VITEEE 2024

Two different ideal diatomic gases $A$ and $B$ are initially in the same state. $A$ and $B$ are then expanded to same final volume through adiabatic and isothermal process, respectively. If $p_A, p_B$ and $T_A, T_B$ represent the final pressures and temperatures at $A$ and $B$ respectively, then

A cyclic process for 1 mole of an ideal is shown in the $V-T$ diagram. The work done in $A B, B C$ and $C A$ respectively is

A short bar magnet of magnetic moment of $0.15 \mathrm{~J} / \mathrm{T}$ is placed in a uniform magnetic field of 0.4 T . The potential energy of the magnet in unstable equilibrium is

Eight dipoles of charges of magnitude $e$ each are placed inside a cube. The total electric flux coming out of the cube will be

The primary of a transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 1000 V is 12 kW . The resistance of the primary is $0.2 \Omega$ and that of the secondary is $2 \Omega$. If the efficiency of the transformer is $80 \%$, then the power loss in the primary is

A metal surface is illuminated with photons of energies $E_1=4 \mathrm{eV}$ and $E_2=2.5 \mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons in two cases is 2 . Work function of metal surface will be

36 cells each of internal resistance $0.5 \Omega$ and emf 1.5 V each are used to send current through an external circuit of $2 \Omega$ resistor. For getting maximum current, $n$ cells are combined in series in each row. If total number of such rows are $m$, then the value of $(n / m)$ will be

Which of the following has maximum dipole moment?

Difference between the maximum and minimum values of $f(x)=-\sin ^3 x+3 \sin ^2 x+5$ in $x \in\left[0, \frac{\pi}{2}\right]$ is

Among the following, the molecules /ions having same bond order are

The activation energy for a reaction is $9.0 \mathrm{~K} \mathrm{cal} \mathrm{mol}^{-1}$. The increase in the rate constant when its temperature is increased from 298 K to 308 K is

Using the Gibbs free energy change, $\Delta G^{\circ}=+63.3 \mathrm{~kJ}$. For the reaction,

$$\mathrm{Ag}_2 \mathrm{CO}_3 \longrightarrow 2 \mathrm{Ag}^{+}(a q)+\mathrm{CO}_3^{2-}(a q)$$

The $K_{\text {sp }}$ of $\mathrm{Ag}_2 \mathrm{CO}_3(s)$ in water at $25^{\circ} \mathrm{C}$ is

$A(g) \longrightarrow B(g)$ is a first order reaction. The initial concentration of $A$ is $0.2 \mathrm{~mol} \mathrm{~L}^{-1}$. After 10 minutes the concentration of $B$ is found to be $0.18 \mathrm{~mol} \mathrm{~L}^{-1}$. The rate constant (in $\min ^{-1}$ ) for the reaction is

The horizontal range of a projectile is $4 \sqrt{3}$ times of its maximum height. The angle of projection will be

The distance of the centres of Moon and the Earth is $D$. The mass of the Earth is 81 times the mass of the Moon. At what distance from the centre of the Earth, the gravitational force on a particle will be zero?

A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. If the mass of each marble is 5 g . What will be velocity with which the marble are striking the disc? Assume that, the marble strikes the disc normally and rebound downwards with the same speed.

Imagine a system of unit in which the unit of mass is 10 kg , length is 1 km and time is 1 min. Then, 1 J in this system is equal to

The resultant of $\mathbf{A}$ and $\mathbf{B}$ is $\mathbf{R}_1$. On reversing the vector $\mathbf{B}$, the resultant becomes $\mathbf{R}_2$. What is the value of $R_1^2+R_2^2$ ?

Moment of a force of magnitude 10 N acting along positive $y$-direction at point $(2 \mathrm{~m}, 0,0)$ about the point $(0,1 \mathrm{~m}, 0)$ in $\mathrm{N}-\mathrm{m}$ is

If gravitational attraction between two points masses be given by $F=G \frac{m_1 m_2}{r^n}$, then the period of a satellite in a circular orbit will be proportional to

The potential energy of a particle of mass 0.1 kg moving along the $X$-axis, is given by $U=5 x(x-4) \mathrm{J}$, where $x$ is in metres. Choose the wrong option.

Variation of internal energy with density of one mole of monoatomic gas is depicted in the below figure, corresponding variation of pressure with volume can be depicted as (assuming the curve is rectangular hyperbola)

In the equation for a stationary wave given by $y=5 \cos \frac{\pi x}{25} \sin 100 \pi t$. Here, $x$ is in cm and $t$ in second. A node will not occur at distance $x$ is equal to

A light ray of wavelength 546 nm is incident on an air-glass interface. If the speed of light in air is $3 \times 10^8 \mathrm{~m} / \mathrm{s}$. Then, wavelength of light ray in glass will be

[Take, refractive index of glass, $\mu=1.5$ ]

In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of 5.0 cm . This pressure is transmitted to a second piston of radius 15.0 cm . If the mass of the car to be lifted is 1350 kg . The force on a small piston is

A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3 A . A thin coil having 10 , turns of wire and of radius 0.01 m carries a current of 0.4 A . The torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of solenoid.

