The number of lone pair of electrons and the hybridization of Xenon ( Xe ) in $\mathrm{XeOF}_2$ are

In the following reaction, the major product $(\mathrm{H})$ is

Increasing order of the nucleophilic substitution of following compounds

Which of the following hydrocarbons reacts easily with $\mathrm{MeMgBr}$ to give methane?

Adiabatic free expansion of ideal gas must be

An optically active alkene having molecular formula $\mathrm{C}_8 \mathrm{H}_{16}$ gives acetone as one of the products on ozonolysis. The structure of the alkene is

$360 \mathrm{~cm}^3$ of a hydrocarbon diffuses in 30 minutes, while under the same conditions $360 \mathrm{~cm}^3$ of $\mathrm{SO}_2$ gas diffuses in one hour. The molecular formula of the hydrocarbon is

The number of terminal and bridging hydrogens in $\mathrm{B}_2 \mathrm{H}_6$ are respectively

The major product (F) in the following reaction is

For a chemical reaction, half-life period $\left(t_{\frac{1}{2}}\right)$ is 10 minutes. How much reactant will be left after 20 minutes if one starts with 100 moles of reactant and the order of the reaction be (i) zero, (ii) one and (iii) two?

Equal volume of two solutions $A$ and $B$ of a strong acid having $\mathrm{pH}=6.0$ and $\mathrm{pH}=4.0$ respectively are mixed together to form a new solution. The pH of the new solution will be in the range

$P$ and $Q$ combines to form two compounds $\mathrm{PQ}_2$ and $\mathrm{PQ}_3$. If $1 \mathrm{~g} ~\mathrm{PQ}{ }_2$ is dissolved in 51 g benzene the depression of freezing point becomes $0 \cdot 8^{\circ} \mathrm{C}$. On the other hand if $1 \mathrm{~g} ~\mathrm{PQ}_3$ is dissolved in 51 g of benzene, the depression of freezing point becomes $0.625^{\circ} \mathrm{C}$. The atomic mass of P and Q are $\left(\mathrm{K}_{\mathrm{f}}\right.$ of benzene $=5 \cdot 1 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1})$

Identify the major product (G) in the following reaction

Increasing order of solubility of AgCl in (i) $\mathrm{H}_2 \mathrm{O}$, (ii) 1 M NaCl (aq.), (iii) 1 M CaCl 2 (aq.) and (iv) $1 \mathrm{M}~ \mathrm{NaNO}_3$ (aq.) solution

Arrange the following compounds in order of their increasing acid strength

Which of the following hydrogen bonds is likely to be the weakest?

How many oxygen atoms are present in 0.36 g of a drop of water at STP?

The molar conductances of $\mathrm{Ba}(\mathrm{OH})_2, \mathrm{BaCl}_2$ and $\mathrm{NH}_4 \mathrm{Cl}$ at infinite dilution are $523 \cdot 28,280 \cdot 0$ and $129.8 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ respectively. The molar conductance of $\mathrm{NH}_4 \mathrm{OH}$ at infinite dilution will be

The common stable oxidation states of Eu and Gd are respectively

Which one among the following compounds will most readily be dehydrated under acidic condition?

$$\begin{aligned} &{ }_5 \mathrm{~B}^{10}+{ }_2 \mathrm{He}^4 \rightarrow \mathrm{X}+{ }_0 \mathrm{n}^1\\ &\text { In the above nuclear reaction ' } X \text { ' will be } \end{aligned}$$

An LPG (Liquified Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure of 3.0 atm . In the course of usage at $27^{\circ} \mathrm{C}$, the mass of the full cylinder is reduced to $24 \cdot 2 \mathrm{~kg}$. The volume of the used gas in cubic metre at the normal usage condition ( atm and $27^{\circ} \mathrm{C}$ ) is (assume LPG to be normal butane and it behaves ideally)

What is the four-electron reduced form of $\mathrm{O}_2$ ?

