$$ \text { Match List-I with List-II and select the correct option: } $$

The electronic configuration of X and Y are given below:

$$ \begin{aligned} & X: 1 s^2 2 s^2 2 p^6 3 s^2 3 p^3 \\ & Y: 1 s^2 2 s^2 2 p^6 3 s^2 3 p^5 \end{aligned} $$

Which of the following is the correct molecular formula and type of bond formed between X and Y ?

$$ \text { Match List-I with List-II } $$

$$ \text { Choose the correct answer from the options given below. } $$

In the following pairs, the one in which both transition metal ions are colourless is

In the reaction between hydrogen sulphide and acidified permanganate solution,

A member of the Lanthanoid series which is well known to exhibit +4 oxidation state is

In which of the following pairs, both the elements do not have $(n-1) d^{10} n s^2$ configuration?

A ligand which has two different donor atoms and either of the two ligates with the central metal atom/ion in the complex is called ___________

Which of the following statements are true about $\left[\mathrm{NiCl}_4\right]^{2-}$ ?

(a) The complex has tetrahedral geometry

(b) Co-ordination number of Ni is 2 and oxidation state is +4

(c) The complex is $\mathrm{sp}^3$ hybridised

(d) It is a high spin complex

(e) The complex is paramagnetic

$$ \text { Which formula and its name combination is incorrect? } $$

$$ \text { In the complex ion }\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-} \text {, the co-ordination number of } \mathrm{Fe} \text { is } $$

Match List-I with List-II for the following reaction pattern

Glucose $\xrightarrow{\text { Reagent }}$ Product $\longrightarrow$ Structural prediction

The correct sequence of $\alpha$-amino acids, hormone, vitamin, carbohydrates respectively is

In the titration of potassium permanganate $\left(\mathrm{KMnO}_4\right)$ against Ferrous ammonium sulphate $(\mathrm{FAS})$ solution, dilute sulphuric acid but not nitric acid is used to maintain acidic medium, because

The group reagent $\mathrm{NH}_4 \mathrm{Cl}(\mathrm{s})$ and aqueous $\mathrm{NH}_3$ will precipitate which of the following ion?

In the preparation of sodium fusion extract, the purpose of fusing organic compound with a piece of sodium metal is to

The sodium fusion extract is boiled with concentrated nitric acid while testing for halogens. By doing so, it

$$ \text { Which of the following is not an aromatic compound } $$

The IUPAC name of the given organic compound is

$$ \mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_2 $$

$$ \text { Among the following, identify the compound that is not an isomer of hexane } $$

Chlorobenzene reacts with bromine gas in the presence of Anhyd $\mathrm{AlBr}_3$ to yield p-Bromochlorobenzene. This reaction is classified as ____________

The organometallic compound $\left(\mathrm{CH}_3\right)_3 \mathrm{CMgBr}$ on reaction with $\mathrm{D}_2 \mathrm{O}$ produces $\qquad$

The major product formed when $1-$ Bromo $-3-$ Chlorocyclobutane reacts with metallic sodium in dry ether is

Phenol can be distinguished from propanol by using the reagent

$$ \text { Match the following with their } \mathrm{pKa} \text { values } $$

$$ A \text { and } B \text { respectively are } $$

Oxidation of Toluene with chromyl chloride followed by hydrolysis gives Benzaldehyde. This reaction is known as ____________

Statement - I : Reduction of ester by DIABL-H followed by hydrolysis gives aldehyde.

Statement - II : Oxidation of benzyl alcohol with aqueous $\mathrm{KMnO}_4$ leads to the formation to Benzaldehyde.

Among the above statements, identify the correct statement.