Which of the following graphs represents the correct variation of inductive reactance $X_L$ with angular frequency $\omega$ ?

A current carrying conductor experiences maximum force in magnetic field when the angle between current element and direction of magnetic field is

In an electric circuit, a capacitor of reactance $55 \Omega$ is connected across the source of 220 V . The value of displacement current is

A transformer has 200 windings in the primary and 400 windings in the secondary. The primary is connected to an AC supply of 110 V and a current of 10 A flows in it. The voltage across the secondary and the current in it, respectively, are

Which of the following graph represents the variation of magnetic flux density $B$ with distance $r$ for a straight long wire carrying an electric current?

The magnetic field in a electromagnetic wave is given by

$$B_y=2 \times 10^{-7} \sin \left(0.5+10^3 x+1.5 \times 10^{11} t\right) \mathrm{T}$$

The frequency of the wave is (in GHz)

A germanium crystal is doped with arsenic atoms and indium atoms simultaneously. Number of arsenic atoms used $=5 \times 10^{22}$ per $\mathrm{m}^3$ and number of indium atoms used $=5 \times 10^{20}$ per $\mathrm{m}^3$, then resulting crystal is a/an

An electromagnetic wave with poynting vector $6 \mathrm{Wm}^{-2}$ is absorbed by a surface area $12 \mathrm{~m}^2$. The force on the surface is

The output of the given arrangement of logic gates for $A=0, B=1$ and $A=1, B=1$ will be

The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be

The number of radial nodes in 3s and 2p respectiely are

Arrange in decreasing order, the energy of $2 s$ orbital in the following atoms $\mathrm{H}, \mathrm{Li}, \mathrm{Na}$ and K .

The bond dissociation energies for $\mathrm{Cl}_2, \mathrm{I}_2$ and ICl are $242.3,151.0$ and $211.3 \mathrm{~kJ} / \mathrm{mol}$ respectively. The enthalpy of sublimation of iodine is $62.8 \mathrm{~kJ} / \mathrm{mol}$. What is the standard enthalpy of formation of $\operatorname{ICl}(\mathrm{g})$ nearly equal to?

The density of 3 M solution of NaCl is $1.25 \mathrm{~g} / \mathrm{mL}$. What is the molality of solution?

A 0.02 M solution of pyridinium hydrochloride has $\mathrm{pH}=3.44$. The ionisation constant of pyridine is

When diluted $\mathrm{H}_2 \mathrm{SO}_4$ is added to aqueous solution of potassium chromate, yellow colour solution turns to orange colour. This signifies that

The osmotic pressure of solution prepared by dissolving 25 mg of $\mathrm{K}_2 \mathrm{SO}_4$ in 2 litre of water at $25^{\circ} \mathrm{C}$ is (Assuming that it is completely dissociated)

The boiling points of 0.01 M aqueous solution of sucrose, NaCl and $\mathrm{CaCl}_2$ would be

4.5 g of aluminium (Atomic mass 27 amu ) is deposited at cathode from $\mathrm{Al}^{3+}$ solution by a certain quantity of electric charge. The volume of hydrogen produced at STP from $\mathrm{H}^{+}$ions in the solution by the same quantity of electric charge will be

For the given redox reaction, what will be the sum of $x, y, m$ and $n$ ?

$$\begin{aligned} x \mathrm{MnO}_4^{-}+y \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4+z \mathrm{H}^{+} \longrightarrow m \mathrm{Mn}^{2+} + & n \mathrm{CO}_2+p \mathrm{H}_2 \mathrm{O} \end{aligned}$$

How many moles of potassium dichromate oxidises 1 mole of ferrous oxalate in acidic medium?

Ozone is determined quantitatively by first reacting it with excess of KI at a particular pH and then titrating the $\mathrm{I}_2$ thus, liberated with a suitable titrant. The pH of the reaction and the titrant used in the titration are respectively.

How long should water be electrolysed by passing through 100 amperes current so that oxygen released can completely burn 27.66 g of diborane? (Weight of $B=10.8 \mathrm{u}$ )

Which of the following oxide is diamagnetic?

Match List I with List II.

Choose the correct answer from the options given below.

Which of the following species has highest nucleophilicity?

Which of the following complex ions is expected to absorb visible light?

Which of the following order in respect to ionisation energy is correct?

Among the following complexes, the one that can exist as facial ( fac ) and meridional (mer) isomers is

Electrophilic substitution of compound $X$ will be fastest at which position

Which of the following compounds does not react with sodium bisulphate?

