Which of the following set of polymers are used as fibre?

(i) Teflon (ii) Starch (iii) Terylene (iv) Orlon

The biodegradable polymer obtained by polymerisation of glycine and aminocaproic acid is

The compound is

Which one of the following is a cationic detergent?

The type of linkage present between nucleotides is

$\alpha-D-(+)$-glucose and $\beta-D-(+)$-glucose are

Propanone and propanal are

Sodium ethanoate on heating with soda lime gives ' $X^{\prime}$. Electrolysis of aqueous solution of sodium ethanoate gives ' $Y^{\prime}$. ' $X^{\prime}$ and ' $Y^{\prime}$ respectively are

But-1-yne on reaction with dil. $\mathrm{H}_2 \mathrm{SO}_4$ in presence of $\mathrm{Hg}^{2+}$ ions at 333 K gives

Biologically active adrenaline and ephedrine used to increase blood pressure contain

In the reaction, Aniline $\xrightarrow[\text { Dil. } \mathrm{HCl}]{\mathrm{NaNO}_2} P \xrightarrow[\text { NaOH }]{\text { Phenol }} Q$

The female sex hormone which is responsible for the development of secondary female characteristics and participates in the control of menstrual cycle is

In the following scheme of reaction.

X, y and Z respectively are

8.8 g of monohydric alcohol added to ethyl magnesium iodide in ether liberates $2240 \mathrm{~cm}^3$ of ethane at STP. This monohydric alcohol when oxidised using pyridinium-chloro-chromate, forms a carbonyl compound that answers silver mirror test (Tollen's test). The monohydric alcohol is

When a tertiary alcohol ' $A^{\prime}\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ reacts with $20 \% \mathrm{H}_3 \mathrm{PO}_4$ at 358 K , it gives a compound ' $B^{\prime}\left(\mathrm{C}_4 \mathrm{H}_8\right)$ as a major product. The IUPAC name of the compound ' $B$ ' is

PCC is

On treating 100 mL of 0.1 M aqueous solution of the complex $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$ with excess of $\mathrm{AgNO}_3, 2.86 \mathrm{~g}$ of AgCl was obtained. The complex is

The complex compounds $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Br}\right] \mathrm{SO}_4$ are

Which of the following statements are true about $\left[\mathrm{CoF}_6\right]^{3-}$ ion ?

I. The complex has octahedral geometry.

II. Coordination number of Co is 3 and oxidation state is +6 .

III. The complex is $s p^3 d^2$ hybridised.

IV. It is a high spin complex.

A haloalkane undergoes $\mathrm{S}_{\mathrm{N}} 2$ or $\mathrm{S}_{\mathrm{N}} 1$ reaction depending on

2-methyl propane can be prepared by Wurtz reaction. The haloalkanes taken along with metallic sodium and dry ether are :

In the analysis of III group basic radicals of salts, the purpose of adding $\mathrm{NH}_4 \mathrm{Cl}(s)$ to $\mathrm{NH}_4 \mathrm{OH}$ is

Solubility product of $\mathrm{CaC}_2 \mathrm{O}_4$ at a given temperature in pure water is $4 \times 10^{-9}\left(\mathrm{~mol} \mathrm{~L}^{-1}\right)^2$. Solubility of $\mathrm{CaC}_2 \mathrm{O}_4$ at the same temperature is

In the reaction between moist $\mathrm{SO}_2$ and acidified permanganate solution.

Which one of the following properties is generally not applicable to ionic hydrides?

Which one of the following nitrate will decompose to give $\mathrm{NO}_2$ on heating ?

Which of the following halides cannot be hydrolysed?

0.48 g of an organic compound on complete combustion produced 0.22 g of $\mathrm{CO}_2$. The percentage of C in the given organic compound is

In the given sequence of reactions, identify ' $P^{\prime}, Q^{\prime}, R^{\prime}$ and ' $S$ respectively.

The first chlorinated organic insecticide prepared is

Which of the following crystals has the unit cell such that $a=b \neq c$ and $\alpha=\beta=90^{\circ}$, $\gamma=120^{\circ}$ ?

MnO exhibits

The number of atoms in 4.5 g of a face-centred cubic crystal with edge length 300 pm is (Given : Density $=10 \mathrm{~g} \mathrm{~cm}^{-3}$ and $N_A=6.022 \times 10^{23}$)

Vapour pressure of a solution containing 18 g of glucose and 178.2 g of water at $100^{\circ} \mathrm{C}$ is (Vapour pressure of pure water at $100^{\circ} \mathrm{C}=760$ torr)

A mixture of phenol and aniline shows negative deviation from Raoult's law. This is due to the formation of

Which one of the following pairs will show positive deviation from Raoult's law?