Arrange the following compounds in their decreasing order of reactivity towards Nucleop addition reaction.

$$ \mathrm{CH}_3 \mathrm{COCH}_3, \mathrm{CH}_3 \mathrm{COC}_2 \mathrm{H}_5, \mathrm{CH}_3 \mathrm{CHO} $$

Which of the following reagents are suitable to differentiate Aniline and N-methylaniline chemical

$$ \text { Which of the following reaction/s does not yield an amine? } $$

$$ \text { Match the compounds given in List - I with the items given in List - II. } $$

The number of orbitals associated with ' N ' shell of an atom is

According to the Heisenberg's Uncertainty principle, the value of $\Delta \mathrm{b} . \Delta \mathrm{x}$ for an object whose mass is $10^{-6} \mathrm{~kg}$ is $\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right)$

Given below are two statements.

Statement-I : Adiabatic work done is positive when work is done on the system and internal energy of the system increases.

Statement - II : No work is done during free expansion of an ideal gas.

In the light of the above statements, choose the correct answer from the options given below.

Which one of the following reactions has $\Delta \mathrm{H}=\Delta \mathrm{U}$ ?

Identify the incorrect statements among the following:

(a) All enthalpies of fusion are positive

(b) The magnitude of enthalpy change does not depend on the strength of the intermolecular interactions in the substance undergoing phase transformations.

(c) When a chemical reaction is reversed, the value of $\Delta \mathrm{rH}^{\circ}$ is reversed in sign.

(d) The change in enthalpy is dependent of path between initial state (reactants) and final state (products)

(e) For most of the ionic compounds, $\Delta_{\text {sol }} \mathrm{H}^{\circ}$ is negative

Which of the following statements is/are true about equilibrium?

(a) Equilibrium is possible only in a closed system of at a given temperature

(b) All the measurable properties of the system remain constant at equilibrium

(c) Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

According to Le Chatelier's principle, in the reaction $\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$, the formation of methane is favoured by

(a) Increasing the concentration of CO

(b) Increasing the concentration of $\mathrm{H}_2 \mathrm{O}$

(c) Decreasing the concentration of $\mathrm{CH}_4$

(d) Decreasing the concentration of $\mathrm{H}_2$

The equilibrium constant at 298 K for the reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . If the initial concentrations of all the four species were 1 M each, then equilibrium concentration of D (in $\mathrm{mol} \mathrm{L}^{-1}$ ) will be

Among the following 0.1 m aqueous solutions, which one will exhibit the lowest boiling point elevation, assuming complete ionization of the compound in solution?

Variation of solubility with temperature t for a gas in liquid is shown by the following graphs. The correct representation is

180 g of glucose, $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6$, is dissolved in 1 kg of water in a vessel. The temperature at which water boils at 1.013 bar is _________ (given, $\mathrm{K}_{\mathrm{b}}$ for water is $052 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. Boiling point for pure water is 373.15 K )

If $N_2$ gas is bubbled through water at 293 K , how many moles of $N_2$ gas would dissolve in 1 litre of water? Assume that $\mathrm{N}_2$ exerts a partial pressure of 0.987 bar.

[Given $\mathrm{K}_{\mathrm{H}}$ for $\mathrm{N}_2$ at 293 K is 76.48 K bar ]

The correct statement/s about Galvanic cell is/are

(a) Current flows from cathode to anode

(b) Anode is positive terminal

(c) If $\mathrm{E}_{\text {cell }}<0$, then it is spontaneous reaction

(d) Cathode is positive terminal

The electronic conductance depends on

For a given half cell, $\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Al}$ on increasing of aluminium ion, the electrode potential will

Match the following select the correct option for the quantity of electricity, in $\mathrm{Cmol}^{-1}$ required to deposit various metals at cathode

Catalysts are used to increase the rate of a chemical reaction. Because it

Half-life of a first order reaction is 20 seconds and initial concentration of reactant is 0.2 M . The concentration of reactant left after 80 seconds is

$$ \text { In the given graph, } \mathrm{E}_{\mathrm{a}} \text { for the reverse reaction will be } $$

For the reaction $2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$ initial concentration of $\mathrm{N}_2 \mathrm{O}_5$ is $2.0 \mathrm{molL}^{-1}$ and after 300 min , it is reduced to $1.4 \mathrm{molL}^{-1}$. The rate of production of $\mathrm{NO}_2\left(\mathrm{in} \mathrm{molL}^{-1} \mathrm{~min}^{-1}\right)$ is

Which of the following methods of expressing concentration are unitless?

