VITEEE 2023

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

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 $$...

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 coa...

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...

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

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?

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 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

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.

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}$...

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)

With increasing temperature, the angle of contact,

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{~k...

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 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?

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 \(0.7 \mathrm{~MPa}\). ...

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-se...

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{~...

Susceptibility of ferromagnetic substance 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

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, ...

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 m...

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...

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

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 a...

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 $$...

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 ...

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.

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

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 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 be...

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.