Match List-I with List-II and select the correct option (Based on mole concept):

List-I		List-II
(a)	$2$ moles of ethene	(i)	$11.2$ L volume at STP
(b)	Mass is equal to $66$ g	(ii)	$56$ g
(c)	$1$ g of $\text{H}_2$	(iii)	$12.04 \times 10^{23}$ Molecules
(d)	$2$ moles of water vapours	(iv)	$1.5$ mole of $\text{CO}_2$

From the given information, select the suitable law of chemical combination:

Cupric Carbonate	% of Cu	% of C	% of O
Natural Sample	51.35	9.74	38.91
Synthetic Sample	51.35	9.74	38.91

Which of the following is the CORRECT statement about $\Psi^2$?

Which of the following represents de Broglie equation?

Match List-I with List-II:

List-I (Element-Atomic number)		List-II (Position in periodic table)
(a)	Ra – 88	(i)	$4^{th}$ period, $13^{th}$ group
(b)	Ga – 31	(ii)	$6^{th}$ period, $6^{th}$ group
(c)	W – 74	(iii)	$5^{th}$ period, $10^{th}$ group
(d)	Pd – 46	(iv)	$7^{th}$ period, $2^{nd}$ group

Choose the correct answer from the options given below.

With respect to resonance structures of $\text{CO}_3^{2-}$ ion, which of the following statements are correct?
(a) All $\text{C}-\text{O}$ bonds in $\text{CO}_3^{2-}$ are equivalent
(b) There are three resonance structures possible for $\text{CO}_3^{2-}$ ion
(c) The position of carbon and oxygen should change in every resonance structure
(d) The formal charge on carbon atom is $-2$

In which of the following option/options, the order of arrangement does not agree with the variation of property indicated against it?
(a) $\text{BF}_3 > \text{NF}_3 > \text{NH}_3$ (Dipole moment)
(b) $\text{HgCl}_2 > \text{NH}_4^+ > \text{SF}_6$ (Bond angle)
(c) $\text{NH}_3 < \text{H}_2\text{O} < \text{HF}$ (Strength of intermolecular hydrogen bonding)
(d) $\text{H}-\text{I} > \text{H}-\text{Br} > \text{H}-\text{Cl}$ (Bond length)

The types of hybrid orbitals of nitrogen in $\text{NO}_2^+, \text{NO}_3^-$ and $\text{NH}_4^+$ respectively are

A gas can be taken from A to B via two different paths ACB and ADB.

When path ACB is used, $60$ J of heat flows into the system and $30$ J of work is done by the system. If path ADB is used, work done by the system is $10$ J.
The heat flow into the system in path ADB is

Which of the following is a correct statement for a thermodynamic system?

A: Entropy of a perfect crystalline solid at absolute zero approaches zero.
B: For spontaneity of a reaction, $T\Delta S > \Delta H$.
Among the two statements given above, identify the correct answer from the options given below.

For the following gaseous reversible reaction:
$3\text{A}_{(g)} + \text{B}_{(g)} \rightleftharpoons \text{A}_3\text{B}_{(g)} \quad (\Delta_r H = -q\text{ kJ})$. The amount of product $\text{A}_3\text{B}_{(g)}$ is affected by ____

For the reversible reaction,
$\text{N}_{2(g)} + 3\text{H}_{2(g)} \rightleftharpoons 2\text{NH}_{3(g)}$
When the partial pressure is measured in atmosphere, the value of $K_p$ at $500^\circ\text{C}$ is $1.44 \times 10^{-5}$. The value of $K_c$ when the concentration is expressed in mol L$^{-1}$ is:

A $0.15$ mole of pyridinium chloride has been added to $500\text{ cm}^3$ of $0.2$ M pyridine solution (a base). Assuming there is no change in volume upon mixing(Given: $pK_b$ of pyridine = 8.82), the pH of the resulting solution is

$a\text{C}_2\text{O}_4^{2-} + b\text{MnO}_4^- + c\text{H}^+ \rightarrow x\text{Mn}^{2+} + y\text{H}_2\text{O} + z\text{CO}_2$
$a$ and $x$ respectively are

Given below are two statements.
Statement-I: In $\text{H}_2\text{O}_2$, each oxygen atom is assigned an oxidation number of $-1$, in $\text{RbO}_2$ each oxygen atom is assigned an oxidation number of $-\dfrac{1}{2}$.
Statement-II: Representation of $\text{HAuCl}_4$ and $\text{MnO}_2$ in stock notation is $\text{HAu(III)Cl}_4$ and $\text{Mn(II)O}_2$, respectively.
Examine the above statements and choose the correct answer.