Kjeldahl's method cannot be used for the estimation of nitrogen in which compound?

Which of the following compounds is most reactive in $\mathrm{S}_{\mathrm{N}} 1$ reaction?

The coagulating power of electrolytes having ions $\mathrm{Na}^{+}, \mathrm{Al}^{3+}$ and $\mathrm{Ba}^{2+}$ for $\mathrm{As}_2 \mathrm{S}_3$ sol increases in the order

If three elements $A, B, C$ crystalise in a cubic solid lattice with $B$ atoms at the cubic centres, $C$ aton at the centre of edges and A atoms at the corners, then formula of the compound is

Which of the following oxides is paramagnetic?

How many electrons are needed to reduce $\mathrm{N}_2$ to $\mathrm{NH}_3 ?$

The bond order of $\mathrm{HeH}^{+}$is

An egg takes 4.0 minutes to boil at sea level where the boiling point of water is $T_1 K$, where as it takes 8.0 minutes to boil on a mountain top where the boiling point of water is $\mathrm{T}_2 \mathrm{~K}$. The activation energy for the reaction that takes place during the boiling of egg is

As per the following equation, 0.217 g of HgO (molecular mass $=217 \mathrm{~g} \mathrm{~mol}^{-1}$ ) reacts with excess iodide. On titration of the resulting solution, how many mL of 0.01 M HCl is required to reach the equivalence point?

$\mathrm{HgO}+4 \mathrm{I}^{-}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{HgI}_4{ }^{2-}+2 \mathrm{OH}^{-}$

The major product 'P' and 'Q' in the above reactions are

Consider the following gas phase dissociation, $\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ with equilibrium constant $K_P$ at a particular temperature and at pressure $P$. The degree of dissociation ( $\alpha$ ) for $\mathrm{PCl}_5(\mathrm{~g})$ is

Compound given below will produce effervescence when mixed with aqueous sodium bicarbonate solution

Which of the following statement(s) is/are correct about the given compound?

$X$ is an extensive property and $x$ is an intensive property of a thermodynamic system. Which of the following statement(s) is (are) correct?

Which pair of ions among the following can be separated by precipitation method?

The compound(s) showing optical activity is/are

Identify 'P' and 'Q' in the following reaction

The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has

Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

The expression $2^{4 n}-15 n-1$, where $n \in \mathbb{N}$ (the set of natural numbers) is divisible by

If $z_1, z_2$ are complex numbers such that $\frac{2 z_1}{3 z_2}$ is a purely imaginary number, then the value of $\left|\frac{z_1-z_2}{z_1+z_2}\right|$ is

The value of the integral $\int\limits_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is

The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $X P \cdot X Q$ is

Let $f(x)=|1-2 x|$, then

If ' $f$ ' is the inverse function of ' $g$ ' and $g^{\prime}(x)=\frac{1}{1+x^n}$, then the value of $f^{\prime}(x)$ is

If the matrix $\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)$ is orthogonal, then the values of $a, b, c$ are

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $|A|^2=25$, then $|\alpha|$ equals to

A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$. If the function ' $f$ ' is differentiable at $x=0$, then $f$ is

Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$, then

If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E / F)-P(F / E)$ equals

The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is

$\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}, \lambda \vec{b}+4 \vec{c}$ and $(2 \lambda-1) \vec{c}$ are non-coplanar for

Let $\omega(\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\left\{\mid a+b \omega+c \omega^2\right\}^2 ; a, b, c$ are distinct non-zero integers} equals

$\int\limits_0^{1 \cdot 5}\left[x^2\right] d x$ is equal to

If the sum of ' $n$ ' terms of an A.P. is $3 n^2+5 n$ and its $m$ th term is 164 , then the value of $m$ is

If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to

If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is

If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{a} \times \vec{b}|^2=k^2-(\vec{a} \cdot \vec{b})^2$, then the values of $k$ and $\theta$ are

