COMEDK 2024 Morning Shift

A and B each have a calculator which can generate a single digit random number from the set \(\{1,2,3,4,5,6,7,8\}\). They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability t...

The probability that a randomly chosen number from one to twelve is a divisor of twelve is

\(\text { If } \frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6), x \in R \text { then }\)

Given \(a, b, c\) are three unequal numbers such that \(\mathrm{b}\) is arithmetic mean of \(a\) and \(c\) and \((b-a),(c-b), a\) are in geometric progression. Then \(a: b: c\) is

\((32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to }\)

A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio of the G.P is

Express the set \(A=\{1,7,17,31,49\}\) in set builder form

\(\text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \cap(B \times A) \text { is equal to }\)

$$\begin{aligned}
&\begin{aligned}
& \text { A, B, C are subsets of the Universal set U } \\
& \text { If } \mathrm{A}=\{x: x \text { is even number, } x \leq 20\} \\
& \mathrm{B}=\{x: x \text { is multiple of } 3, x \leq 15\} \\
& \mathrm{...

The mean of the numbers \(a, b, 8,5,10\) is 6 and the variance is 6.80 , then which of the following gives possible values of \(a\) & \(b\)

Find the direction in which a straight line must be drawn through the point \((1,2)\) so that its point of intersection with the line \(x+y=4\) may be at a distance of \(\sqrt{\frac{2}{3}}\) from this point.

The perpendicular distance of a line from the origin is 5 units and its slope is \(-1\).
The equation of the line is

The vector equation of two lines are
$$\begin{aligned} & \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\ & \vec{r}=(s+1) \hat{\imath}+(2 s-1) \hat{\jmath}-(2 s+1) \hat{k} \end{aligned}$$
Then the shortest distance between t...

\(P\) is a point on the line segment joining the points \((3,2,-1)\) and \((6,2,-2)\). If \(x\) coordinate of \(\mathrm{P}\) is 5, then its \(y\) co-ordinate is

The foot of the perpendicular from \((2,4,-1)\) to the line \(x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)\) is

If \(\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)\) then \(\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=\)

\(4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }\)

\(\text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)=\)

\(\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=\)

The vector \((\vec{r})\) whose magnitude is \(3 \sqrt{2}\) units which makes an angle of \(\frac{\pi}{4}\) and \(\frac{\pi}{2}\) with \(y\) and \(z\)- axis respectively is

A coil offers a resistance of \(20 \mathrm{~ohm}\) for a direct current. If we send an alternating current through the same coil, the resistance offered by the coil to the alternating current will be :

A transformer which steps down \(330 \mathrm{~V}\) to \(33 \mathrm{~V}\) is to operate a device having impedance \(110 \Omega\). The current drawn by the primary coil of the transformer is :

The capacitance of a parallel plate capacitor is \(400 \mathrm{~pF}\). It is connected to an ac source of \(100 \mathrm{~V}\) having an angular frequency \(100 \mathrm{~rad~s}^{-1}\). If the rms value of the current is \(4 \mu \mathrm{A}\),...

A coil of inductance \(1 \mathrm{H}\) and resistance \(100 \Omega\) is connected to an alternating current source of frequency \(\frac{50}{\pi} \mathrm{~Hz}\). What will be the phase difference between the current and voltage?

The ratio of the radii of the nucleus of two element \(\mathrm{X}\) and \(\mathrm{Y}\) having the mass numbers 232 and 29 is:

The closest approach of an alpha particle when it make a head on collision with a gold nucleus is \(10 \times 10^{-14} \mathrm{~m}\), then the kinetic energy of the alpha particle is :

Find the binding energy of the tritium nucleus:
[Given: mass of \(1 \mathrm{H}^3=3.01605 \mathrm{~u} ; \mathrm{~m}_{\mathrm{p}}=1.00782 \mathrm{~u} ; \mathrm{~m}_{\mathrm{n}}=1.00866 \mathrm{~u}\).]

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as \(\epsilon=2 U\). A similar capacitor with no dielectric is charged to \(U_0=78 \mathrm{~V}\). It is then connected to t...

Which of the following statement is true regarding the centre of mass of a system?