Select the INCORRECT statement/s from the following:

(a) 22 books have infinite significant figures

(b) In the answer of calculation $2.5 \times 1.25$ has four significant figures,.

(c) Zero's preceding to first non-zero digit are significant

(d) In the answer of calculation $12.11+18.0+1.012$ has three significant figures

$$ \text { Given below and the atomic masses of the elements: } $$

$$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|} \hline \text { Element: } & \mathrm{Li} & \mathrm{Na} & \mathrm{Cl} & \mathrm{~K} & \mathrm{Ca} & \mathrm{Br} & \mathrm{Sr} & \mathrm{I} & \mathrm{Ba} \\ \hline \text { Atomic Mass }\left(\mathrm{g} \mathrm{~mol}^{-1}\right): & 7 & 23 & 35.5 & 39 & 40 & 80 & 88 & 127 & 137 \\ \hline \end{array} $$

If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$

$B=\{x: x$ is a natural number and $2 \leq x<5\}$

$\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a prime number $\leq 4\}$

Then $(B-C) \cup A$ is,

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.

Statement (I): Minimum number of elements in AUB is 3

Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

Domain of the function $f$, given by $f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}$ is

If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of the following is not true?

The mean deviation about the mean for the date $4,7,8,9,10,12,13,17$ is

A random experiment has five outcomes $\mathrm{w}_1, \mathrm{w}_2, \mathrm{w}_3, \mathrm{w}_4$ and $\mathrm{w}_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b$ and $\frac{1}{12}$ such that $12 a+12 b-1=0$. Then the probabilities of occurrence of the outcome $w_3$ is

A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is

$$ \text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is } $$

Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm{f}(\mathrm{x})=\sin \mathrm{x}$ and $\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $g(x)=\cos x$, where $R$ is the set of real numbers

Consider the following statements:

Statement (I): $f$ and $g$ are one-one

Statement (II): $\mathrm{f}+\mathrm{g}$ is one-one

Which of the following is correct?

$$ \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)= $$

$2 \cos ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ is valid for all values of ' $x$ ' satisfying

Consider the following statements:

Statement (I): In a LPP, the objective function is always linear.

Statement (II): Ina LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

The maximum value of $\mathrm{z}=3 \mathrm{x}+4 \mathrm{y}$, subject to the constraints $\mathrm{x}+\mathrm{y} \leq 40, \mathrm{x}+2 \mathrm{y} \leq 60$ and $\mathrm{x}, \mathrm{y} \geq 0$ is

Consider the following statements.

Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prime}$ are also independent.

Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.

Which of the following is correct?

If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})$, then

Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. If she visits temple $A, \frac{1}{3}$ is the probability that she meets her friend, whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple B is

If $Z_1$ and $Z_2$ are two non-zero complex numbers, then which of the following is not true?

Consider the following statements :

Statement(I) : The set of all solutions of the linear inequalities $3 \mathrm{x}+8<17$ and $2 \mathrm{x}+8 \geq 12$ are $\mathrm{x}<3$ and $x \geq 2$ respectively.

Statement(II) : The common set of solutions of linear inequalities $3 x+8<17$ and $2 x+8 \geq 12$ is $(2,3)$ Which of the following is true?

$$ \text { The number of diagonals that can be drawn in an octagon is } $$

If the number of terms in the binomial expansion of $(2 \mathrm{x}+3)^{3 \mathrm{n}}$ is 22 , then the value of n is

If $4^{\text {th }}, 10^{\text {th }}$ and $16^{\text {th }}$ terms of a G.P. are $x, y$ and $z$ respectively, then

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

If $A$ and $B$ are two matrices such that $A B$ is an identity matrix and the order of matrix $B$ is $3 \times 4$, then the order of matrix $A$ is

If $A=\left[\begin{array}{ll}k & 2 \\ 2 & k\end{array}\right]$ and $\left|A^3\right|=125$, then the value of $k$ is

If $A$ is a square matrix satisfying the equation $A^2-5 A+7 I=0$, where $I$ is the $I$ dentity matrix and 0 is null matrix of same order, then $A^{-1}=$

The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

Consider the following statements :

Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$

Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the following is correct?

