COMEDK 2022

Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is

If A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2P(B) = 3P(C). What is P(B)?

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing, is

If \(S = {{{2^2} - 1} \over 2} + {{{3^2} - 2} \over 6} + {{{4^2} - 3} \over {12}}\, + \,...\) upto 10 terms, then S is equal to

The first and fifth terms of an A.P. are \(-14\) and 2 respectively and the sum of its n terms is 40. The value of n is

Total number of elements in the power set of A containing 17 elements is

If \(A=\{3,5,7\}\) and \(B=\{1,2,3,5\}\), then \(A \times B \cap B \times A\) is equal to

Let the equation of the pair of lines \(y=p x\) and \(y=q x\) can be written as \((y-p x)(y-q x)=0\). Then the equation of the pair of the angle bisectors of the line \(x^2-4 x y-5 y^2=0\) is

The distance of the point \((1,2)\) from the line \(x+y+2=0\) measured along the line parallel to \(2 x-y=5\) is equal to

The slope of lines which makes an angle 45\(^\circ\) with the line \(2x-y=-7\)

If 2 and 3 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is

The line \(\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}\) is parallel to the plane

The angle between the lines \({{x + 4} \over 3} = {{y - 1} \over 5} = {{z + 3} \over 4}\) and \({{x + 1} \over 1} = {{y - 4} \over 1} = {{z - 5} \over 2}\) is

The point of intersection of the lines \({{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}\) and \({{x -5} \over 2} = {{y - 2} \over 1} = z\) is

Find the general solution of \(\sin 2x + \cos x = 0\).

If \(\sin A+\sin B=a\) and \(\cos A+\cos B=b\), then \(\cos (A+B)\) equals?

What is \({{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}\) equal to?

If \(\theta\) be the angle between the vectors \(a = 2\widehat i + 2\widehat j - \widehat k\) and \(b = 6\widehat i - 3\widehat j + 2\widehat k\), then

If x, y and z are non-zero real numbers and \(a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k\) and \(c = x\widehat i + y\widehat j + z\widehat k\) are such that \(a \times b = z\widehat i - 3\widehat j + \widehat k\), then [a b...

If \(\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}\) and \(\mathbf{r}=\hat{i}+\hat{k}\), then the unit vector in the direction of \(3 p+q-2 r\) is

During the phenomenon of resonance

A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circuit, the DC ammeter shows 6 A. When AC current flows through circuit, what is the average readings in DC ammeter and the A...

A series L-C-R circuit is connected to an AC source of 220 V and 50 Hz shown in figure. If the readings of the three voltmeters \(V_1,V_2\) and \(V_3\) are 65 V, 415 V and 204 V respectively, the value of inductance and capacitance will be

An alternating voltage = 200 \(\sin 100t\) is applied to a series combination of \(R=30\Omega\) and an inductor of 400 mH. The power factor of the circuit is,

The AC voltage across a resistance can be measured using a

During \(\alpha\)-decay, atomic mass of parent nuclei is

Which of the following series spectrum of hydrogen atom lies in ultraviolet region?

The wavelength of the second line of Balmer series is 486.4 nm. What is the wavelength of the first line of Lyman series?

If R and C denote resistance and capacitance of a material, then the dimension of CR will be :

In the network shown in figure, the equivalent capacitance between points P and Q is

A bullet of mass $m$ hits a mass \(M\) and gets embedded in it. If the block rises to a height \(h\) as a result of this collision, the velocity of the bullet before collision is

From a circular disc of radius R, a square is cut out with a radius as its diagonal. The centre of mass of remaining portion is at a distance (from the centre)

Maximum amplitude of message signal in amplitude modulation is 20 cm. If the amplitude of carrier wave is 40 cm, then modulation index of modulated wave is

A galvanometer having a resistance of 4 \(\Omega\) is shunted by a wire of resistance 2 \(\Omega\). If the total current is 1.5 A, the current passing through shunt is

A cell of emf 2 V is connected with a load of resistance 1.5 \(\Omega\). The power delivered by the cell to the load is maximum, then power transferred to the load is

Ultraviolet light of wavelength 99 mm falls on a metal plate of work function 1.0 eV. If the mass of the electron is 9.1 \(\times\) 10\(^{-31}\) kg, the wavelength of the fastest photoelectron emitted is

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

A copper and a steel wire of same diameter are connected end to end. A deforming force F\(_1\) is applied to the wire which causes an elongation of 1 cm. The two wires will have

A force F applied on the wire of radius r and length L and change in the length of the wire is \(l\). If the same force F is applied on the wire of the same material and radius 4r and length \(4l\), then change in length of the other wire i...

Television frequencies are of the order of 100 MHz, while radio frequencies are of the order of 1 MHz. Using these as typical frequencies, the ratio of the emf generated in a loop antenna by a television wave to that generated by a radio wa...

A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5 A, then the average force on each electron in the coil due to the magnetic field i...

Speed of electromagnetic wave in a medium having relative permittivity \(\varepsilon_r\) and relative permeability \(\mu_r\) is (speed of light in air, \(c=3\times10^8\) m/s)

A 30 mW laser beam has a cross-sectional area of 15 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by
[Permuittivity of space, \(\varepsilon_0=9\times10^{-12}\)
Speed of light, \(c=3\times10^8\) m/s]

Which of the following diagram represents the variation of the electric field with distance r from the centre of a uniformly charged non-conducting sphere of radius R?

Charge on electron is

Two charged spheres of \(-20\mu\)C and \(60\mu\)C are kept at a certain distance. They are touched and kept again at the same distance. What is the ratio of force experienced before and after?

A raft of density 600 g/m\(^3\) and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

Water is poured in a tank through a cylindrical tube of area of cross-section A and ejecting water at a constant speed 4 m/s. the tank contains a hole of area \(\frac{A}{2}\) at bottom. Level of water in the tank will not go up beyond

If the earth were to spin faster, acceleration due to gravity at the poles

The height at which the acceleration due to gravity becomes \(\frac{g}{16}\) (where, g = acceleration due to gravity on the surface of the earth) in terms of R is, if R is the radius of earth.