List of top Questions asked in CUET (PG)

Match List-I with List-II and choose the correct option:

LIST-I (Function)LIST-II (Value)
(A) \( \int_{\gamma} \frac{1}{z-a} \, dz \), where \( \gamma: |z-a|=r, r > 0 \)(III) \( 2i\pi \)
(B) \( \int_{\gamma} \frac{z+2}{z} \, dz \), where \( \gamma: z = 2e^{it}, 0 \le t \le \pi \)(IV) \( i\pi \)
(C) \( \int_{\gamma} \frac{e^{2z}}{(z-1)(z-2)} \, dz \), where \( \gamma: |z|=3 \)(II) \( 2i\pi(e^4 - e^2) \)
(D) \( \int_{\gamma} \frac{z^2 - z + 1}{2(z-1)} \, dz \), where \( \gamma: |z|=2 \)(I) \( -4 + 2i\pi \)


Choose the correct answer from the options given below:

Let \( R \) be the planar region bounded by the lines \( x = 0 \), \( y = 0 \) and the curve \( x^2 + y^2 = 4 \) in the first quadrant. Let \( C \) be the boundary of \( R \), oriented counter clockwise. Then, the value of:

\[ \oint_C x(1 - y) \, dx + (x^2 - y^2) \, dy \] is equal to:

Match List-I with List-II and choose the correct option:

LIST-ILIST-II
(A) The solution of an ordinary differential equation of order 'n' has(III) 'n' arbitrary constants
(B) The solution of a differential equation which contains no arbitrary constant is(IV) particular solution
(C) The solution of a differential equation which is not obtained from the general solution is(I) singular solution
(D) The solution of a differential equation containing as many arbitrary constants as the order of a differential equation is(II) complete primitive


Choose the correct answer from the options given below:

If p is a prime number and a group G is of the order p2, then G is:

The S.I. unit of compressibility is:
Specific heat of saturated water vapour at 100\(^{\circ}\)C is.
The gas constant is:
The molecular density of a gas is n and diameter of its molecule is d. The mean free path of molecule is:
Which of the following statements are correct:
A. Specific heat of saturated water vapour at 100\(^{\circ}\)C is negative.
B. There is only one triple point of a substance.
C. Boiling point of every liquid rises with increase in pressure.
D. Latent heat can not become zero.
Choose the CORRECT answer from the options given below:
In the steady state of temperature, the flow of heat across the body depends upon its:
A. thermal capacity
B. thermal conductivity
C. temperature difference across its opposite faces
D. thermal resistivity
Choose the CORRECT answer from the options given below:
Degree of degeneracy will be large when:
Quantum statistics changes into classical statistics if: (Symbols have their usual meaning)
Fermions have spin value equal to:
According to the Dulong and Petit's law, the atomic heat of an element at constant volume:
If an electromagnetic wave is totally reflected, the radiation pressure in terms of average Poynting vector S\(_{av}\) is:
The electric potential inside a charged conducting sphere is constant. The charge distribution inside the sphere will be:
In the context of conductors in electrostatic equilibrium, the relationship between electric field and the conductor's surface is:
The electric field just outside a charged conductor is E. The electric field just inside the conductor is:
A parallel-plate capacitor has a dielectric slab of thickness d and dielectric constant K inserted between the plates. The capacitance change compared to the vacuum case (when no slab is inserted) is:
The gravitational field at a point in space is:
For a system of particles, if the external net force acting on the system is zero, the system's center of mass is:
True conditions for sustained interference of light waves are:
A. Two interfering sources must be coherent.
B. Two interfering waves must be propagated along the same line.
C. Two interfering waves must have equal amplitude.
D. If the interfering waves are polarized, they must be in the same state of polarization.
Choose the correct answer from the options given below:
A long, straight wire carries a current of 10 A. The magnitude of the magnetic field at a distance of 5 cm from the wire is:
A point charge +Q is placed at the origin. The electric potential at point (3a,4a,0) in terms of k, Q and a is:
A conducting sphere of radius R carries a total charge Q. The electric field at a distance r>R from the center is: