COMEDK 2020

If \(A = \left[ {\matrix{ 1 & { - 2} & 2 \cr 0 & 2 & { - 3} \cr 3 & { - 2} & 4 \cr } } \right]\), then A . adj (A) is equal to

The value of \(\left| {\matrix{ x & p & q \cr p & x & q \cr p & q & x \cr } } \right|\) is

The focus of the parabola is

The number of positive divisors of 252 is

The remainder obtained when 5124 is divided by 124 is

The orthocentre of the triangle with vertices A(0, 0), B(0, 3/2), C(\(-\)5, 0) is

ABC is a triangle with \(\angle A=30^\circ\) and BC = 10 cm. The area of the circumcircle of the triangle is

ABC is a triangle, G is the centroid, D is the mid-point of BC. If A = (2, 3) and G = (7, 5), then the point D is

\({1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} =\)

In the group \((G\,{ \otimes _{15}})\), where \(G = \{ 3,6,9,12\}\), \({ \otimes _{15}}\) is multiplication modulo 15, the identity element is

A group (G *) has 10 elements. The minimum number of elements of G, which are their own inverses is

A graph G has m vertices of odd degree and ‘n’
vertices of even degree. Then which of the
following statements is necessarily true?

Which of the following is not a group with
respect to the given operation?

The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line \(2x+y-7=0\) is

A vector perpendicular to the plane containing the points \(A(1, - 1,2),B(2,0, - 1),C(0,2,1)\) is

If \(\sin 3\theta = \sin \theta\), how many solutions exist such that \(- 2\pi < \theta < 2\pi\)?

\({\sin ^2}17.5^\circ + \sin 72.5^\circ\) is equal to

If a and b are vectors such that \(|a + b|=|a-b|\), then the angle between a and b is

If \(a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k\), then a vector perpendicular to a and in the plane containing b and c is

OA and BO are two vectors of magnitudes 5 and 6 respectively. If \(\angle BOA=60^\circ\), then OA . OB is equal to

For a series L-C-R circuit at resonance, which statement is not true?

An electron of an atom transits from \(n_1\) to \(n_2\). In which of the following maximum frequency of photon will be emitted?

Two protons are kept at a separation of 40 \(\mathop A\limits^o\). F\(_n\) is the nuclear force and F\(_e\) is the electrostatic force between them. Then,

Two radioactive materials X\(_1\) and X\(_2\) have decay constant 5\(\lambda\) and \(\lambda\), respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X\(_1\) to X\(_2\) will be \(1/e\) aft...

Two capacitors \(C_1\) and \(C_2\) are charged to 120 V
and 200 V, respectively. When they are
connected in parallel, it is found that potential
on each one of them is zero. Therefore,

A body of mass 1000 kg is moving horizontally
with a velocity 50 m/s. A mass of 250 kg is
added. Find the final velocity.

Ground waves have wavelength

If voltage \(V=(200\pm 8)V\) and current \(I=(20\pm0.5)A\), then the percentage error in resistance R is

Point out the right statements about the validity
of Kirchhoff’s junction rule,

If \(P=Q=R=10\Omega\) and \(S=20\Omega\), then what resistance should be joined with S to balance the Wheatstone's network?

To the potentiometer wire of length L and 10\(\Omega\) resistance, a battery of emf 2.5 V and a resistance R are connected in series. If a potential difference of 1 V is balanced across L/2 length, the value of R in \(\Omega\) will be

Light of frequency 1015 Hz falls on a metal surface of work function 2.5 eV. The stopping potential of photoelectrons (in V) is

A proton accelerated through a potential V has de-Broglie wavelength \(\lambda\). Then, the de-Broglie wavelength of an \(\alpha\)-particle, when accelerated through the same potential V is

The Poisson's ratio of a material is 0.1. If the longitudinal strain of a rod of this material is \(10^{-3}\), then the percentage change in the volume of the rod will be

A steel wire of length 4.7 m and cross-sectional area \(3.0\times10^{-5}\) m\(^2\) stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of \(4.0\times10^{-5}~\mathrm{m^2}\) under a given load. What is the r...

A coil of wire of a certain radius has 100 turns
and a self inductance of 15 mH. The self
inductance of a second similar coil of 500 turns
will be

A coil of 100 turns carries a current of 5 mA and
creates a magnetic flux of 10\(^{-5}\) Wb. The
inductance is

In step-up transformer, relation between number of turns in primary (N\(_P\)) and number of turns in secondary (N\(_S\)) coils is

Which of the following has/have zero average
value in a plane electromagnetic wave?

Consider a thin spherical shell of radius R
consisting of uniform surface charge density s.
The electric field at a point of distance x from its
centre and outside the shell is

A charge of 0.8 C is divided into two charges Q\(_1\) and Q\(_2\). These are kept at a separation of 30 cm. The force on Q\(_1\) is maximum when

An electric dipole has a pair of equal and opposite point charges \(q\) and \(-q\) separated by a distance \(2x\). The axis of the dipole is defined as

An electric dipole is placed in a uniform electric
field with the dipole axis making an angle \(\theta\) with
the direction of the electric field. The
orientation of the dipole for stable equilibrium
is

Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is

The potential energies associated with four
orientations of an electric dipole in an electric
field are
(i) \(-5U_0\) (ii) \(-7U_0\) (iii) \(3U_0\) (iv) \(5U_0\)
where \(U_0\) is positive. Rank the orientations according to the angle betwee...

A ball floats on the surface of water in a
container exposed to the atmosphere. When the
container is covered and the air is partially
removed, then the ball

A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by 50%, then the energy of the soap film will be changed by

A fluid is in streamline flow across a horizontal
pipe of variable area of cross-section. For this
which of the following statements is correct?

A satellite can be in a geostationary orbit around a planet if it is at a distance R from the centre of the planet. If the planet starts rotating about its axis with double the angular velocity, then to make the satellite geostationary, its...

Two spherical bodies of masses M and 5M and
radii R and 2R are released in free space with
initial separation between their centres equal to
12 R. If they attract each other due to
gravitational force only, then the distance
covered by the ...