Statement I: Staggered conformation of ethane is more stable than the eclipsed conformation.
Statement II: The torsional strain in staggered conformation is more.
Read the above statements and choose the correct answer from the options given below.

Carboxylic acids are more acidic than phenols because

The correct IUPAC name of is

$\text{C}-\text{Cl}$ bond in methyl chloride compared to $\text{C}-\text{Cl}$ bond in chlorobenzene is

The compound with molecular formula $\text{C}_{20}\text{H}_{42}$ is

The number of chain isomers possible for the hydrocarbon with molecular formula $\text{C}_5\text{H}_{12}$ is

Statement-I: Nitrogen in pyridine cannot be estimated by Kjeldahl's method.
Statement-II: Nitrogen in pyridine changes to ammonium sulphate when heated with conc. $\text{H}_2\text{SO}_4$ in Kjeldahl's method.
Read the above given statements and choose the correct answer from the given options.

The intermediates in heteropolar reactions are

The relative lowering of vapour pressure produced by dissolving $18$ g of urea (Molar mass $= 60\text{ g mol}^{-1}$) in $100$ g of water is

When $0.0106$ mole of acetic acid was dissolved in $1$ kg of water, the freezing point depression for this strength of acid was $0.0205$ K. If the calculated freezing point depression is $0.0197$ K, Van't Hoff factor (i) and degree of dissociation of acetic acid respectively are

Match List-I (Laws) with the List-II (Mathematical expressions):

List-I		List-II
(a)	Henry's law	(i)	$p_1 = p_1^0 x_1$
(b)	Raoult's law	(ii)	$p = K_H \chi$
(c)	First law of thermodynamics	(iii)	$\Lambda_m = v_+ \lambda_+ + v_- \lambda_-$
(d)	Kohlrausch's law	(iv)	$\Delta U = q + w$

Codes:

Which of the following is CORRECT with respect to the property mentioned against it?

The conductivity of centimolar solution of KCl at $298$ K is $0.021\text{ Ohm}^{-1}\text{cm}^{-1}$ and the resistance of the cell containing the solution at $298$ K is $60\,\Omega$. The value of cell constant ($G^*$) is __________.

Given below are the half-cell reactions:
$\text{Mn}^{2+} + 2e^- \rightarrow \text{Mn} \quad (E^0 = -1.18\text{ V})$
$2(\text{Mn}^{3+} + e^- \rightarrow \text{Mn}^{2+}) \quad (E^0 = +1.51\text{ V})$
The $E^0_{cell}$ for $3\text{Mn}^{2+} \rightarrow \text{Mn} + 2\text{Mn}^{3+}$ will be _____________.

$\Lambda^0_{m(\text{NH}_4\text{OH})}$ is equal to ____

During the electrolysis of acidified water, $16$ g of $\text{O}_2$ gas is formed at anode. The volume of $\text{H}_2$ gas liberated at cathode under STP conditions is

The activation energy for the reaction $X \rightarrow Y$ is $150\text{ kJ mol}^{-1}$. The change in enthalpy for the above reaction is $-135\text{ kJ mol}^{-1}$. Then the activation energy for $Y \rightarrow X$ is

For a 1st order change $R \rightarrow P$, the concentration of Reactant R changes from $0.1$ M to $0.025$ M in $40$ minutes. The rate of reaction when the concentration of R is $0.01$ M is ____

For a reaction having three steps, the overall rate constant is $k = \dfrac{k_1 k_2}{k_3}$. The values of $E_{a_1}, E_{a_2}$ and $E_{a_3}$ (activation energies stepwise) are $40$, $50$ and $60$ kJ mol$^{-1}$ respectively. Then the overall $E_a$ (activation energy) of the reaction is ____

Which one of the following graph is not applicable for a 1st order reaction ($R \rightarrow P$)?

The calculated spin only magnetic moment of $\text{Cr}^{2+}$ ion is

The highest oxidation state of manganese in fluoride is $+4$ ($\text{MnF}_4$), but the highest oxidation state in oxides is $+7$ ($\text{Mn}_2\text{O}_7$), because

Which of the following will not act as an oxidising agent?

