VITEEE 2023

A particle of mass $$10 \mathrm{~kg}$$ moving eastwards with a speed $$10 \mathrm{~m} / \mathrm{s}$$ collides with another particle of the same mass moving northward with the same speed $$10 \mathrm{~m} / \mathrm{s}$$. The two particles coalesce on collision. The new particle of mass $$20 \mathrm{~kg}$$ will move in the north-east direction with velocity.

A geostationary satellite revolves around the Earth in a circular orbit of radius $$4 R$$. Here, $R$ is the radius of the Earth. Then, the time period of another satellite moving in a circular orbit of radius $$2 R$$ is:

A ball is allowed to fall from a height of $$10 \mathrm{~m}$$. If there is $$30 \%$$ loss of energy due to impact, then after one impact ball will go up to.

The elastic limit of $$1 \mathrm{~kg}$$ mass is $$3.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$$. Find the maximum load that can be applied to a brass wire of a $$1 \mathrm{~mm}$$ diameter without exceeding the elastic unit.

The focal length of thin convex lens for red and blue rays are $$100 \mathrm{~cm}$$ and $$98.01 \mathrm{~cm}$$, respectively. There, the dispersive power of the material of the lens is

The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immersed in water, the frequence becomes $$60 \mathrm{~Hz}$$ and on immersing the weights in a certain liquid, the frequency becomes $$40 \mathrm{~Hz}$$. The specific gravity of the liquid is

Two gases occupy two containers $$A$$ and $$B$$. The gas in $$A$$ of volume $$0.20 \mathrm{~m}^3$$, exerts a pressure of $$1.40 \mathrm{~MPa}$$ and that in $$B$$, of volume $$0.30 \mathrm{~m}^3$$ exerts a pressure of $$0.7 \mathrm{~MPa}$$. The two containers and united by a tube of negligible volume and the gases are allowed to exchange. Then, if the temperature remains constants. the final pressure in the container will be (in MPa).

0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cross-section $$A$$ closed by a massless piston. The cylinder is attached with a conducting rod of length L$$_1$$ cross-section area $$(1 / 9) \mathrm{m}^2$$ and thermal conductivity $$k_1$$ whose other end is maintained at $$0^{\circ} \mathrm{C}$$. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height $$L / 2$$ from the bottom of cylinder is (neglect any kind of heat loss from system)

A copper sphere cools from $$82^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 10 minutes and to $$42^{\circ} \mathrm{C}$$ in the next $$10 \mathrm{~min}$$. Calculate the temperature of the surrounding?

Susceptibility of ferromagnetic substance is

$$\mathrm{MnO}_4^{-}$$ is good oxidising agent in different medium changing to

$$\mathrm{MnO}_4^{-} \rightarrow \mathrm{Mn}^{2+} \rightarrow \mathrm{MnO}_4^{2-} \rightarrow \mathrm{MnO}_2 \rightarrow \mathrm{Mn}_2 \mathrm{O}_3$$

Change in oxidation number respectively are :

When $${ }_{92} \mathrm{U}^{235}$$ undergoes fission, $$0.1 \%$$ of its original mass is changed into energy. How much energy is released if $$5 \mathrm{Kg}$$ of $${ }_{92} \mathrm{U}^{235}$$ undergoes fission?

Which of the following compounds is used as the starting material for the preparation of potassium dichromate?

The standard $$E_{\text {red }}^{\circ}$$ values of $$A, B$$ and $$C$$ are $$+0.52 \mathrm{~V},-23.6 \mathrm{~V},-0.44 \mathrm{~V}$$ respectively. The order of their reducing power is

The stability of dihalides of $$\mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}$$ and decreases gradually in the sequence.

