COMEDK 2024 Evening Shift

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

\(\text { The solution set for the inequality } 13 x-5<15 x+4<7 x+12 ; x \in W \text { is }\)

A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand d...

Consider an infinite geometric series with first term '\(a\)' and common ratio '\(r\)'.
If the sum of infinite geometric series is 4 and the second term is \(\frac{3}{4}\) then

If two positive numbers are in the ratio \(3+2 \sqrt{2}: 3-2 \sqrt{2}\), then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is

Two finite sets have '\(m\)' and '\(n\)' number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of \(\mathrm{m}\) and \(\mathrm{n}\) are ...

Which of the following relations on the set of real numbers \(\mathrm{R}\) is an equivalence relation?

The shaded region in the Venn diagram represents

The mean of five observations is 4 and their variance is 5.2 . If three of these observations are 1, 2 and 6, then the other two observations are

The line joining two points \(A(2,0) B(3,1)\) is rotated about \(A\) in anticlockwise direction through an angle of \(15^{\circ}\). If \(B\) goes to \(C\) in the new position, then the coordinates of \(C\) is

The area of the triangle whose vertices are \((-2, a)(2,-6)\) and \((5,4)\) is 35 sq units then the value of '\(\mathrm{a}\)' is

The points on the \(x\)-axis whose perpendicular distance from the line \(\frac{x}{3}+\frac{y}{4}=1\) is 4 units are

If the straight lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-t}\) and \(\frac{x-1}{t}=\frac{y-4}{2}=\frac{z-5}{1}\) are intersecting then \(t\) can have

The measure of the angle between the lines \(x=k+1, \quad y=2 k-1, \quad z=2 k+3, \quad k \in R \quad\) and \(\quad \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-1}{-2}\) is

The co-ordinate of the foot of the perpendicular from \(P(1,8,4)\) on the line joining \(R(0,-1,3)\) and \(Q(2,-3,-1)\) is

\(\text { Value of } \cos 105^{\circ} \text { is }\)

\(\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to }\)

\(\text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y=\)

\(\text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are }\)

Find the value of '\(b\)' such that the scalar product of the vector \(\hat{\imath}+\hat{\jmath}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}\) and $$b \hat{\imath}+2 \hat{\jmat...

When an A.C. source is connected to a inductive circuit,

In the \(\mathrm{A} . \mathrm{C}\). circuit given below, voltmeters \(\mathrm{V}_1\) and \(\mathrm{V}_2\) read \(100 \mathrm{~V}\) each. Find the reading of the voltmeter \(\mathrm{V}_3\) and the ammeter \(\mathrm{A}\).

The distance of closest approach when an alpha particle of kinetic energy \(6.5 \mathrm{~MeV}\) strikes a nucleus of atomic number 50 is

The binding energy per nucleon for \(\mathrm{C}^{12}\) is \(7.68 \mathrm{~MeV}\) and that for \(\mathrm{C}^{13}\) is \(7.47 \mathrm{~MeV}\). The energy required to remove a neutron from \(\mathrm{C}^{13}\) is

If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength \(\lambda\). When it jumps from the second to the first orbit, the corresponding wavelength of the photon will be

An electron has a mass of \(9.1 \times 10^{-31} \mathrm{~kg}\). It revolves round the nucleus in a circular orbit of radius \(0.529 \times 10^{-10} \mathrm{~m}\) at a speed of \(2.2 \times 10^6 \mathrm{~ms}^{-1}\). The magnitude of its angu...

\(\text { If the nuclear radius of }{ }^{27} \mathrm{Al} \text { is } 3.6 \text { fermi, the nuclear radius of }{ }^{125} \mathrm{Fe} \text { is }\)

A parallel plate capacitor having a dielectric constant 5 and dielectric strength \(10^6 \mathrm{~V} \mathrm{~m}^{-1}\) is to be designed with voltage rating of \(2 \mathrm{~kV}\). The field should never exceed \(10 \%\) of its dielectric s...

Figure below shows a network of resistors, cells, and a capacitor at steady state.

What is the current through the resistance 4 \(\Omega\) ?