Match List-I with List-II

List-I (Complex)		List-II (Geometry)
(a)	$[\text{Co(NH}_3\text{)}_6]^{3+}$	(i)	Trigonal bipyramidal
(b)	$[\text{NiCl}_4]^{2-}$	(ii)	Octahedral
(c)	$[\text{Ni(CN)}_4]^{2-}$	(iii)	Tetrahedral
(d)	$[\text{Fe(CO)}_5]$	(iv)	Square planar

Choose the correct answer from the options given below.

Given below are two statements:
Statement-I: The $\text{M}-\text{C}$ $\sigma$ bond is formed by the donation of lone pair of electrons on the carbonyl carbon into a vacant d-orbital of the metal.
Statement-II: The $\text{M}-\text{C}$ $\pi$ bond is formed by the donation of a pair of electrons from a filled d-orbital of metal into the vacant antibonding $\pi^*$ orbital of carbon monoxide.
In the light of the above statements, choose the correct answer from the options given below:

How many ions per molecule are produced from the complex $[\text{Co(NH}_3\text{)}_6]\text{Cl}_2$ in solution?

Which of the following is the most stable complex ion?

In $\text{S}_\text{N}1$ reaction, the alkyl halide that on hydrolysis produces racemic mixture is

The compound from which chlorobenzene cannot be prepared easily is

Organic compound 'D' is

Glycerol is a trihydric alcohol. It contains ____.

$R-\text{CH}_2\text{OH}$ is converted into $R-\text{CHO}$ by reacting with ________.

Match List-I with List-II and select the correct options

List-I (Functional group)		List-II (Functional group reagent)
(a)		(i)	Neutral ferric chloride test
(b)	$\text{C}_6\text{H}_5\text{NH}_2$	(ii)	Azo dye test
(c)	$\text{CH}_3\text{CH}_2\text{CHO}$	(iii)	Ceric ammonium nitrate test
(d)		(iv)	Tollen's reagent test

The compound that does not answer iodoform test is

The major product '$A$' in the given reaction is
Benzaldehyde $\xrightarrow{\large{\text{Acetophenone, OH}^-/293\text{K}}}$ '$A$' (Major product)

Match the reagents in List-I with products obtained from their carbonyl compounds in List-II.

List-I		List-II
(a)	$\text{NH}_2\text{OH}$	(i)	Cyanohydrin
(b)	$R-\text{NH}_2$	(ii)	Oxime
(c)	$R-\text{OH}$	(iii)	Schiff base
(d)	$H-C \equiv N$	(iv)	Acetal

$\text{C}_3\text{H}_6 \xrightarrow{\large{(i)\text{ BH}_3;\ (ii)\text{ H}_2\text{O}_2/\text{NaOH}}} P \xrightarrow{\large{\text{CrO}_3,\text{ anhydrous medium}}} Q \xrightarrow{\large{(i)\text{ CH}_3\text{MgBr};\ (ii)\text{ H}_2\text{O}}} R + \text{Mg(OH)Br}$
The organic compounds $P, Q$ and $R$ are

Basic strength of alkylamines in aqueous phase is not decided by ________.

Nitration of aniline in strong acidic medium gives significant amount of m-nitroaniline because

Incorrect statement about $\alpha$-amino acids of proteins among the following is

Consider the following statements:
Statement-I: All monosaccharides are reducing sugars.
Statement-II: Sucrose can reduce ammoniacal silver nitrate solution.
Choose the correct answer from the options given below.

Match List-I with List-II

List-I (Vitamins)		List-II (Deficiency Diseases)
(a)	$\text{B}_1$	(i)	Convulsions
(b)	$\text{B}_2$	(ii)	RBC deficiency in haemoglobin
(c)	$\text{B}_6$	(iii)	Retarded growth
(d)	$\text{B}_{12}$	(iv)	Burning sensation of the skin

Choose the correct answer from the options given below.

Match the compounds of List-I with their effects in List-II:

List-I		List-II
(a)	Chloramphenicol	(i)	Malaria
(b)	Thyroxine	(ii)	Anaesthetic
(c)	Chloroquine	(iii)	Goiter
(d)	Chloroform	(iv)	Typhoid fever

When salt BA is treated with Conc. $\text{H}_2\text{SO}_4$ reddish brown gas is liberated. The aqueous solution of BA gives pale yellow precipitate with $\text{AgNO}_3$ solution. Which of the following anion ($\text{A}^-$) is present in the salt BA?

