis is described by the equation $$y(x,t)=0.005$$ $$\cos \left(\alpha x-\beta t\right).$$ If the wavelength and the time period of the wave are $$0.08$$ $$m$$ and $$2.0s$$, respectively, then $$\alpha$$ and $$\beta$$ in appropriate units are

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $$18$$ $$cm$$ during winter. Repeating the same experiment during summer, she measures the column length to be $$x$$ $$cm$$ for the second resonance. Then

A horizontal overhead powerline is at height of $$4m$$ from the ground and carries a current of $$100A$$ from east to west. The magnetic field directly below it on the ground is $$\left({\mu }_0=4\pi \times {10}^{-7}Tm{A}^{-1}\right)$$

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $$A=$$ $$10c{m}^2$$ and length $$=20$$ $$cm$$ . If one of the solenoid has $$300$$ turns and the other $$400$$ turns, their mutual inductance is $$\left({\mu }_0=4\pi \times {10}^{-7}Tm{A}^{-1}\right)$$

Consider a uniform square plate of side $${}^{\prime }{a}^{\prime }$$ and mass $${}^{\prime }{m}^{\prime }$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

The treatment of $$C{H}_{3}MgX$$ with $$C{H}_{3}C\equiv C-H$$ produces

The hydrocarbon which can react with sodium in liquid ammonia is

In the following sequence of reactions, the alkene affords the compound ‘B’ CH3 - CH = CH - CH3 \buildrel {{O_3}} \over \longrightarrow A $$\underset{Zn}{\overset{H{}_{2}O}{⟶}}$$ B The compound B is

Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $${\Delta }_o$$ be the highest?

The coordination number and the oxidation state of the element ‘E’ in the complex [E(en)2(C2O4)]NO2 (where (en) is ethylene diamine) are, respectively,

Four species are listed below i. $$HC{O}_3^{-}$$ ii. $$H_3{O}^{+}$$ iii. $$HS{O}_4^{-}$$ iv. $$HS{O}_{3}F$$ Which one of the following is the correct sequence of their acid strength?

The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

Which one of the following constitutes a group of the isoelectronic species?

The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the electron in the atom from n = 1 to n = 2 is

In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the correct statement?