Arrhenius equation may not be represented as

$$\mathrm{H}$$-bonding is maximum in

Last three digits in $$(9)^{50}$$ be

$$\mathrm{PH}_3$$ has much lower boiling point than $$\mathrm{NH}_3$$ because :

If $$\alpha$$ is a non -real fifth root of unity, then the value of $$3^{\left|1+\alpha+\alpha^2+\alpha^{-2}-\alpha^{-1 \mid}\right|}$$, is

The area enclosed by $$y=x^3+1$$ and $$y=x+2$$ in first quadrant, is

If matrix $$A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]$$ is given to be symmetric, then the value of $$a b$$ is

A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the faces at a point that is directly above the centre of the face at a height 3a/4 above the base. The minimum value of F for which the cube begins to topple an edge is (assume that cube does not slide)

Three blocks of masses $$m_1, m_2$$ and $$m_3$$ are connected by massless strings, as shown, on a frictionless table. They are pulled with a force, $$T_3=40 \mathrm{~N}$$. If $$m_1=10 \mathrm{~kg}, m_2=8 \mathrm{~kg}$$ and $$m_3=2 \mathrm{~kg}$$, the tension $$T_2$$ will be

A particle of mass $m$ is projected with a velocity $$v$$ making an angle of $$45^{\circ}$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $$h$$ is.

A solid sphere having mass $$m$$ and radius $$R$$ moves down a plane inclined at an angle '$$\theta$$'. Find the ratio between its acceleration when it rolls without slipping and its acceleration when it slides down the same plane without any rotation.

The position of a projectile launched from the origin at $$t=0$$ is given $$\mathbf{r}=(40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}) \mathrm{m}$$ at $$t=2 \mathrm{~s}$$. If the projectile was launded at an angle $$\theta$$ from the horizontal, then $$\theta$$ is (take, $$g=10 \mathrm{~m} / \mathrm{s}^2$$ )

In the formula $$X=3 Y Z^2, X$$ and $$Z$$ have dimensions of capacitance and magnetic induction respectively. The dimensions of $$Y$$ is MKS system are.

The gravitational field in a region is given by $$\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}$$. The change in the gravitational potential energy of a particle of mass $$1 \mathrm{~kg}$$ when it is taken from the origin to a point ($$5 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$) is

Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The magnetic field $$B$$ at a point $$P$$ lying on the perpendicular line joining the wires and at a distance $$x$$ from the mid-point is

Two parallel conductors carry current in opposite directions as shown in the figure. One conductor carries a current of $$20 \mathrm{~A}$$. Point $$C$$ is a distance $$d / 2$$ to the right of a 20 A current. If $$d=18 \mathrm{~cm}$$ and $$i$$ is adjusted so that the magnetic field at $$C$$ is zero, the value of the current $$i$$ is

A parallel plate capacitor with air between the plates has a capacitance of $$15 \mathrm{~pF}$$. the separation between the plates is $$d$$. The space between the plates is now filled with two dielectrics constant $$k_1=3$$ and thickness $$d / 3$$ while the other one has dielectric constant $$k_2=6$$ and thickness $$2 d / 3$$. Capacitance of the capacitor is now

The upper end of a wire of diameter $$24 \mathrm{~mm}$$ and length $$1 \mathrm{~m}$$ is damped and its other end is twisted through an angle is $$30^{\circ}$$. The angle of shear is

With increasing temperature, the angle of contact,

The de-Broglie wavelength of a proton $$\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$$ acclerated through a potential difference of $$2 \mathrm{~kV}$$ is

The susceptibility of a magnetism at $$300 \mathrm{~K}$$ is $$1.5 \times 10^{-5}$$. The temperature at which the susceptibility increases to $$4.5 \times 10^{-5}$$ is

A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $$10^{-2} \mathrm{~T}$$. If it is now turned through an angle of $$60^{\circ}$$ about on axis in its plane. Find the charge indicted in the coil. (Area of a coil $$=10^{-2} \mathrm{~m}^2$$ )

The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ counts per minute at $$t=6 \mathrm{~min}$$. The time (in minutes) at which the activity reduces to half its value is.

The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The wavelength of the $$k_\beta$$-line emitted by the same element will be

A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is

Assuming the diodes to be of silicon with forward resistance zero, the current $$i$$ in the following circuit is

What is the voltage gain in a common emitter amplifier, where input resistance is $$6 \Omega$$ and load resistance $$48 \Omega, \beta=0.3$$ ?