How many coulombs are required to oxidise 0.1 mole of $\mathrm{H}_2 \mathrm{O}$ to oxygen?

A current of 3 A is passed through a molten calcium salt for 1 hr 47 min 13 s . The mass of calcium deposited is (Molar mass of $\mathrm{Ca}=40 \mathrm{~g} \mathrm{~mol}^{-1}$ )

The value of ' $A$ ' in the equation $\lambda_{\mathrm{m}}=\lambda_{\mathrm{m}}^{\circ}-A \sqrt{C}$ is same for the pair

For the reaction, $A \rightleftharpoons B, E_a=50 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta H=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}$. When a catalyst is added $E_a$ decreases by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the $E_a$ for the backward reaction in the presence of catalyst?

For the reaction, $\mathrm{PCl}_5 \longrightarrow \mathrm{PCl}_3+\mathrm{Cl}_2$, rate and rate constant are $1.02 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $3.4 \times 10^{-5} \mathrm{~s}^{-1}$ respectively at a given instant. The molar concentration of $\mathrm{PCl}_5$ at that instant is

Which one of the following does not represent Arrhenius equation?

Identify the incorrect statement

For the coagulations of positively charged hydrated ferric - oxide sol, the flocculating power of the ions is in the order:

Gold sol is not a

The incorrect statement about Hall -Heroult process is

Select the correct statement :

$\mathrm{NO}_2$ gas is

Identify the incorrect statement from the following.

The correct decreasing order of boiling point of hydrogen halides is

The synthetically produced radioactive noble gas by the collision of ${ }_{98}^{249} \mathrm{Cf}$ with ${ }_{20}^{48} \mathrm{Ca}$ is

The transition element $(\approx 5 \%)$ present with lanthanoid metal in misch metal is

Match the following.

I. $\mathrm{Zn}^{2+}\quad$ (i) $d^8$ configuration

II. $\mathrm{Cu}^{2+}\quad$ (ii) Colourless

III. $\mathrm{Ni}^{2+}\quad$ (iii) $\mu=1.73 \mathrm{BM}$

Which of the following statements related to lanthanoids is incorrect?

A metalloid is

A pair of isoelectronic species having bond order of one is

Identify the wrong relation for real gases :

From the diagram $(Z)=\frac{V_{\text {real }}}{V_{\text {ideal }}}$

$\Delta_r H$ for the reaction, $C \rightarrow A$ is

For which one of the following mixtures is composition uniform throughout?

The energy associated with first orbit of $\mathrm{He}^{+}$ is

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of $m$ and $n$, respectively are

If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

If in two circles, arcs of the same length subtend angles $30^{\circ}$ and $78^{\circ}$ at the centre, then the ratio of their radii is

If $\triangle A B C$ is right angled at $C$, then the value of $\tan A+\tan B$ is

The real value of ' $\alpha$ ' for which $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely real is

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is 180 cm , then

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

In the expansion of $(1+x)^n$ $\frac{C_1}{C_0}+2 \frac{C_2}{C_1}+3 \frac{C_3}{2}+\ldots+n \frac{C_n}{C_{n-1}}$ is equal to

If $S_n$ stands for sum to $n$-terms of a GP with $a$ as the first term and $r$ as the common ratio, then $S_n: S_{2 n}$ is

If $A M$ and GM of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation is

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

The equation of parabola whose focus is $(6,0)$ and directrix is $x=-6$ is

$\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{2} \cos x-1}{\cot x-1}$ is equal to

The negation of the statement "For every real number $x ; x^2+5$ is positive" is

Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a+k$, $b+k, c+k, d+k$ and $e+k$ is

Let $f: R \rightarrow R$ be given $f(x)=\tan x$. Then, $f^{-1}(1)$ is

Let $f: R \rightarrow R$ be defined by $f(x)=x^2+1$. Then, the pre images of 17 and $-$3 , respectively are

Let $(g \circ f)(x)=\sin x$ and $f \circ g(x)=(\sin \sqrt{x})^2$. Then,

Let $A=\{2,3,4,5, \ldots, 16,17,18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R(c, d)$ if and only if $a d=b c$ for all $(a, b),(c, d)$ in $A \times A$. Then, the number of ordered pairs of the equivalence class of $(3,2)$ is

If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then $x(y+z)+y(z+x)+z(x+y)$ equals to

If $2 \sin ^{-1} x-3 \cos ^{-1} x=4, x \in[-1,1]$, then $2 \sin ^{-1} x+3 \cos ^{-1} x$ is equal to