Which of the following graph shows the variation of velocity with mass for the constant momentum?

A metal ball of \(20 \mathrm{~g}\) is projected at an angle \(30^{\circ}\) with the horizontal with an initial velocity \(10 \mathrm{~ms}^{-1}\). If the mass and angle of projection are doubled keeping the initial velocity the same, the rat...

A body is moving along a circular path of radius '\(r\)' with a frequency of revolution numerically equal to the radius of the circular path. What is the acceleration of the body if radius of the path is \(\left(\frac{5}{\pi}\right) m\) ?

A \(500 \mathrm{~W}\) heating unit is designed to operate on a \(400 \mathrm{~V}\) line. If line voltage drops to \(160 \mathrm{~V}\), the percentage drop in heat output will be:

A cell of emf E and internal resistance r is connected to two external resistances \(\mathrm{R_1}\) and \(\mathrm{R_2}\) and a perfect ammeter. The current in the circuit is measured in four different situations:
(a) without any external re...

The resistance of the galvanometer and shunt of an ammeter are \(90 \mathrm{~ohm}\) and \(10 \mathrm{~ohm}\) respectively, then the fraction of the main current passing through the galvanometer and the shut respectively are:

On increasing the temperature of a conductor, its resistance increases because

The current through a conductor is '\(\mathrm{a}\)' when the temperature is \(0^{\circ} \mathrm{C}\). It is '\(\mathrm{b}\)' when the temperature is \(100^{\circ} \mathrm{C}\). The current through the conductor at \(220^{\circ} \mathrm{C}\)...

The threshold frequency for a metal surface is '\(n_0\)'. A photo electric current '\(I\)' is produced when it is exposed to a light of frequency \(\left(\frac{11}{6}\right) \mathrm{n}_{\mathrm{o}}\) and intensity $$\mathrm{I}_{\mathrm{n}}$...

The difference in energy levels of an electron at two excited levels is \(13.75 \mathrm{~eV}\). If it makes a transition from the higher energy level to the lower energy level then what will be the wave length of the emitted radiation?
[giv...

The mass of a particle \(\mathrm{A}\) is double that of the particle \(\mathrm{B}\) and the kinetic energy of \(\mathrm{B}\) is \(\frac{1}{8}\)th that of A then the ratio of the de- Broglie wavelength of A to that of B is:

If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) respectively, then the corresponding ratio of increase in their lengths would be

Select the unit of the coefficient of mutual induction from the following.

Around the central part of an air cored solenoid of length \(20 \mathrm{~cm}\) and area of cross section \(1.4 \times 10^{-3} \mathrm{~m}^2\) and 3000 turns, another coil of 250 turns is closely wound. A current \(2 \mathrm{~A}\) in the sol...

A metallic rod of \(2 \mathrm{~m}\) length is rotated with a frequency \(100 \mathrm{~Hz}\) about an axis passing through the centre of the circular ring of radius \(2 \mathrm{~m}\). A constant magnetic field \(2 \mathrm{~T}\) is applied pa...

If potential (in volt) in a region is expressed as \(\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathrm{y}+2 \mathrm{yz}\), the electric field (in \(N C^{-1}\)) at point \((1,0,1)\) is

Two metal spheres, one of radius \(\frac{R}{2}\) and the other of radius \(2 \mathrm{R}\) respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is

A square shaped aluminium coin weighs \(0.75 \mathrm{~g}\) and its diagonal measures \(14 \mathrm{~mm}\). It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges \((+Q\) and $$-Q)$...

Two charges '\(-q\)' each are fixed, separated by distance '\(2 d\)'. A third charge '\(q\)' of mass '\(m\)' placed at the mid-point is displaced slightly by '\(x\)' \((x< < d)\) perpendicular to the line joining the two fixed charges as sh...

Five charges, '\(q\)' each are placed at the comers of a regular pentagon of side '\(a\)' as shown in figure. First, charge from '\(A\)' is removed with other charges intact, then charge at '\(A\)' is replaced with an equal opposite charge....

64 rain drops of the same radius are falling through air with a steady velocity of \(0.5 \mathrm{~cm} \mathrm{~s}^{-1}\). If the drops coalesce, the terminal velocity would be