The solution of $3(x - 1) \leq 2(x - 3)$ is

If $\alpha$ and $\beta$ are acute angles such that $\alpha - \beta$ and $\alpha + \beta$ satisfy the equation $\tan^2\theta - 4\tan\theta + 1 = 0$, then $\alpha$ and $\beta$ are respectively,

$\sum\limits_{n=1}^{4} (-1)^{2n} \cdot i^{2n} = $

How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with $5$?

$10$ distinct points are taken on a circle. Then using these points
Statement I: The number of triangles that can be formed is $100$
Statement II: The number of chords that can be formed is $45$
Which of the following is correct?

If we insert two numbers between $\sqrt{2}$ and $4$ so that the resulting sequence is in G.P, then the inserted numbers in the order are

The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is

The value at $x = 2$ for $\dfrac{x^3 + 3x^2 + 3x + 1}{x^4 + 4x^3 + 6x^2 +4x + 1}$

The maximum value of $\sin\left(x + \dfrac{\pi}{6}\right) + \cos\left(x + \dfrac{\pi}{6}\right)$ is attained at $x = $

The line $L_2$ passing through $(3, -1)$ divides the line segment $L_1$ joining the points $(-1, 2)$ and $(3, 6)$ in the ratio $1 : 3$ internally. The equation of line $L_2$ is:

The area of the triangle with vertices $(3, 8), (-4, 2)$ and $(5, 1)$ is $\dfrac{P}{4}$, then the value of $P$ is

In the figure

Statement-I: When $\alpha > \beta \geq 0$, the section is hyperbola
Statement-II: When $\beta > 90^\circ$, the section is ellipse
Which of the following is correct?

If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \geq 2 \\ x + 1 & \text{if } x < 2 \end{cases}$, then $\lim\limits_{x \to 1} f(x) + \lim\limits_{x \to 2} f(x) = $

If $\lim\limits_{x \to 3}\left(\dfrac{x^2 - ax - 3b}{x - 3}\right) = 5$, then $a + b = $

The mean and standard deviation of $100$ items are $50$ and $4$, respectively then the sum of all squares of the items is

Let R be the relation in the set $\mathbb{N}$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is the correct answer?

If $n(A) = 2$ and the number of relations from set A to set B is $1024$, then $n(B)$ is

If $A = \{1, 2, 3, 4, \ldots, 10\}$, then the number of non-empty subsets of A containing only even number is

If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is

If A and B are invertible matrices of same order, then which of the following is not correct?

Let X be a matrix of order $2 \times n$ and Z be a matrix of order $2 \times p$. If $n = p$, then the order of the matrix $8X - 9Z$ is:

A row matrix has only

Consider the following statements:
Statement I: If A is a non-singular matrix, then $A^{-1}$ exists.
Statement II: If A and B are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.

Match List-I with List-II

List-I		List-II
a)	A matrix which is not a square matrix	i)	Symmetric matrix
b)	A square matrix $A = A'$	ii)	Null matrix
c)	The diagonal elements of a diagonal matrix are same	iii)	Rectangular matrix
d)	A matrix which is both symmetric and skew symmetric	iv)	Scalar matrix

The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has

If A and B are invertible square matrices of order n, then which of the following is not correct?

Which of the following is correct?

The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is

$\tan^{-1}\left(\dfrac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\dfrac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\left(\dfrac{1}{1 + n(n+1)}\right) = $

If $\sin^{-1} x + \sin^{-1} y = \dfrac{\pi}{2}$, then $x^2$ is equal to

$f(x) = (x-1)^2$ for $x \geq 1$, $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is

The domain of the function $\sqrt{\dfrac{x-7}{9-x}}$ is

If $f(x) = \begin{cases} ax + 7 & \text{if } x < 1 \\ 3x - 1 & \text{if } x = 1 \\ \dfrac{b}{x + 3} & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then

If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $

If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $

A YouTube short video is getting viral according to $f(t) = -2t^3 + 3t^2 + 5$. At what time does the video get maximum number of shares? ($t$ is in hours)

In a Mahakumbh, a drone camera is moving along $3y = x^3 - 3$. When $y$-coordinate changes $9$ times as fast as $x$-coordinate, it captures good quality pictures. Then one of the precise positions of the drone at that instant is