A transmitting antenna is kept on the surface of the Earth. The minimum height of receiving antenna required to receive the signal in line of sight at $$4 \mathrm{~km}$$ distance from it is $$x \times 10^{-2} \mathrm{~m}$$. The value of $$x$$ is

In a $$n$$-$$p$$-$$n$$ transistor $$10^{10}$$ electrons enter the emitter in $$10^{-6}$$ s. $$6 \%$$ of the other electrons are lost in the base. The current transfer ratio will be.

Which of the following is an intensive property?

Which one of the following concentration terms is/are independent of temperature?

Match the following Column I and Column II

Match the Column I with Column II.

Mark the correct option

In the reaction, $$\mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI}$$. In a 4L flask, 0.8 mole of each $$\mathrm{H}_2$$ and $$\mathrm{I}_2$$ are taken. All equilibrium, 1 mole of $$\mathrm{HI}$$ is formed. What will be the value of equilibrium constant $$K_C$$ ?

The uncertainty in the momentum of an electron is $$2.0 \times 10^{-8} \mathrm{~kg} \mathrm{~ms}^{-1}$$. The uncertainty in its position will be

A metal has bcc structure and the edge length of its unit cell is $$8 \mathop A\limits^o$$. The volume of the unit cell ( in $$\mathrm{cm}^3$$) will be

The value of $$\Delta E$$ for combustion of $$32 \mathrm{~g}$$ of $$\mathrm{CH}_4$$ is $$-1770778 \mathrm{~J}$$ at $$298 \mathrm{~K}$$. The $$\Delta H$$ combustion for $$\mathrm{CH}_4$$ in $$\mathrm{J} \mathrm{~mol}^{-1}$$ at this temperature will be (Given that, $$R=8.314 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$$ )

Consider the following cell reaction.

$$\begin{aligned} & 2 \mathrm{Fe}(s)+\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q) \longrightarrow \\ & 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{H}_2 \mathrm{O}(l), E^{\circ}=1.67 \mathrm{~V} \\ \end{aligned}$$

At $$[\mathrm{Fe}^{2+}]=10^{-5} \mathrm{M}, {\mathrm{P}}{ }_2=3 \mathrm{~atm}$$ and $$\mathrm{pH}=2.5$$, the cell potential at $$25^{\circ} \mathrm{C}$$ is

The ionic conductance of following cation in a given concentration are in the order.

The structure of $$\mathrm{XeOF}_4$$ is

Which is correct about zero order reaction?

In context of the lanthanoides, which of the following statements is not correct?

Plot of $$\log x / m$$ against $$\log p$$ is a straight line inclined at an angle of $$45^{\circ}$$. When the pressure is $$2 \mathrm{~atm}$$ and Freundlich parameter, $$k$$ is 10, the amount of solute adsorbed per gram of adsorbent.

ortho-silicate ion is

Choose the wrong statements.

I. $$\mathrm{CO}_2$$ is responsible for greenhouse effect.

II. Acid rain contains mainly $$\mathrm{HNO}_3$$.

III. NO is more harmful than $$\mathrm{NO}_2$$.

IV. $$\mathrm{CO}_2$$ can absorb infrared.

Mark the correct option

Addition of water to butyne occurs in acidic medium and in the presence of $$\mathrm{Hg}^{2+}$$ ions as a catalyst. The compound obtained

The total number of metal-metal bond present in $$\left[\mathrm{Co}_2(\mathrm{CO})_8\right]$$ is

Which one of the following compounds is formed in the laboratory from benzene by a substitution reaction?

Atomic number of $$\mathrm{Mn}, \mathrm{Fe}$$ and $$\mathrm{Co}$$ are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complex ions are diamagnetic?

I. $$\left[\mathrm{CO}\left(\mathrm{NH}_3\right)_6\right]^{3+}$$

II. $$\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$$

III. $$\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$$

IV. $$\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$$

Choose the correct option.

In a set of reactions nitrobenzene gave a product $$C$$. Identify the product $$C$$.

