COMEDK 2024 Afternoon Shift

A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is non-negative?

The probability of inviting three friends on 5 consecutive days, exactly one friend a day and no friend is invited on more than two days is

The inequality \(4 x-3 \geq \frac{10 x-1}{3}\) represents which of the following interval when \(x \in R\)

\(\text { If } 6^{\text {th }} \text { term of a geometric progression is }-\frac{1}{32} \text { and } 9^{\text {th }} \text { term is } \frac{1}{256} \text { then } r \text { is }\)

The sum of four numbers in a geometric progression is 60 , and the arithmetic mean of the first and the last number is 18 . Then the numbers are

The sum of first three terms of a geometric progression is 16 and the sum of next three terms is 128 . The sum to \(\mathrm{n}\) terms of the geometric progression is

\(\text { Let } \mathrm{A} \text { and } \mathrm{B} \text { be two sets then } A-(A \cap B) \text { is equal to }\)

\(\text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is }\)

A relation \(R\) is defined from \(\{2,3,4\}\) to \(\{3,6,7,10\}\). If \(x R y \Leftrightarrow x\) and \(y\) are co prime numbers. Then range of \(R\) is

Let 'P' be the mean deviation of the first five odd natural numbers about their mean and 'Q' be the mean deviation of the first five prime numbers about their mean. The \(Q-P=\)

Let \(\mathrm{ABC}\) be a triangle with equations of its sides \(\mathrm{AB}, \mathrm{BC}\). \(\mathrm{CA}\) respectively are \(x-2=0, y-5=0\) and \(5 x+2 y-10=0\). Then the orthocentre of triangle lies on the line

For what value of \(\mathrm{a}\) and \(\mathrm{b}\) the intercepts cut off on the co-ordinate axes by the line \(a x-b y+8=0\) are equal in length but opposite in signs to those cut off by the line \(2 x-3 y+6=0\) on the axes

The lines
\(\vec{r}=(2 \hat{\jmath}-3 \hat{k})+\lambda(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})\) and \(\vec{r}=(2 \hat{\imath}+6 \hat{\jmath}+3 \hat{k})+\mu(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})\) are

A line makes the same angle \(\theta\) with each of the \(x\) and \(z\)-axes. If the angle \(\beta\), which it makes with the \(y\)-axis is such that \(\sin ^2 \beta=3 \sin ^2 \theta\), then \(\cos ^2 \theta\) equals

If the line \(\frac{1-x}{-3}=y=\frac{z+2}{2}\) is perpendicular to the line \(\frac{3 x-1}{2 b}=3-y=\frac{z-1}{a}\), then find the value of \(3 a+3 b\)

\(\left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)=\)

\(\frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}=\)

\(\text { If } \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta+\frac{2 \pi}{3}\right)}=\frac{z}{\cos \left(\theta-\frac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to }\)

Let a, b, c be three vector such that \(a \neq 0\) and \(\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4\) and \(|\vec{b} \times \vec{c}|=\sqrt{15}\). If \(\vec{b}-2 \vec{c}=\lambda \vec{a}\) then \(\lambda\) equals to

\(\text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is }\)

A group of devices having a total power rating of 500 watt is supplied by an \(\mathrm{AC}\) voltage \(E=200 \sin \left(3.14 t+\frac{\pi}{4}\right)\). Then the r.m.s. value of the circuit current is

A transformer has 400 turns in its primary winding and 800 turns in its secondary winding. The primary voltage is \(20 \mathrm{~V}\) and the load in the secondary is 4 ohm. The current in the primary, assuming it to be an ideal transformer,...

An AC voltage source of variable angular frequency \(\omega\) and fixed amplitude \(\mathrm{V}_0\) is connected in series with a capacitance \(\mathrm{C}\) and an electric bulb of resistance \(\mathrm{R}\) (inductance zero). When \(\omega\)...

The radius of a nucleus as measured by electron scattering is \(4.8 \mathrm{~fm}\). The mass number of nucleus is most likely to be

In a hydrogen atom, if electron is replaced by a particle which is 40 times heavier but has the same charge, then, the ratio of the radius of the first excited state of a normal hydrogen atom to the ground state of the above atom is

A nucleus with mass number 190 initially at rest emits an alpha particle. If the \(\mathrm{Q}\) value of the reaction is \(4.5 \mathrm{~MeV}\), the kinetic energy of the alpha particle is

The shortest wavelengths of Paschen, Lymen and Balmer series are in the ratio

The resistance of a wire at room temperature \(20^{\circ} \mathrm{C}\) is found to be \(10 \Omega\). If resistance of the wire increases by \(10 \%\), then the temperature of the wire will be (The temperature coefficient of the material of ...