$\int e^{-x \log 2} \cdot 2^x\,dx = $

If '$n$' is a natural number, then $\int \dfrac{\sin^n x}{\cos^{n+2} x}\,dx = $

$\int\limits_{a-6}^{b-6} f(x + 6)\,dx$ is equal to

One of the possible functions $f(x)$ which satisfies $\int\limits_{-2}^{2} f(x)\,dx = 0$ is

The area enclosed by the curve $x = \sqrt{3}\cos\theta, y = \sqrt{3}\sin\theta$ is

The area of the region bounded by the curve $y^2 = x^3$, the $y$-axis and the lines $y = 1$ and $y = 8$ is

Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime}\right)^2=\sqrt{y^{\prime \prime}-3}$ is

$\int xf(x)\,dx + \dfrac{f(x)}{2} = 0$, then $f(x)$ is equal to

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $

Integrating factor of the differential equation $(1 + x^2)\dfrac{dy}{dx} + xy = 1$ is

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to

The three points $A(2, 4, 3), B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of "a" is

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = \dfrac{y - 2}{1} = \dfrac{z - 3}{1}$ is

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is

The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$. Let $z = px + qy$ where $p, q > 0$. The relation between $p$ and $q$, so that the maximum $z$ occurs at both points $(15, 15)$ and $(0, 20)$ is

Recent studies suggest that $12\%$ of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:
A: Both parents are left handed, chances of having left handed children $= 24\%$
B: Both parents are right handed, chances of having left handed children $= 9\%$
C: Father left handed and mother right handed, chances of having left handed children $= 17\%$
D: Father right handed and mother left handed, chances of having left handed children $= 22\%$
Given $P(A) = P(B) = P(C) = P(D) = 1/4$ and L denotes child is left handed. What is the probability that $P(A \mid L)$?

The probability that a man and his wife live after $20$ years are $\dfrac{1}{4}$ and $\dfrac{1}{3}$ respectively. The probability that neither the man nor his wife live after $20$ years is

Probability of obtaining an even prime number on each die when a pair of dice is rolled is

Probability of occurrence of an event A is $\dfrac{1}{2}$ and that of B is $\dfrac{3}{10}$. If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Probability of at least one of the events A and B occur is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A}) + P(\bar{B})$ is

Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and electric current (A) given in List-II.

List-I	List-II
(a) Torque	(i) $[M^{-1}L^{-2}T^{4}A^{2}]$
(b) Gravitational constant	(ii) $[M^{1}L^{2}T^{-1}]$
(c) Capacitance	(iii) $[M^{-1}L^{3}T^{-2}]$
(d) Planck's constant	(iv) $[M^{1}L^{2}T^{-2}]$

Codes:

The velocity of a particle moving along $x$-axis is given as $V = x^2 - 5x + 4$ (in m/s) where $x$ denotes the $x$-coordinate of the particle in metres. The magnitude of the acceleration of the particle when the velocity of the particle zero is

A car covers the first half of the distance between two places at $40$ km/h and another half at $50$ km/h. The average speed of the car is

Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at $45^\circ$ to the horizontal, then the ratio of maximum heights attained is

A horizontal force of $5$ N is applied on a stationary body of mass $5$ kg, which is initially at rest on a frictionless table. The change in kinetic energy of the body in $10$ s is

A mass M is hung with a light inextensible string as shown in figure. Find the tension of the horizontal string.

A man weighs $80$ kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $6 \text{ m/s}^2$. What would be his weight in kg? ($g = 10 \text{ m/s}^2$)

Two bodies with kinetic energies in the ratio of $3:1$ are moving with equal linear momentum. The ratio of their masses is

If the earth were to suddenly contract to half of its present radius, what would be the duration of the day?

The angular momentum of a moving body remains constant, if

Suppose the acceleration due to gravity at the earth's surface is $g \text{ m/s}^2$ and at the surface of moon it is $g' \text{ m/s}^2$. An M kg passenger goes from the earth to the moon in a spaceship moving with a constant velocity (Neglect all other objects in the sky). Which curve best represents the weight (net gravitational force) as a function of time?