Methyl acetate and ethyl acetate can be distinguished by

In the given reaction, the final product B will be

Identify the product $C$ in the following given reaction?

$$\mathrm{C}_2 \mathrm{H}_5 \mathrm{I} \xrightarrow{\mathrm{KOH}} A \xrightarrow{\mathrm{Br}_2} B \xrightarrow{\mathrm{KCN}} C$$

Which of the following compounds on reaction with $\mathrm{CH}_3 \mathrm{MgBr}$ will give a tertiary alcohol?

Which of the following cannot be made by using Williamson synthesis?

Which of the following is not a fat soluble vitamin?

$\log \left(\log _{a b} a+\frac{1}{\log _b a b}\right)$ is $($ where $a b \neq 1)$

Match List I with List II.

Choose the correct answer from the options given below

In the following reaction the final product M will be

If $a, b$ and $c$ are distinct positive numbers, not equal to unity. Such that $a b c=1$, then the value of $\log _b a \cdot \log _c a+\log _c b$ $\cdot \log _a b+\log _a c \log _b c$ is

Which of the following pairs form the same osazone?

6 couples decided to form a committee of four members, the number of different committees that can be formed in which no couple finds place is

Given, $\frac{x^2+y^2}{x^2-y^2}+\frac{x^2-y^2}{x^2+y^2}=k$, then $\frac{x^8+y^8}{x^8-y^8}$ is equal to

Sum of first ' $n$ ' terms of a series $a_1+a_2+\ldots+a_n$ is given by $S_n=\frac{n\left(n^2-1\right)(n+2)}{4}$, then the value of $\lim _\limits{n \rightarrow \infty} \sum_\limits{r=2}^n \frac{1}{a_r}$ is

The sum of the series $1 \cdot 2^2+2 \cdot 4^2+3 \cdot 6^2+\ldots$ upto 10 terms is

The sum of $1+\frac{1}{4}+\frac{1 \cdot 3}{4 \cdot 8}+\frac{1 \cdot 3 \cdot 5}{4 \cdot 8 \cdot 12}+\ldots \infty$ is

If 6 letter words, with or without meaning can be formed out of these letters of the word "MATHEMATICS", repetition of letters is not allowed is $960 P$. Then, ' $P$ ' equals

If the coefficient of $x^2$ and $x^3$ in the expansion of $\left(1+8 x+b x^2\right)(1-3 x)^9$ in the power of $x$ are equal, then $b$ is

If the coefficients of $x^7$ and $x^8$ in the expansion of $\left[2+\frac{x}{3}\right]^n$ are equal, then value of $n$ is

The volume of the parallelopiped whose edges are represented by $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$, $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is

Coefficient of $x^3$ in the expansion of $\left(x^2-x+1\right)^{10}\left(x^2+1\right)^{15}$ is equal to

If the unit vectors $\mathbf{a}$ and $\mathbf{b}$ are inclined at $2 \theta$ and $|\mathbf{a}-\mathbf{b}|<1$, then if $0<\theta<\pi, \theta$ lies in the interval.

Two red counters, three green counters and four blue counters are placed in a row in random order. The probability that no two blue counters are adjacent is

$\tan 65^{\circ}, \tan 40^{\circ}+\tan 25^{\circ}$ and $\tan 25^{\circ}$ are in

If the distance between the planes $8 x+12 y-14 z=2$ and $4 x+6 y-7 z=2$ can be expressed as $\frac{1}{\sqrt{N}}$, then the value of $\frac{N(N+1)}{2}$ is

If $A, B$ are two square matrices, such that $A B=A, B A=B$, then $(A+B)^7$ equals

If $A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]$, then $\left(B B^T A\right)^5$ is equal to

The complex number $z$ satisfying $z+|z|$ $=1+7 i$, then the value of $|z|^2$ equals

The value of ' $a$ ' for which the lines $\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}$ and $\frac{x-a}{-1}=\frac{y-7}{2}$ $=\frac{z+2}{-3}$ intersect, is

If $P=\operatorname{cosec} \frac{\pi}{8}+\operatorname{cosec} \frac{2 \pi}{8}+\operatorname{cosec} \frac{3 \pi}{8}$ $+\operatorname{cosec} \frac{13 \pi}{8}+\operatorname{cosec} \frac{14 \pi}{8}+\operatorname{cosec} \frac{15 \pi}{8}$ and $\phi=8 \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18}$, then the value of $P+Q$ is

In a triangle $A B C$ as shown in the diagram, where $A B=5, A C=10$ and $B D=1$, then perimeter of $\triangle A B C$ is

The value of $$\sin ^{-1}\left\{\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sec ^{-1} \sqrt{2}\right)\right\}$$ is

Period of $f(x)=\{x\}+\left\{x+\frac{1}{3}\right\}+\left\{x+\frac{2}{3}\right\}$ is equal to (where $\{\cdot\}$ is fractional part function)