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

A line passes through $(-1,-3)$ and perpendicular to $x+6 y=5$. Its $x$ intercept is

The length of the latus rectum of $x^2+3 y^2=12$ is

If $y=\frac{\cos x}{1+\sin x}$, then

(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$

(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$

(c) $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$

(d) $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$

Match the following:

In the following, $[\mathrm{x}]$ denotes the greatest integer less than or equal to x .

The function $f(x)=\left\{\begin{array}{ll}e^x+a x & , x<0 \\ b(x-1)^2 & , x \geq 0\end{array}\right.$ is differentiable at $x=0$. Then

$$ \text { A function } f(x)=\left\{\begin{array}{cl} \frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right. $$

If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is

The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is

The function $f(x)=\tan x-x$

The value of $\int_{-1}^1 \sin ^5 \mathrm{x} \cos ^4 \mathrm{xdx}$ is

$$ \text { The value of } \int_0^{2 \pi} \sqrt{1+\sin \left(\frac{x}{2}\right)} d x \text { is } $$

$\int_0^1 \log \left(\frac{1}{x}-1\right) d x$ is

The area bounded by the curve $y=\sin \left(\frac{x}{3}\right)$, $x$ axis, the lines $x=0$ and $x=3 \pi$ is

A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the co-efficient of static friction between the block on the floor with the floor itself is

A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force $\mathrm{F}=20 \mathrm{~N}$ acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take $\mathrm{g} \simeq 10 \mathrm{~ms}^{-2}$ )

A body of mass 0.25 kg travels along a straight line from $x=0$ to $x=2 \mathrm{~m}$ with a speed $v=k x^{3 / 2}$ where $k$ $=2 \mathrm{SI}$ units. The work done by the net during this displacement is

During an elastic collision between two bodies, which of the following statements are correct?

I. The initial kinetic energy is equal to the final kinetic energy of the system.

II. The linear momentum is conserved.

III. The kinetic energy during $\Delta \mathrm{t}$ (the collision time) is not conserved.

Three particles of mass $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed at the vertices A, B and C respectively of an equilateral triangle ABC of side 1 m . The centre of mass of the system from vertex A (located at origin) is

Two fly wheels are connected by a non-slipping belt as shown in the figure. $I_1=4 \mathrm{~kg} \mathrm{~m}^2, r_1=20 \mathrm{~cm}$, $\mathrm{I}_2=20 \mathrm{~kg} \mathrm{~m}^2$ and $\mathrm{r}_2=30 \mathrm{~cm}$. A torque of 10 Nm is applied on the smaller wheel. Then match the entries of column I with appropriate entries of column II.

If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii, velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively, then

The total energy of a satellite in a circular orbit at a distance $(R+h)$ from the centre of the Earth varies as [ $R$ is the radius of the Earth and $h$ is the height of the oribit from Earth's surface]

Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of $1: 3$. If they are stretched by the same force, then increase in their lengths will be in the ratio of

A horizontal pipe carries water in a streamlined flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^{-2}$, the velocity of water is $1 \mathrm{~ms}^{-1}$ and the pressure is 2000 Pa . What is the pressure of water at another point where the cross-sectional area is $5 \mathrm{~cm}^2$ ?