$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NO}_2 \xrightarrow{\mathrm{Fe} / \mathrm{HCl}} A \xrightarrow[273 \mathrm{~K}]{\mathrm{NaNO}_2 / \mathrm{HCl}} B \xrightarrow[\Delta]{\mathrm{H}_2 \mathrm{O} / \mathrm{H}^{+}} C$$

The reaction,

is called

The acidic strength of following compounds are in the order

Which of the following products is formed in the given reaction?

In the given reaction,

The product P is

In a set of reactions acetophenone gave a product $$B$$. Identify the product $$B$$.

$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCH}_3 \xrightarrow{\mathrm{C}_6 \mathrm{H}_5 \mathrm{MgBr}} A \xrightarrow{\mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}} B$$

Out of 9 consonants and 4 vowels, how many words of 4 consonants and 3 vowels can be formed?

Let $$a_n$$ be a sequence of numbers which is defined by relation $$a_1=2, \frac{a_n}{a_{n+1}}=3^{-n}$$, then $$\log _2\left(a_{50}\right)$$ is equal to (take $$\log _2 3=1.6$$ )

The number of peptide bonds in a linear tetrapeptide (made of different amino acids) are

The value of $$\frac{1}{2}\left(\frac{1}{5}\right)^2+\frac{2}{3}\left(\frac{1}{5}\right)^3+\frac{3}{4}\left(\frac{1}{5}\right)^4+\ldots . . \infty$$ is

The sum of all the numbers of four different digits that can be made using the digits 0, 1, 2 and 3 is

Glucose contains $$-\mathrm{CHO}$$ group and Which of the following solution or reagent can be used to distinguish these two compounds?

Let $$a, b$$ and $$c$$ be three unit vectors such that $$a \times(b \times c)=\frac{\sqrt{3}}{2}(b+c)$$. If $$b$$ is not parallel to $$c$$, then the angle between $$a$$ and $$b$$ is

If $$\theta_1, \theta_2$$ and $$\theta_3$$ are the angles made by a line with the positive direction of $$X, Y$$ and $$Z$$-axes, then $$\cos 2 \theta_1+\cos 2 \theta_2+\cos 2 \theta_3$$ is equal to

If $$x^n=a_0+a_1(1+x)+a_2(1+x)^2+\ldots \ldots \ldots+ a_n(1+x)^n=b_0+b_1(1-x)+b_2(1-x)^2+\ldots . .+ b_n(1-x)^n$$, then for $$n=201,\left(a_{101}, b_{101}\right)$$ is equal to

If $$R$$ is a relation from a finite set A having $$m$$ elements to finite set $$B$$ having $$n$$ elements, then the number of relation from $$A$$ to $$B$$ is

A unit vector perpendicular to both the vectors $$\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathbf{k}}$$ is

Let $$A$$ and $$B$$ be two independent events such that the odds in favour of $$A$$ and $$B$$ are $$1: 1$$ and $$3: 2$$, respectively. Then, the probability that only one of the two occurs is

The determinant of the matrix $$\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]$$ is

If $$x+\frac{1}{x}=1$$ and $$p=x^{4000}+\frac{1}{x^{4000}}$$ and $$q$$ is the digit at unit place in the number $$2^{2 n}+1$$, then the value of $$(p+q)$$ is equal to

Suppose, $$A=\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$$ is an adjoint of the matrix $$\left[\begin{array}{rrr}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$$. The value of $$\frac{a_1+b_2+c_3}{b_1 a_2}$$ is

The plane is perpendicular to the planes $$x-y+2 z-4=0$$ and $$2 x-2 y+z=0$$ and passes through $$(1,-2,1)$$ is

The distance between the point $$(7,2,4)$$ and the plane determined by the points $$(2,5,-3),(-2,-3,5)$$ and $$(5,3,-3)$$ is

The image of the point $$(2,3,7)$$ in the plane $$2 x+5 y-3 z-19=0$$, is

If $$z_1, z_2$$ and $$z_3$$ are the vertices $$A, B$$ and $$C$$ respectively of an isosceles right angled triangle with right angled at $$C$$, then $$\left(z_1-z_3^{\prime}\right)\left(z_2-z_3\right)$$ equals to