$\lim \limits_{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ equal to

The sum of the infinite terms of the series $\cot ^{-1}\left(1^2+\frac{3}{4}\right)+\cot ^{-1}\left(2^2+\frac{3}{4}\right)$ $+\cot ^{-1}\left(3^2+\frac{3}{4}\right)+\ldots$ is equal to

The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\right)$ of the trapezium is

$$ \int_0^\pi\left[\cos ^2\left(\frac{3 \pi}{8}-\frac{x}{4}\right)-\cos ^2\left(\frac{11 \pi}{8}+\frac{x}{4}\right)\right] d x$$ equals to

If tangent to the curve $f(x)=x^3-\alpha x^2-x+\beta$ at point $(1,3)$ on the curve, cut equals non zero intercepts on co-ordinate axes, then

If $(\cos x)^y=(\sin y)^x$, then $\frac{d y}{d x}$ equals

If the curves $\frac{x^2}{a}+\frac{y^2}{4}=1$ and $y^3=16 x$ intersect at right angles, then ' $a$ ' equals to

$\lim _\limits{x \rightarrow 0} \frac{1}{x} \int_0^x(1+\sin 3 t)^{\frac{1}{t}} d t$ is equal to

If the tangent at the point $P$ on the circle $x^2+y^2+2 x+2 y=7$ meets the straight line $3 x-4 y=15$ at the point $Q$ on the $X$-axis, then length of $P Q$ is

The differential equation corresponding to the family of curves $y=e^x(a x+b)$ is

If two different circles $x^2+y^2+2 a x+2 b y+1$ $=0$ and $x^2+y^2+2 b x+2 a y+1=0$ touches each other, then $(a+b)^2$ is equal to

The area of circle touching parabola $y=x^2$ at $(1,1)$ and having directrix of $y=x^2$ as its normal is $125 A \pi$, then $A$ is

The area of the region(s) enclosed by the curves $y=x^2$ and $y=\sqrt{|x|}$ is

Consider the ellipse $\frac{x^2}{\cos ^2 \alpha}+\frac{y^2}{\sin ^2 \alpha}=1$, where $\alpha \in\left(0, \frac{\pi}{4}\right)$. Then, locus of point of intersection of one of the directrix and tangent at upper end of minor axis is

Select the letter that is related to the third letter in the same way as the second letter is related to the first letter.

TUV : VYB : : PRA : ?

In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written as in that language?

If $e$ is the eccentricity of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\theta$ is the angle between the asymptotes, then $\cos \frac{\theta}{2}$ is

What is the ratio of total sale of branch $B_2$ for both year to the total sale of branch $B_4$ for both year?

What is the average sales of all the branches (in thousand numbers) for the year of 2010?

In a certain code language, 'HONEY' is coded as ' $65^{\prime}$ ' and 'MONEY' is coded as ' $70^{\prime}$ '. How will 'SUNNY' be coded in the same language?

Select the antonym of the word 'Gregarious'.

The narrator call a person dull if he/she

The city of London appear as if it is............

Pick out the correct synonym of the word 'Solitude'.

Four letter-clusters have been given, out of which three are alike in same manner and one is different. Select the letter cluster that is different.

From the given options, choose the correct one that will replace the question mark (?) in the following series.

ZBO, YEJ, XHE, WKZ, ?

Two point charges of $+3 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at a certain distance apart from each other. Electric potential at a distance 60 cm from the mid-point of dipole on axial line is 150 V , then the value of dipole length is

The questions given below consist of a question followed by two statements labelled as I and II. We have to decide whether these statements given enough information required to answer the question or not.

Question in which year was Ritika born?

Statement

I. Ritika at present is 25 years younger to her mother.

II. Ritika's sister who was born in 1964, is 35 years younger to her mother.

Give answer

The maximum power rating of a $20 \Omega$ resistor is 2 kW . Then, it cannot be used with 300 V DC source because the

The magnitude of resistance $X$ in the circuit shown below in the figure, when no current flows through the $5 \Omega$ resistor, is

The work done in moving a charge particle of charge $2 \times 10^{-8} \mathrm{C}$ between two points having potential difference of 36 V is

Three charges, each of $+4 \mu \mathrm{C}$, are placed at the corners $A, B, C$ of a square $A B C D$ of side 1 m . What is the magnitude (in $\mathrm{NC}^{-1}$ ) of electric field at point $O$ towards point $D$ ?

Select the number from among the given options that can replace the question mark (?) in the following series.

$$38,77,233, ?, 4679$$

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements

Some plates are knives.

Some knives are bottles.

Many bottles are bowls.

Conclusions

I. Some plates are bowls.

II. Not a single plate is bowl.

Fill in the blank with the most suitable choice.

I ................ the job if you had paid me enough.