[Density of water $=1000 \mathrm{kgm}^{-3}$ ]

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods, the temperature at the junction x is

A gas is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system along these two paths are $Q_1$ and $Q_2$ and $W_1$ and $W_2$ respectively. Then

At $27^{\circ} \mathrm{C}$ temperature, the mean kinetic energy of the atoms of an ideal gas is $\mathrm{E}_1$. If the temperature is increased to $327^{\circ} \mathrm{C}$, then the mean kinetic energy of the atoms will be

The variations of kinetic energy $K(x)$, potential energy $U(x)$ and total energy as a function of displacement of a particle in SHM is as shown in the figure. The value of $\left|x_0\right|$ is

The angle between the particle velocity and wave velocity in a transverse wave is [except when the particle passes through the mean position]

A metallic sphere of radius $R$ carrying a charge $q$ is kept at certain distance from another metallic sphere of radius $\mathrm{R} / 4$ carrying a charge Q . What is the electric flux at any point inside the metallic sphere of radius R due to the sphere of radius $\mathrm{R} / 4$ ?

You are given a dipole of charge $+q$ and $-q$ separated by a distance $2 R$. A sphere ' $A$ ' of radius ' $R$ ' passes through the centre of the dipole as shown below and another sphere ' $B$ ' of radius ' $2 R$ ' passes through the charge +q . Then the electric flux through the sphere A is

A potential at a point A is -3 V and that at another point B is 5 V . What is the work done in carrying a charge of 5 m C from B to A ?

Charges are uniformly spread on the surface of a conducting sphere. The electric field from the centre of sphere to a point outside the sphere varies with distance $r$ from the centre as

Match Column-I with Column - II related to an electric dipole of dipole moment $\vec{p}$ that is placed in a uniform electric field $\vec{E}$.

Which of the following statements is not true?

$$ \text { In the following circuit, the terminal voltage across the cell is } $$

Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2\left(E_2>E_1\right.$ and $\left.r_2>r_1\right)$ respectively, are connected in parallel as shown in figure. The equivalent emf of the combination is $\mathrm{E}_{\text {eq. }}$. Then

The variations of resistivity $\rho$ with absolute temperature T for three different materials $\mathrm{X}, \mathrm{Y}$ and Z are shown in the graph below. Identify the materials $\mathrm{X}, \mathrm{Y}$ and Z .

Given, a current carrying wire of non-uniform cross-section, which of the following is constant throughout the length of wire?

The graph between variation of resistance of a metal wire as a function of its diameter keeping other parameters like length and temperature constant is

Two thin long parallel wires separated by a distance ' $r$ ' from each other in vacuum carry a current of I ampere in opposite directions. Then, they will

A solenoid is 1 m long and 4 cm in diameter. It has five layers of windings of 1000 turns each and carries a current of 7A. The magnetic field at the centre of the solenoid is

Two similar galvanometers are covered into an ammeter and a milliammeter. The shunt resistance of ammeter as compared to the shunt resistance of milliammeter will be

Which of the following statements is true in respect of diamagnetic susbtances?

Which of the following graphs represents the variation of magnetic field $B$ with perpendicular distance ' $r$ ' from an infinitely long, straight conductor carrying current?

The anode voltage of a photocell is kept fixed. The frequency of the light falling on the cathode is gradually increased. Then the correct graph which shows the variation of photo current I with the frequency $v$ of incident light is

When a bar magnet is pushed towards the coil, along its axis, as shown in the figure, the galvanometer pointer deflects towards X . When this magnet is pulled away from the coil, the galvanometer pointer

A square loop of side 2 m lies in the Y-Z plane in a region having a magnetic field $\overrightarrow{\mathrm{B}}=(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \mathrm{T}$. The magnitude of magnetic flux through the square loop is

In domestic electric mains supply, the voltage and the current are

A sinusoidal voltage produced by an AC generator at any instant t is given by an equation $\mathrm{V}=311 \sin 314$ t. The rms value of voltage and frequency are respectively