The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 \(\mu\)F capacitor.

A ball is moving in a circular path of radius \(5 \mathrm{~m}\). If tangential acceleration at any instant is \(10 \mathrm{~ms}^{-2}\) and the net acceleration makes an angle of \(30^{\circ}\) with the centripetal acceleration, then, the in...

The resistance of a \(10 \mathrm{~m}\) long wire is \(10 \Omega\). Its length is increased by \(25 \%\) by stretching the wire uniformly. The new resistance is

A voltmeter of resistance \(1000 \Omega .0 .5 \mathrm{~V} /\) div is to be converted into a voltmeter to make it to read \(=1 \mathrm{~V} / \mathrm{div}\). The value of high resistance to be connected in series with it is

Three bulbs of \(40 \mathrm{~W}, 60 \mathrm{~W}\), and \(100 \mathrm{~W}\) are arranged in series with a \(220 \mathrm{~V}\) source. The maximum light is obtained from

Four resistors, each of resistance R, are connected as shown in the figure below.

A photon emitted during the de-excitation of electron from a state \(\mathrm{n}\) to the second excited state in a hydrogen atom, irradiates a metallic electrode of work function \(0.5 \mathrm{~eV}\), in a photocell, with a stopping voltage...

A particle of mass \(2 \mathrm{mg}\) has the same wavelength as a neutron moving with a velocity of \(3 \times 10^5 \mathrm{~ms}^{-1}\). The velocity of the particle is (mass of neutron is \(1.67 \times 10^{-27} \mathrm{Kg}\))

The temperature of a wire is doubled. The Young's modulus of elasticity

A conducting circular loop is placed in a uniform magnetic field \(\mathrm{B}=0.125 \mathrm{~T}\) with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of $$2 \mathrm{~mm} \mathrm{~s}^{-1}$...

A transformer of \(100 \%\) efficiency has 200 turns in the primary and 40000 turns in the secondary. It is connected to a \(220 \mathrm{~V}\) main supply and secondary feeds to a \(100 \mathrm{~K} \Omega\) resistance. The potential differe...

The magnetic flux linked with a coil is given by the equation: \(\phi=8 t^2+t+10\). The e.m.f. induced in the coil in the \(3^{\text {rd }}\) second will be

The current in a coil changes steadily from \(3 \mathrm{~A}\) to \(5 \mathrm{~A}\) in \(0.2 \mathrm{~s}\) when an emf of \(2 \mu \mathrm{V}\) is induced in it. The self-inductance of the coil is

Column - I lists the waves of the electromagnetic spectrum. Column - II gives approximate frequency range of these waves. Match Column - I and Column - II and choose the correct match from the given choices.

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Two point charges \(\mathrm{M}\) and \(\mathrm{N}\) having charges \(+q\) and \(-q\) respectively are placed at a distance apart. Force acting between them is \(\mathrm{F}\). If \(30 \%\) of charge of \(\mathrm{N}\) is transferred to $$\mat...

If 216 drops of the same size are charged at \(200 \mathrm{~V}\) each and they combine to form a bigger drop, the potential of the bigger drop will be

A neutral water molecule is placed in an electric field \(E=2.5 \times 10^4 \mathrm{NC}^{-1}\). The work done to rotate it by \(180^{\circ}\) is \(5 \times 10^{-25} \mathrm{~J}\). Find the approximate separation of centre of charges.

Three point charges are located on a circular arc at \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) as shown in the figure below. The total electric field at the centre of the \(\operatorname{arc}(\mathrm{C})\) is

What is the relation obeyed by the angles of contact \(\theta_1, \theta_2\) and \(\theta_3\) of 3 liquids of different densities \(P_1, P_2\) and \(P_3\) respectively \((\mathrm{P}_1 < \mathrm{P}_2 < \mathrm{P}_3\)) when they rise to the sa...

The acceleration due to gravity at pole and equator can be related as

A satellite is revolving around the earth in a circular orbit with kinetic energy of \(1.69 \times 10^{10} \mathrm{~J}\). The additional kinetic energy required for just escaping into the outer space is