Consider three points $P(\cos \alpha, \sin \beta), Q(\sin \alpha, \cos \beta)$ and $R(0,0)$, where $0<\alpha, \beta<\frac{\pi}{4}$. Then

An $n \times n$ matrix is formed using 0, 1 and $-$1 as its elements. The number of such matrices which are skew symmetric is

Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then the rank of the matrix $\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right)$ is

Let $f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)$, then

The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is

If $\operatorname{adj} B=A,|P|=|Q|=1$, then $\operatorname{adj}\left(Q^{-1} B P^{-1}\right)=$

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ is $\alpha, \vec{b}$ and $\vec{c}$ is $\beta$ and $\vec{c}$ and $\vec{a}$ is $\gamma$. Then the minimum value of $\cos \alpha+\cos \beta+\cos \gamma$ is

Let $f(x)$ be a second degree polynomial. If $f(1)=f(-1)$ and $p, q, r$ are in A.P., then $f^{\prime}(p), f^{\prime}(q), f^{\prime}(r)$ are

The line parallel to the $x$-axis passing through the intersection of the lines $a x+2 b y+3 b=0$ and $b x-2 a y-3 a=0$ where $(a, b) \neq(0,0)$ is

A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect?

The number of reflexive relations on a set $A$ of $n$ elements is equal to

Let $f(x)$ be continuous on $[0,5]$ and differentiable in $(0,5)$. If $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq \frac{1}{5}$ for all $x$ in $(0,5)$, then $\forall x$ in $[0,5]$

$\lim\limits_{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right)}{\sin ^2 x}$ equals

If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ is equal to

If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the parallelogram for which $\vec{\alpha}$ and $\vec{\beta}$ are adjacent sides is

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then

If for a matrix $A,|A|=6$ and adj $A=\left[\begin{array}{ccc}1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]$, then $k$ is equal to

If $a, b, c$ are positive real numbers each distinct from unity, then the value of the determinant $\left|\begin{array}{ccc}1 & \log _a b & \log _a c \\ \log _b a & 1 & \log _b c \\ \log _c a & \log _c b & 1\end{array}\right|$ is

The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is

The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112. If its first term is 11, then the number of terms is

The value of the integral $\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x$ is

If the sum of the squares of the roots of the equation $x^2-(a-2) x-(a+1)=0$ is least for an appropriate value of the variable parameter $a$, then that value of ' $a$ ' will be

If $\left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12}$, then the value of $a_2+a_4+a_6+\ldots+a_{12}$ is

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors. Suppose $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$. Then $\vec{a}$ is

The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is

If $\left|Z_1\right|=\left|Z_2\right|=\left|Z_3\right|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose vertices are $Z_1, Z_2, Z_3$ is

Let $f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|$. Suppose $A$ and $B$ are respectively maximum and minimum values of $f(\theta)$.Then $(A,B)$ is equal to

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be

Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{-3}^3 f(x) d x$ has the value

If $a, b, c$ are in A.P. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, then

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of points in $[\alpha,\beta]$ at which $f$ is not differentiable is

The maximum number of common normals of $y^2=4 a x$ and $x^2=4 b y$ is equal to

The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is

The number of solutions of $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$ is

Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to

Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $\lim \limits_{n \rightarrow \infty} \frac{\left(a_n\right) n!}{{ }^{3 n} P_n}$ equals

If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}, 0<\theta, \phi<\frac{\pi}{4}$, then $\cot (2 \theta)$ has the value

If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x+1$, then

If the equation $\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0$ has a solution, the $p$ must lie in the interval

If $0 \leq a, b \leq 3$ and the equation $x^2+4+3 \cos (a x+b)=2 x$ has real solutions, then the value of $(a+b)$ is

Let $f(x)=x^3, x \in[-1,1]$. Then which of the following are correct?