A series LCR circuit containing an AC source of 100 V has an inductor and a capacitor of reactances $24 \Omega$ and $16 \Omega$ respectively. If a resistance of $6 \Omega$ is connected in series, then the potential difference across the series combination of inductor and capacitor only is

$$ \text { Match the following types of waves with their wavelength ranges } $$

A ray of light passes from vaccum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of two halves) is cut into two halves perpendicular to the principal axis as shown in figure. Choose the incorrect option for the reported lens pieces

The image formed by an objective lens of a compound microscope is

If $r$ and $r^1$ denotes the angles inside the prism having angle of prism $50^{\circ}$ considering that during interval of time from $t=0$ to $t=t, r$ varies with time as $r=10^{\circ}+t^2$. During the time $r^1$ will vary with time as

$$ \text { If } \mathrm{AB} \text { is incident plane wave front then refracted wave front in }\left(\mathrm{n}_2>\mathrm{n}_1\right) $$

The total energy carried by the light wave when it travels from a rarer to a non-reflecting and nonabsorbing medium

If the radius of first Bohr orbit is $r$, then the radius of the second Bohr orbit will be

$$ \text { Match the following types of nuclei with examples shown } $$

$$ \begin{array}{|l|l|} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { A. Isotopes } & \text { i. } \mathrm{Li}^7, \mathrm{Be}^7 \\ \hline \text { B. Isobars } & \text { ii. }{ }_8 \mathrm{O}^{18},{ }_9 \mathrm{~F}^{19} \\ \hline \text { C. Isotopes } & \text { iii. }{ }_1 \mathrm{H}^1,{ }_1 \mathrm{H}^2 \\ \hline \end{array} $$

Which of the following statements is incorrect with reference of 'Nuclear force'?

The range of electrical conductivity $(\sigma)$ and resistivity $(\rho)$ for metals, among the following, is

The circuit shown in figure contains two ideal diodes $D_1$ and $D_2$. If a cell of emf $3 V$ and negligible internal resistance is connected as shown, then the current through $70 \Omega$ resistance, (in ampere) is

In determining the refractive index of a glass slab using a travelling microscope, the following readings are tabulated

(a) Reading of travelling microscope for ink mark $=5.123 \mathrm{~cm}$

(b) Reading of travelling microscope for ink mark through glass slab $=6.123 \mathrm{~cm}$

(c) Reading of travelling microscope for chalk dust on glass slab $=8.123 \mathrm{~cm}$

From the data, the refractive index of a glass slab is

In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit.

He unplugged a resistance of $5200 \Omega$ in R . When $\mathrm{K}_1$ is closed and $\mathrm{K}_2$ is open, the deflection observed in the galvanometer is 26 div. When $K_2$ is also closed and a resistance of $90 \Omega$ is removed in S , the deflection between 13 div. The resistance of galvanometer is nearly

While determining the coefficient of viscosity of the given liquid, a spherical steel ball sinks by a distance $\mathrm{h}=0.9 \mathrm{~m}$. The radius of the ball $\mathrm{r}=\sqrt{3} \times 10^{-3} \mathrm{~m}$. The time taken by the ball to sink in three trails are tabulated as follows.

$$ \begin{array}{|l|l|} \hline \text { Trial No. } & \text { Time taken by the ball to fall by } \mathrm{h} \text { (in second) } \\ \hline 1 . & 2.75 \\ \hline 2 . & 2.65 \\ \hline 3 . & 2.70 \\ \hline \end{array} $$

The difference between the densities of the steel ball and the liquid is $7000 \mathrm{~kg} \mathrm{~m}^{-3}$. If $\mathrm{g}=10 \mathrm{~ms}^{-2}$, then the coefficient of viscosity of the given liquid at room temperature is

A particle is in uniform circular motion. The equation of its trajectory is given by $(x-2)^2+y^2=25$, where x and y are in meter. The speed of the particle is $2 \mathrm{~ms}^{-1}$, when the particle attains the lowest ' y ' co-ordinate, the acceleration of the particle is (in $\mathrm{ms}^{-2}$ )