COMEDK 2023 Morning Shift

If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\frac{3}{2} P(A)\) and \(P(C)=\frac{1}{2} P(B)\), then \(P(A \cup C)\) equals to

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will be

The sum of \(n\) terms of the series, \(\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots\) is

The value of \(\frac{1}{2 !}+\frac{2}{3 !}+\ldots+\frac{99}{100 !}\) is equal to

If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an \(\mathrm{AP}\) is

If \(A=\{a, b, c\}, B=\{b, c, d\}\) and \(C=\{a, d, c\}\) then \((A-B) \times(B \cap C)\) is equal to

If \(n(A)=p\) and \(n(B)=q\), then the numbers of relations from the set \(A\) to the set \(B\) is

Let the equation of pair of lines \(y=m_1 x\) and \(y=m_2 x\) can be written as \(\left(y-m_1 x\right)\left(y-m_2 x\right)=0\). Then, the equation of the pair of the angle bisector of the line \(3 y^2-5 x y-2 x^2=0\) is

The distance of the point \((3,4)\) from the line \(3 x+2 y+7=0\) measured along the line parallel to \(y-2 x+7=0\) is equal to

The slope of lines which makes an angle \(60^{\circ}\) with the line \(y-3 x+18=0\)

3 and 5 are intercepts of a line \(L=0\), then the distance of \(L=0\) from \((3,7)\) is

The place \(x-2 y+z=0\) is parallel to the line

The lines \(\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}\) and \(\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}\) are perpendicular to each other, then \(a\) equals to

If two lines \(L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\) and \(L_2: \frac{x-3}{1}=\frac{y-k}{2}=z\) intersect at a point, then \(2 k\) is equal to

The general solution of \(2 \cos 4 x+\sin ^2 2 x=0\) is

If \(\cos A=m \cos B\) and \(\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)\), then \(\lambda\) is equal to

The expression \(\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}\) can be written as

The angle between the vectors \(\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) is

If the vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are coplanar,...

\(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\), then unit vector parallel to $$\mathbf{a}+\mathbf{b}-...

The instantaneous values of alternating current and voltages in a circuit given as
$$\begin{aligned} & i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \mathrm{amp} \\ & e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \text { volt } \end{aligned}$$
The ...

In the series L-C-R circuit shown, the impedance is

In the case of an inductor

In an electrical circuit \(R, L, C\) and \(\mathrm{AC}\) voltage source are all connected in series. When \(L\) is removed from the circuit, the phase difference between the voltage and the current in the circuit is \(\pi / 3\). If instead ...

The mass density of a nucleus varies with mass number \(A\) as

The wavelength of the first line of Lyman series for \(\mathrm{H}\) - atom is equal to that of the second line of Balmer series for a \(\mathrm{H}\)-like ion. The atomic number \(\mathrm{Z}\) of \(\mathrm{H}\)-like ion is

The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of

A capacitor of capacity \(2 ~\mu \mathrm{F}\) is charged upto a potential \(14 \mathrm{~V}\) and then connected in parallel to an uncharged capacitor of capacity \(5 ~\mu \mathrm{F}\). The final potential difference across each capacitor wi...

A dielectric of dielectric constant \(K\) is introduced such that half of its area of a capacitor of capacitance \(C\) is occupied by it. The new capacity is

In the figure below, the capacitance of each capacitor is \(3 \mu \mathrm{F}\). The effective capacitance between \(A\) and \(B\) is

If \(C\) be the capacitance and \(V\) be the electric potential, then the dimensional formula of \(\mathrm{CV}^2\) is

In the figure, pendulum bob on left side is pulled a side to a height \(h\) from its initial position. After it is released it collides with the right pendulum bob at rest, which is of same mass. After the collision, the two bobs stick toge...

In the diagram shown below, \(m_1\) and \(m_2\) are the masses of two particles and \(x_1\) and \(x_2\) are their respective distances from the origin \(O\).

The centre of mass of the system is

One end of the string of length $l$ is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed \(v\), the net force on the particle (direct...

A TV tower has a height \(72 \mathrm{~m}\). The maximum distance upto which TV transmission can be received is (Take, radius of the earth as \(\left.6.4 \times 10^6 \mathrm{~m}\right)\)

A galvanometer having a resistance of \(8 \Omega\) is shunted by a wire of resistance \(2 \Omega\). If the total current is \(1 \mathrm{~A}\), the part of it passing through the shunt will be

Two cells with the same emf \(E\) and different internal resistances \(r_1\) and \(r_2\) are connected in series to an external resistance \(R\). If the potential difference across the first cell is zero then value of \(R\).

When a certain metal surface is illuminated with light of frequency \(\nu\), the stopping potential for photoelectric current is \(V_0\). When the same surface is illuminated by light of frequency \(\frac{\nu}{2}\), the stopping potential i...

Let \(K_1\) be the maximum kinetic energy of photoelectrons emitted by light of wavelength \(\lambda_1\) and \(K_2\) corresponding to wavelength \(\lambda_2\). If \(\lambda_1=2 \lambda_2\), then

Two wire of same material having radius in ratio 2 : 1 and lengths in ratio 1: 2. If same force is applied on them, then ratio of their change in length will be

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area \(A\) and the second wire has cross-sectional area \(3 A\). If the length of the first wire is increased by \(\Delta l\) on applying a...

The magnetic flux linked with a coil satisfies the relation \(\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}\), where \(t\) is time in second. The emf induced in the coil at \(t=2 \mathrm{~s}\) is

The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in vacuum is

A plane electromagnetic wave of frequency \(20 \mathrm{~MHz}\) travels through a space along \(x\)-direction. If the electric field vector at a certain point in space is \(6 \mathrm{~Vm}^{-1}\), then what is the magnetic field vector at tha...

When \(10^{19}\) electrons are removed from a neutral metal plate, the electric charge on it is

A block of wood floats in water with \((4 / 5)\) th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in \(\mathrm{kgm}^{-3}\))

A balloon with mass $m$ is descending down with an acceleration \(a\) (where, \(a < g\) ). How much mass should be removed from it so that it starts moving up with an acceleration \(a\) ?

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are \(v_1\) and \(v_2\), respectively. If \(A\) is the cross-sectional area of the wing and \(\rho\) is the density of air, then the upward lift is

Starting from the centre of the earth having radius \(R\), the variation of \(g\) (acceleration due to gravity) is shown by

If escape velocity on earth surface is \(11.1 \mathrm{~kmh}^{-1}\), then find the escape velocity on moon surface. If mass of moon is \(\frac{1}{81}\) times of mass of earth and radius of moon is \(\frac{1}{4}\) times radius of earth.