If $A$ is a square matrix, such that $A^2=A$, then $(I+A)^3$ is equal to

If $A=\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$, then $A^{10}$ is equal to

If $f(x)=\left|\begin{array}{ccc}x-3 & 2 x^2-18 & 2 x^3-81 \\ x-5 & 2 x^2-50 & 4 x^3-500 \\ 1 & 2 & 3\end{array}\right|$, then $f(\mathrm{l}) \cdot f(3)+f(3) \cdot f(5)+f(5) \cdot f(\mathrm{l})$ is

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ $\operatorname{matrix} A$ and $|A|=4$, then $\alpha$ is equal to

If $A=\left|\begin{array}{cc}x & 1 \\ 1 & x\end{array}\right|$ and $B=\left|\begin{array}{ccc}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|$, then $\frac{d B}{d x}$ is

Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x & 2 x \\ \sin x & x & x\end{array}\right|$. Then, $\lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}$ is

Which one of the following observations is correct for the features of logarithm function to any base $b>1$ ?

The function $f(x)=|\cos x|$ is

If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is

Let the function satisfy the equation $f(x+y)=f(x) f(y)$ for all $x, y \in R$, where $f(0) \neq 0$. If $f(5)=3$ and $f^{\prime}(0)=2$, then $f^{\prime}(5)$ is

The value of $C$ in $(0,2)$ satisfying the mean value theorem for the function $f(x)=x(x-1)^2, x \in[0,2]$ is equal to

$\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is

For the function $f(x)=x^3-6 x^2+12 x-3$; $x=2$ is

The function $x^x ; x>0$ is strictly increasing at

The maximum volume of the right circular cone with slant height 6 units is

If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

$$\int \frac{\sin x}{3+4 \cos ^2 x} d x$$

$\int_{-\pi}^\pi\left(1-x^2\right) \sin x \cdot \cos ^2 x d x$ is

$$\int \frac{1}{x\left[6(\log x)^2+7 \log x+2\right]} d x \text { is }$$

$\int \frac{\sin \frac{3 x}{2}}{\sin \frac{x}{2}} d x$ is

$\int\limits_1^5(|x-3|+|1-x|) d x=$

$$\lim _\limits{n \rightarrow \infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\ldots+\frac{1}{5 n}\right)= $$

The area of the region bounded by the line $y=3 x$ and the curve $y=x^2$ sq units is

The area of the region bounded by the line $y=x$ and the curve $y=x^3$ is

The solution of $e^{d y / d x}=x+1, y(0)=3$ is

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ are the sides of a $\triangle A B C$, The length of the median through $A$ is

The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is

Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{b}$ is a unit vector, if

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three non-coplanar vectors and $p, q$ and $r$ are vectors defined by $\mathbf{p}=\frac{\mathbf{a} \times \mathbf{c}}{[\mathbf{a b c}]}, \mathbf{q}=\frac{\mathbf{c} \times \mathbf{a}}{[\mathbf{a b c} \mathbf{b}}, \mathbf{r}=\frac{\mathbf{a} \times \mathbf{b}}{[\mathbf{a} \mathbf{b}]}$, then $(\mathbf{a}+\mathbf{b}) \cdot \mathbf{p}+(\mathbf{b}+\mathbf{c}) \cdot \mathbf{q}+(\mathbf{c}+\mathbf{a}) \cdot \mathbf{r}$ is

If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are mutually perpendicular, then $k$ is equal to

The distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is

The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}$ are the plane $2 x-2 y+z=5$ is

The equation $x y=0$ in three-dimensional space represents

The plane containing the point $(3,2,0)$ and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is

Corner points of the feasible region for an LPP are $(0,2),(3,0),(6,0),(6,8)$ and $(0,5)$. Let $Z=4 x+6 y$ be the objective function. The minimum value of $z$ occurs at

A die is thrown 10 times. The probability that an odd number will come up at least once is

A random variable $X$ has the following probability distribution:

If the mean of the random variable $X$ is $1 / 3$, then the variance is

If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is equal to

The ratio of molar specific heats of oxygen is

For a particle executing simple harmonic motion (SHM), at its mean position

A motor-cyclist moving towards a huge cliff with a speed of $18 \mathrm{kmh}^{-1}$, blows a horn of source frequency 325 Hz . If the speed of the sound in air is $330 \mathrm{~ms}^{-1}$, the number of beats heard by him is

A body has a charge of $-3.2 \mu \mathrm{C}$. The number of excess electrons will be

A point charge $A$ of $+10 \mu \mathrm{C}$ and another point charge $B$ of $+20 \mu \mathrm{C}$ are kept 1 m apart in free space. The electrostatic force on $A$ due to $B$ is $F_1$ and the electrostatic force on $B$ due to $A$ is $\mathbf{F}_2$. Then

A uniform electric field $E=3 \times 10^5 \mathrm{NC}^{-1}$ is acting along the positive $Y$-axis. The electric flux through a rectangle of area $10 \mathrm{~cm} \times 30 \mathrm{~cm}$ whose plane is parallel to the ZX -plane is

The total electric flux through a closed spherical surface of radius $r$ enclosing an electric dipole of dipole moment $2 a q$ is (Give $\varepsilon_0=$ permittivity of free space)

Under electrostatic conditien of a charged conductor, which among the following statements is true?