Three numbers are chosen at random without replacement from $\{1,2, \ldots 10\}$. The probability that the minimum of the chosen numbers is 3 or their maximum is 7 , is

The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation

$$\frac{d p(t)}{d t}=0.5 p(t)-450$$

If $p(0)=850$, then the time at which the population becomes zero is

If $P$ is a non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is 1 , then the sum of the elements of each row in $P^{-1}$ is

The solution set of the equation $\left(x \in\left(0, \frac{\pi}{2}\right)\right) \tan (\pi \tan x)=\cot (\pi \cot x)$, is

If $f(x)=\int_0^{\sin ^2 x} \sin ^{-1} \sqrt{t} d t$ and $g(x)=\int_0^{\cos ^2 x} \cos ^{-1} \sqrt{t} d t$, then the value of $f(x)+g(x)$ is

The value of $\int\limits_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x$ is

Let $f:[0,1] \rightarrow \mathbb{R}$ and $g:[0,1] \rightarrow \mathbb{R}$ be defined as follows :

$\left.\begin{array}{rl}f(x) & =1 \text { if } x \text { is rational } \\ & =0 \text { if } x \text { is irrational }\end{array}\right]$ and

$\left.\begin{array}{rl}g(x) & =0 \text { if } x \text { is rational } \\ & =1 \text { if } x \text { is irrational }\end{array}\right]$ then

A radioactive nucleus decays as follows :

$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 $$

If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the atomic number and mass number of ' $X$ ' are

A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then

The variation of density of a solid cylindrical rod of cross sectional area $\alpha$ and length $L$ is $\rho=\rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from one end $(x=0)$ is

A simple pendulum is taken at a place where its distance from the earth's surface is equal to the radius of the earth. Calculate the time period of small oscillations if the length of the string is 4.0 m . (Take $g=\pi^2 \mathrm{~ms}^{-2}$ at the surface of the earth.)

Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $E(t)=E_0 \sin \omega t$ in the $x$-direction, where $E_0=2$ Newton/Coulomb and $\omega=1000 \mathrm{rad} / \mathrm{sec}$. The maximum speed attained by the particle is

The minimum force required to start pushing a body up a rough (having co-efficient of friction $\mu$ ) inclined plane is $\vec{F}_1$ while the minimum force needed to prevent it from sliding is $\overrightarrow{F_2}$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta=2 \mu$, then the ratio $F_1 / F_2$ is

Acceleration-time $(a-t)$ graph of a body is shown in the figurd. Corresponding velocity-time $(v-t)$ graph is

One end of a stecl wire is fixed to the ceiling of an elevator moving up with an acceleration $2 \mathrm{~m} / \mathrm{s}^2$ and a load of 10 kg hangs from the other end. If the cross section of the wire is $2 \mathrm{~cm}^2$, then the longitudinal strain in the wire will be ( $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\mathrm{Y}=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity $v_1$ in time $t_1$. On other day if she remains stationary on the escalator moving with velocity $v_2$, then escalator takes her up in time $t_2$. The time taken by her to walk up with velocity $v_1$ on the moving escalator will be

A quantity $X$ is given by $\varepsilon_0 L \frac{\Delta V}{\Delta t}$, where $\varepsilon_0$ is the permittivity of free space, $L$ is the length, $\Delta V$ is a potential difference and $\Delta t$ is a time interval. The dimension of $X$ is same as that of

A diode is connected in parallel with a resistance as shown in Figure. The most probable current (I) - voltage (V) characteristic is

The minimum wavelength of Lyman series lines is $P$, then the maximum wavelength of these lines is

An electron in Hydrogen atom jumps from the second Bohr orbit to the ground state and the difference between the energies of the two states is radiated in the form of a photon. This photon strikes a material. If the work function of the material is 4.2 eV , then the stopping potential is (Energy of electron in $n$-th orbit $\left.=-\frac{13 \cdot 6}{n^2} \mathrm{eV}\right)$