A storage battery of emf \(28.0 \mathrm{~V}\) and internal resistance \(0.5 \Omega\) is being charged by a \(140 \mathrm{~V}\) dc supply using a series resistor of \(27.5 \Omega\). The terminal voltage of the battery during charging is

Two identical moving coil galvanometers have \(10 \Omega\) resistance and full-scale deflection at \(2 \mu \mathrm{A}\) current. One of them is converted into a voltmeter of range \(10 \mathrm{~mV}\) and the other into an ammeter of range $...

An electron starting from rest and moving with the velocity \(\mathrm{v}\) through a potential difference \(\mathrm{V}\) is shown by the graphs below. Identify the correct graph.

A wire of uniform cross section and resistance 4 ohms is bent in the shape of square ABCD. Point A is connected to a point \(\mathrm{P}\) on DC by a wire AP of resistance \(1 \mathrm{ohm}\). When a potential difference is applied between $$...

The potential difference between the points \(\mathrm{P}\) and \(\mathrm{Q}\) of the arrangement shown in figure is

\(\mathrm{K}_1\) and \(\mathrm{K}_2\) are maximum kinetic energies of photoelectrons emitted when lights of wavelength \(\lambda_1\) and \(\lambda_2\) respectively are incident on a metallic surface. If \(\lambda_1=3 \lambda_2\), then

The velocity of an electron so that its momentum is equal to that of a photon of wavelength \(660 \mathrm{~nm}\) is

In an inductor of self-inductance \(2 \mathrm{~mH}\), current changes with time (in sec) according to the relation, \(I=(3 t^2-3 t+8) A\). The emf becomes zero at

A wire ' 1 ' \(\mathrm{cm}\) long bent into a circular loop is placed perpendicular to the magnetic field of flux density '\(B^{\prime} W b \mathrm{~m}^{-2}\). Within \(0.1 \mathrm{sec}\), the loop is changed into a square of side '\(a\)' $...

A metallic rod of length '\(a\)' is rotated with an angular frequency of \(0.2 \mathrm{~rads}^{-1}\) about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of '\(\mathrm{B}\)' T parallel to the ax...

An electromagnetic wave of frequency \(3 \mathrm{~MHz}\) passes from vacuum into a dielectric medium \((\mu_r=1)\) of relative permittivity 4.0. Then,

A tiny ball of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) is suspended from the fixed support using an insulating string of length \(1 \mathrm{~m}\). The horizontal uniform electric field \(\mathrm{E}\) is switched on. The angle made by ...

Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point \(\mathrm{P}\) and then accelerated through point \(\mathrm{Q}\) by the electric field. Points \(\mathrm{P}\) and $$\mathr...

A uniformly charged solid sphere of radius \(\mathrm{R}\) has potential \(\mathrm{V}_0\) (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials $$\frac{3 \mathrm{~V}_0}{2}, \frac{\math...

3 point charges each of \(-\mathrm{q}\) are placed on the circumference of a circle of diameter \(2 \mathrm{a}\) at \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) respectively as shown in figure. The electric field at \(\mathrm{O}\) is

Water flows from a tap with steady flow, through a cross sectional area of \(10^{-3} \mathrm{~m}^2\) with a speed of \(0.5 \mathrm{~ms}^{-1}\). Assume the pressure is constant throughout the stream of water. The cross sectional area of the ...

Modulus of rigidity of an incompressible liquid is

A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth is \(\mathrm{V}\) and the magnitude of the gravitational field strength is \(\mathrm{g}\). The gravitational potential ...

Energy required for moving a body of mass \(\mathrm{m}\) from a circular orbit of radius 3R to a higher orbit of radius 4R around the earth is.

An iron piece of mass \(200 \mathrm{~g}\) is kept inside a furnace for some time and then put in a calorimeter of water equivalent \(20 \mathrm{~g}\) containing \(230 \mathrm{~g}\) of water at \(20 \mathrm{C}\). The steady state temperature...

A cubical box of side \(2 \mathrm{~m}\) contains helium gas. It was observed that in a time of 1 second, an atom travelling with the root-mean-square speed parallel to one of the edges of the cube, made 250 hits with one of the walls, witho...

If pressure of an ideal gas is increased by keeping temperature constant the kinetic energy will