A cube of side 1 cm contains 100 molecules each having an induced dipole moment of $0.2 \times 10^{-6} \mathrm{C}-\mathrm{m}$ in an external electric field of $4 \mathrm{NC}^{-1}$. The electric susceptibility of the materials is ................ $\mathrm{~C^2N}^{-1} \mathrm{~m}^{-2}$

A capacitor of capacitance $5 \mu \mathrm{~F}$ is charged by a battery of emf 10 V . At an instant of time, the potential difference across the capacitors is 4 V and the time rate of change of potential difference across the capacitor is $0.6 \mathrm{Vs}^{-1}$. Then, the time rate at which energy is stored the capacitor at $\geq$ instant is

E is the electric field inside a conductor whose material has conductivity $\sigma$ and resistivity $\rho$. The current density inside the conductor is $\mathbf{J}$. The correct form of Ohm's law is

In the circuit shown, the end $A$ is at potential $V_0$ and end $B$ is grounded. The electric current $I$ indicated in the circuit is

The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval $0 \leq t \leq 20 \mathrm{~s}$ is

The $I-V$ graph for a conductor at two different temperatures $100^{\circ} \mathrm{C}$ and $400^{\circ} \mathrm{C}$ is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius)

An electric blub of $60 \mathrm{~W}, 120 \mathrm{~V}$ is to be connected to 220 V source. What resistance should be connected in series with the bulb, so that the bulb glows properly?

In an experiment to determine the temperature coefficient of resistance of a conductor, a coil of wire $X$ is immersed in a liquid. It is heated by an external agent. A meter bridge set up is used to determine resistance of the coil $X$ at different temperatures. The balancing points measured at temperatures $t_1=0^{\circ} \mathrm{C}$ and $t_2=100^{\circ} \mathrm{C}$ are 50 cm and 60 cm respectively. If the standard resistance taken out is $S=4 \Omega$ in both trials, the temperature coefficient of the coil is

A moving electron produces

A coil having 9 turns carrying a current produces magnetic field $B_1$ at the centre. Now the coil is rewounded into 3 turns carrying same current. Then, the magnetic field at the centre $B_2=$

19. A particle of specific charge $q / m=\pi \mathrm{C} \mathrm{kg}^{-1}$ is projected the origin towards positive $X$-axis with the velocity $10 \mathrm{~ms}^{-1}$ in a uniform magnetic field $\mathbf{B}=-2 \hat{\mathbf{k} T}$. The velocity $\mathbf{v}$ of particle after time $t=\frac{1}{12} \mathrm{~s}$ will be (in $\mathrm{ms}^{-1}$)

The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is 64 times the magnetic field at a distance $x$ on its axis from the centre of the coil. Then, the value of $x$ is

Magnetic hysterisis is exhibited by ............ magnetic materials

Magnetic susceptibility of Mg at 300 K is $1.2 \times 10^{-5}$. What is its susceptibility at $200 \mathrm{~K} ?$

A uniform magnetic field of strength $B=2 \mathrm{mT}$ exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere $S_1$, a right circular cone $S_2$ and a circular surface $S_3$. The magnetic flux through $S_1$ and $S_2$ are respectively.

In the figure, a conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then, the

An induced current of 2 A flows through a coil. The resistance of the coil is $10 \Omega$. What is the change in magnetic flux associated with the coil in 1 ms ?

A square loop of side length $a$ is moving away from an infinitely long current carrying conductor at a constant speed $v$ as shown. Let $x$ be the instantaneous distance between the long conductor and side $A B$. The mutual inductance $M$ of the square loop-long conductor pair changes with time $t$ according to which of the following graphs?

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

In an $L-C-R$ series circuit, the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

The figure shows variation of $R, X_L$ and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. Then, for what frequency point is the circuit capacitive?