If $$\alpha, \beta$$ and $$\gamma$$ are the cube roots of $$P,(P<0)$$, then for any $$x, y$$ and $$z$$ which does not make denominator zero, the expression $$\frac{x \alpha+y \beta+z \gamma}{x \beta+y \gamma+z \alpha}$$ equals to

If $$\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2$$, then the range of $$a$$ is

Let $$z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots \ldots \ldots$$ 9, then $$\frac{1}{10}\left\{\left|1-z_1\right|\left|1-z_2\right| \ldots .\left|1-z_a\right|\right\}$$ equals to

The minium value of $$\left[2-\cos \theta+\sin ^2 \theta\right]$$ is

If $$\sin A, \sin B$$ and $$\cos A$$ are in GP, then the roots of $$x^2+2 x \cot B+1=0$$ are always

The maximum slope of the curve $$y=\frac{1}{2} x^4-5 x^3+18 x^2-19 x+7$$ occurs at the point

The value of $$\int_\lambda^{\lambda+\pi / 2}\left(\cos ^4 x+\sin ^4 x\right) d x$$ is

The equation $$3 \cos ^{-1} x-\pi x-\pi / 2=0$$ has

$$\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$$ equals to

If $$\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)$$, then the value of $$y$$ is

For $$x \in R, f(x)=|\log 2-\sin x|$$ and $$g(x)=f(f(x))$$, then

$$\lim _\limits{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \ldots 3 n}{n^{2 n}}\right)^{1 / n}$$ is equal to

If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to

The solution of $$d y / d x=1+x+y+x y$$ is

The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\left(y^2 / x^2\right)}\right)$$ is

The area of the region containing the points $$(x, y)$$ satisfying $$4 \leq x^2+y^2 \leq 2|x|+|y|$$, is

If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2\right)^3}{\left(d^4 y / d x^4\right)^5}+\left(\frac{d^4 y}{d x^4}\right)=x^2+4$$, then $$m-n$$ is equal to

The line $$a x+b y+c=0$$ will be a tangent to the circle $$x^2+y^2=r^2$$, then

Six persons A, B, C, D, E and F are sitting in a row. A and F are sitting at two extreme ends of the row. B is to the immediate right of A and D is 2nd left of F. What is the position of E with respect to A ?

I. $$\mathrm{E}$$ is to the right of $$\mathrm{A}$$.

II. $$\mathrm{E}$$ is to the left of $$\mathrm{C}$$.

What is the average income of the company over the years?

Which of the following pairs of years, shows the equal expenditure of the company?

In a certain code language, 'RUBBER' is coded as '102' and 'JELLY' is coded as '76'. How will 'LABEL' be coded in the same language?

If the 4th term in the expansion of $$\left(p x+\frac{1}{x}\right)^n, n \in N$$ is $$\frac{5}{2}$$ and three normals to the parabola $$y^2=x$$ are drawn through a point $$(q, 0)$$, then

In a code language, 'SAUCE' is written as 'ASVEC'. How will 'MEANT' be written as in that language?

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

1. Few gentlemen are rich.

2. Few gentlemen are not fools.

3. Everyone is either a fool or rich.

Conclusions

I. No gentleman is rich.

II. Few gentlemen being fools is a possibility.

III. No one is both a fool and rich.

The rain calls itself the 'dotted silver threads' as

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

$$2,0,3,2,4,6,5,12,6, ?, 7,30 $$

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

$$3,10,24, ? , 73, 108$$

What is '$$\mathrm{I}$$' in the above lines?

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

Pick out the correct synonym of the word-'Prerogative'.

Fill in the blank with most suitable word. I ............. for forty minutes to see the doctor before my name was announced.

Select the antonym for the word 'Dishevelled'

Electric field in the region is given by $$\mathbf{E}=\left(M / x^4\right) \hat{\mathbf{i}}$$, then the correct expression for the potential in the region is (assume potential at infinity is zero)

A constant voltage is applied between the two ends of a uniform metallic wire, Some heat is developed in it. The heat developed is halved if

How is P related to R?

I. $$Q$$ is the son of $$R$$.

II. $$\mathrm{Q}$$ is the brother of $$\mathrm{P}$$.