Imagine a new planet having the same density as that of the earth, but it is two times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is $g$ and that on the surface of the new planet is $g'$, then

There are two wires of same material and same length while the diameter of second wire is two times the diameter of the first wire. Then the ratio of extensions produced in the wires by applying same load will be

A 30 cm long capillary tube is dipped in water, water rises upto a height of $10$ cm due to capillarity. If this experiment is conducted in a freely falling water in an elevator, then the length of the water column becomes

Instrument fitted in the carburetor of the automobile to provide the correct mixture of air and fuel necessary for combustion works on

Following are statements of a few processes taking place in nature.
I. Free expansion of a gas
II. The combustion of a mixture of petrol and air ignited by a spark
III. The leaking of gas from the kitchen cylinder.
IV. The transfer of heat from one heated part of a liquid to the other colder part.
Which amongst these processes are irreversible in nature?

In thermodynamic processes, which of the following statements is not true?

The graph of pressure P and volume V of $1$ mole of an ideal gas at constant temperature is

A mass of $1$ kg is executing SHM. Its displacement is given by $x = 6.0\cos(100t + \pi/4)$ cm. What is the maximum kinetic energy?

A source of frequency $\nu$ gives $6$ beats/second when sounded with a source of frequency $200$ Hz. The second Harmonic of frequency $2\nu$ of the source gives $8$ beats/second when sounded with a source of frequency $420$ Hz. The value of $\nu$ is

A $200$ J of work is done in moving a charge $5$ C from a point A where the potential is $-20$ V to another point B where potential is V volt. The value of V at B is

An electric dipole of dipole moment $\vec{P}$ is placed in the uniform electric field $\vec{E}$. Then which of the following statements are correct?
Statement-I: The torque on the dipole is $\vec{P} \times \vec{E}$
Statement-II: The potential energy of the dipole is $-\vec{P} \cdot \vec{E}$
Statement-III: The net force on the dipole is non-zero.

Consider three point charges $-2Q, Q$ and $-Q$ and three surfaces $S_1, S_2$ and $S_3$ as shown in the figure. Match the entries of List-I with that of List-II.

List-I	List-II
(a) Net flux through $S_1$	(i) $\dfrac{-2Q}{\varepsilon_0}$
(b) Net flux through $S_2$	(ii) $\dfrac{-Q}{\varepsilon_0}$
(c) Net flux through $S_3$	(iii) Zero

What will be the total electric flux through the faces of the cube as given in the figure with side of length '$a$' if a charge Q is placed at B midpoint of an edge of the cube (see figure)?

An electron falls through a distance $1.5$ cm in $2.0 \times 10^4$ N/C from rest. The time taken to cover this distance in second is ____
$(e = 1.6 \times 10^{-19}\text{ C}, m_e = 9.11 \times 10^{-31}\text{ kg})$

A point charge is placed in a moving train. A passenger A sitting in the train and person B on the ground observe the fields due to this charge. Then

In the circuit shown in the figure, the potential difference across the $4 \mu\text{F}$ capacitor is

A parallel plate capacitor has a uniform electric field '$E$' in the space between the plates. If the distance between the plates is '$d$' and area of each plate is '$A$', the energy stored in the capacitor is

In the figure, the values of currents $I_1, I_2$ and $I_3$ respectively are

Which of the following circuits is correct for verification of Ohm's law?

In a conducting region, $10^{19}$ electrons and $10^{19}$ protons move to the left, while $10^{19}$ $\alpha$-particles move to the right per second. The resulting electric current is $(e = 1.6 \times 10^{-19}\text{ C})$ _________

Current flowing through a wire decreases linearly from $10$ A to zero in $4$ s as shown in the graph. Find the total charge flowing through the wire in the given time interval.

Given below are two statements:
Statement-I: The resistivity of a conductor is independent of its temperature.
Statement-II: The resistivity of a semiconductor decreases with increase in temperature.
Select the correct option.

The number of electrons moving per second through the filament of a lamp of $60$ W operating at $120$ V is nearly $(e = 1.6 \times 10^{-19}\text{ C})$ _____________.

Pick out the WRONG statements about magnetic substances.
($\chi$ = magnetic susceptibility)
($\mu_r$ = relative permeability).
I. Substances with $-1 \leq \chi < 0$ are diamagnetic.
II. Substances with $\chi \gg 1$ are paramagnetic.
III. Substances with $\chi \ll 1$ are ferromagnetic.
IV. Substances with $\mu_r \gg 1$ are ferromagnetic.