A ball falls from a height $h$ upon a fixed horizontal floor. The co-efficient of restitution for the collision between the ball and the floor is ' $e$ '. The total distance covered by the ball before coming to rest is [neglect the air resistance]

Manufacturers supply a zener diode with zener voltage $\mathrm{V}_{\mathrm{z}}=5.6 \mathrm{~V}$ and maximum power dissipation $P_{\mathrm{z}, \max }=\frac{1}{4} \mathrm{~W}$. This zener diode is used in the following circuit. Calculate the minimum value of the resistance $R_s$ in the circuit so that the zener diode will not burn when the input voltage is $\mathrm{V}_{\mathrm{in}}=10 \mathrm{~V}$.

A force $\vec{F}=a \hat{i}+b \hat{j}+c \hat{k}$ is acting on a body of mass $m$. The body was initially at rest at the origin. The co-ordinates of the body after time ' $t$ ' will be

Figure shows the graph of angle of deviation $\delta$ versus angle of incidence i for a light ray striking a prism. The prism angle is

Two charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance $2 L_{\mathrm{p} p a t}$ $C$ is the mid point of $A$ and $B$. The workdone in moving a charge $+Q$ along the semicircle $\operatorname{CSD}\left(W_V\right)$ and along the line $\mathrm{CBD}\left(W_2\right)$ are

Which logic gate is represented by the following combinations of logic gates?

The number of undecayed nuclei $N$ in a sample of radioactive material as a function of time $(t)$ is shown in the figure. Which of the following graphs correctly show the relationship between $N$ and the activity ' $A$ '?

For an ideal gas, a cyclic process ABCA as shown in P-T diagram, when presented in P-V plot, would be

The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(25 \pm 0.4)$ Volt and $\mathrm{I}=(200 \pm 3)$ Ampere. The percentage error in ' $R$ ' is

A particle of charge ' $q$ ' and mass ' $m$ ' moves in a circular orbit of radius ' $r$ ' with angular speed ' $\omega$ '. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

The de-Broglie wavelength of a moving bus with speed $v$ is $\lambda$. Some passengers left the bus at a stoppage. Now when the bus moves with twice of its initial speed, its kinetic energy is found to be twice of its initial value. What is the de-Broglie wavelength of the bus now?

The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass $m$ is represented by $y=2 \sin \left(\frac{\pi t}{2}+\phi\right) \mathrm{cm}$. The maximum acceleration of the particle is

What are the charges stored in the $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ capacitors in the circuit as shown in figure once the current (I) become steady?

Three different liquids are filled in a U-tube as shown in figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ respectively. From the figure we may conclude that

A piece of granite floats at the interface of mercury and water contained in a beaker as in figure. If the densities of granite, water and mercury are $\rho, \rho_1$ and $\rho_2$ respectively, the ratio of the volume of granite in water to the volume of granite in mercury is

$10^{20}$ photons of wavelength 660 nm are emitted per second from a lamp. The wattage of the lamp is (Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )

The apparent coefficient of expansion of a liquid, when heated in a copper vessel is $C$ and when heated in silver vessel is $S$. If $A$ is linear coefficient of expansion of copper, then linear coefficient of expansion of silver is

The equation of a stationary wave along a stretched string is given by $y=5 \sin \frac{\pi x}{3} \cos 40 \pi t$. Here $x$ and $y$ are in cm and $t$ in second. The separation between two adjacent nodes is

Temperature of a body $\theta$ is slightly more than the temperature of the surrounding $\theta_0$. Its rate of cooling $(R)$ versus temperature of the body $(\theta)$ is plotted. Its shape would be

Let $\bar{V}, V_{m s}, V_p$ denotes the mean speed, root mean square speed and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement(s) is/are correct?

A wave disturbance in a medium is described by $y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)$ where $x, y$ are in meters and $t$ is in second. Which statement(s) is/are correct?

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially $S_1$ is at rest and $S_2$ is moving with velocity $v$ along $x$-axis. After collision $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after collision