Electromagnetic waves are incident normally on a perfectly reflecting surface having surface area $A$. If $I$ is the intensity of the incident electromagnetic radiation and $c$ is the speed of light in vacuum, the force exerted by the electromagnetic wave on the reflecting surface is

The final image formed by an astronomical telescope is

If the angle of minimum deviation is equal to angle of a prism for an equilateral prism, then the speed of light inside the prism is

A luminous point object $O$ is placed at a distance $2 R$ from the spherical boundary separating two transparent media of refractive indices $n_1$ and $n_2$ as shown, where $R$ is the radius of curvature of the spherical surface. If $n_1=\frac{4}{3}, n_2=\frac{3}{2}$ and $R=10 \mathrm{~cm}$, the image is obtained at a distance from $P$ equal to

An equiconvex lens of radius of curvature 14 cm is made up of two different materials. Left half and right half of vertical portion is made up of material of refractive index 1.5 and 1.2 respectively as shown in the figure. If a point object is placed at a distance of 40 cm , calculate the image distance.

A galaxy is moving away from the Earth so that a spectral line at 600 nm is observed at 601 nm . Then, the speed of the galaxy with respect to the Earth is

Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids 2 and 3 make $30^{\circ}$ and $90^{\circ}$ with pass axis of polaroid sheet 1 . If $I_0$ is the intensity of the incident unpolarised light entering sheet 1 , the intensity of the emergent light through sheet 3 is

In Young's double slit experiment, an electron beam is used to produce interference fringes of width $\beta_1$. Now the electron beam is replaced by a beam of protons with the same experimental set-up and same speed. The fringe width obtained is $\beta_2$. The correct relation between $\beta_1$ and $\beta_2$ is

Light of energy $E$ falls normally on a metal of work function $\frac{E}{3}$. The kinetic energies $K$ of the photo electrons are

The photoelectric work function for photo metal is 2.4 eV . Among the four wavelengths, the wavelength of light for which photoemission does not take place is

In alpha particle scattering experiment, if $v$ is the initial velocity of the particle, then the distance of closest approach is $d$. If the velocity is doubled, then the distance of closest approach becomes

The ratio of area of first excited state to ground state of orbit of hydrogen atom is

The ratio of volume of $\mathrm{Al}^{27}$ nucleus to its surface area is (Given, $R_0=1.2 \times 10^{-15} \mathrm{~m}$)

Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 n$. Assuming all the kinetic energy is carried away by the fast neutrons only and total binding energies of ${ }_{92}^{235} \mathrm{U},{ }_{56}^{144} \mathrm{Ba}$ and ${ }_{36}^{89} \mathrm{Kr}$ to be $1800 \mathrm{MeV}, 1200$ MeV and 780 MeV respectively, the average kinetic energy carried by each fast neutron is (in MeV)

The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$, there are $N_0$ undecayed nuclei. Then, $N_0$ is equal to [Take $e^2=7.5$ ]

Depletion region in an unbiased semiconductor diode is a region consisting of only free electrons only holes

The upper level of valence band and lower level of conduction band overlap in the case of

In the diagram shown, the Zener diode has a reverse breakdown voltage of $V_Z$. The current through the load resistance $R_L$ is $I_L$. The current through the Zener diode is

A $p-n$ junction diode is connected to a battery of emf 5.7 V in series with a resistant $5 \mathrm{k} \Omega$ such that it is forward biased. If the barrier potential of the diode is 0.7 V , neglecting the diode resistance, the current in the circuit is

An athlete runs along a circular track of diameter 80 m . The distance travelled and the magnitude of displacement of the athlete when he covers $3 / 4$ th of the circle is (in m )

Among the given pair of vectors, the resultant of two vectors can never be 3 units. The vectors are

A block of certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is 30$^\circ$. The coefficients of static and kinetic frictions between the block and the inclined plane are 0.6 and 0.5 respectively. Then, the magnitude of the acceleration of the block is [Take g = 10 ms$^{-2}$]

A particle of mass 500 g is at rest. It is free to move along a straight line. The power delivered to the particle varies with time according to the following graph

The momentum of the particle at $t=5$ s is

Dimensional formula for activity of a radioactive substance is

A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along .......... .

A body of mass 1 kg is suspended by a weightless string which passes over a frictionless pulley of mass 2 kg as shown in the figure. The mass is released from a height of 1.6 m from the ground. With what velocity does it strike the ground?

What is the value of acceleration due to gravity at a height equal to half the radius of the Earth, from its surface ?

A thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ( $Y=$ Young's modulus of the material of the wire)

Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$. The velocity of water at a point where the radius of the pipe is 10 cm is

A solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\theta_1$ and vapour at temperature $\theta_2$. Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively, then the minimum heat energy supplied to the cube until it vaporises is

One mole of an ideal monoatomic gas is taken round the cyclic process MNOM. The work done by the gas is