If a paramagnetic bar is brought near a bar magnet, then it is

Two identical circular current loops carrying equal currents are placed with their axes inclined at $45^\circ$ to each other as shown in the figure. The resultant magnetic field at P is

Biot-Savart law indicates that an electron moving with a velocity $\vec{V}$ produces a magnetic field $\vec{B}$ around it such that

A proton, an electron and an $\alpha$-particle enter at right angles to a uniform magnetic field with the same velocity. If $R_p, R_e$ and $R_\alpha$ are the radii of circular paths of these particles, then

In the figure shown, the conductor PQ of length $l$ is moved from $x = 0$ to $x = b$ and then up to $x = 2b$ with a constant velocity $\vec{v}$. A uniform magnetic field $\vec{B}$ is perpendicular to the plane of the paper and extends from $x = 0$ to $x = b$ and it is zero from $x > b$. The magnitude of emf Induced in the conductor is

In Faraday-Henry's experiment, a coil is connected to a galvanometer. For the deflection of pointer in the galvanometer, which of the following statement/s is/are WRONG?
The pointer in the galvanometer deflects -
(a) When the bar magnet is moved towards the stationary coil along its axis.
(b) When the bar magnet is moved away from the stationary coil along its axis.
(c) When the coil is moved towards the stationary bar magnet along its axis.
(d) When the coil and the magnet are moved without relative motion between them.

A small town with a demand of $900\text{ kW}$ of electric power at $220\text{ V}$ is situated $20\text{ km}$ away from an electric power generating station. Each wire of the two-wire transmission line has a resistance per unit length of $5 \times 10^{-4} \, \Omega\text{ m}^{-1}$. The town gets power from the line through a $45000\text{ V}$ to $220\text{ V}$ step-down transformer at a substation in the town. The line power loss in the form of heat is:

A light bulb rated $100$ W is connected to an AC source of $220$ V, $50$ Hz. The rms current through the bulb is

In a circuit containing a pure resistor connected to an AC source,

What range of electromagnetic spectrum is considered as light?

Match the following Maxwell's equations:
(The symbols used here have their usual meanings)

List-I		List-II
(a)	Gauss' law for electrostatics	(i)	$\oint \vec{E} \cdot d\vec{A} = \dfrac{Q}{\varepsilon_0}$
(b)	Gauss' law for magnetism	(ii)	$\oint \vec{B} \cdot d\vec{l} = \mu_0 \left[i_c + \varepsilon_0 \dfrac{d\phi_E}{dt}\right]$
(c)	Faraday's law	(iii)	$\oint \vec{B} \cdot d\vec{A} = 0$
(d)	Ampere-Maxwell's law	(iv)	$\oint \vec{E} \cdot d\vec{l} = -\dfrac{d\phi_B}{dt}$

From the graph of angle of deviation versus angle of incidence for an equilateral prism, the refractive index of material of prism is

The critical angle for a monochromatic light going from medium A to medium B is $\theta$. If the speed of light in medium A is $V$, then the speed of light in medium B is

The incorrect statement about refractive index for a pair of media is

The direction of a ray of light incident on a concave mirror is shown by PQ, while direction in which the ray would travel after reflection is shown by four rays marked as A, B, C and D as shown in the figure. Which of the four rays correctly shows the direction of the reflected ray?

With reference to the figure shown below, match the following:

List-I		List-II
(a)	Angle of reflection	(i)	$60^\circ$
(b)	Value of $\alpha$	(ii)	$120^\circ$
(c)	Angle of deviation	(iii)	$30^\circ$

In Young's double slit experiment, how many maxima can be seen on a screen (including central maxima) if $d = \dfrac{5\lambda}{2}$ (where $\lambda$ is wavelength of light and $d$ is distance between the two slits).

Variation of photoelectric current with anode potential is shown below. Choose the correct option ($V_0$ = stopping potential)

Work function of the metal is

An electron transition takes place from excited state to ground state in hydrogen atom, then

Bohr's second postulate implies quantisation of

The radius of first orbit in hydrogen atom is $5.3 \times 10^{-11}$ m. The kinetic energy $E_K$, potential energy $E_P$ and total energy $E_T$ of electron in first orbit are

A wafer of pure germanium crystal has two parts X and Y. The end X is obtained by doping with arsenic and Y with indium. It is connected to a battery as shown in the figure. Which of the following statements is correct?

In which of the following figures, diode is reverse biased?

An n-type and p-type semiconductor can be obtained by respectively doping pure silicon with