List of top Questions asked in CUET (PG)- 2025

If \( x = r\cos\theta, y = r\sin\theta \) then Match the LIST-I with LIST-II

LIST-ILIST-II
A.\( \frac{\partial r}{\partial x} \)I.\( \frac{1}{r} \)
B.\( \frac{\partial r}{\partial y} \)II.\( \frac{y}{r} \)
C.\( \frac{\partial(x,y)}{\partial(r,\theta)} \)III.\( \frac{x}{r} \)
D.\( \frac{\partial(r,\theta)}{\partial(x,y)} \)IV.\( r \)


(Note: There is a typo in the question; it should be \( y = r \sin\theta \))

For the differential equation \(\left(1+\frac{d^2y}{dx^2}\right)^{3/2} = y\frac{d^2y}{dx^2}\) the order, degree and linearity respectively are:

For Particular Integral, Match the LIST-I with LIST-II

LIST-ILIST-II
A.\( \frac{1}{(D-1)} x^2 \)I.\( xe^x \)
B.\( \frac{1}{D^2+D+1} \cos x \)II.\( \sin x \)
C.\( \frac{1}{(D-1)^2} e^x \)III.\( \frac{x^2 e^x}{2} \)
D.\( \frac{1}{D^3-3D^2+4D-2} e^x \)IV.\( -(x^2 + 2x + 2) \)


(Note: List-I Item A is assumed to be \( \frac{1}{D-1} x^2 \) based on the options)

When light ray refracts on entering from one medium to another medium of different refractive indices, it follows:
Two thin convex lenses of focal lengths 2 cm and 6 cm are separated by a distance of 4 cm in air. Arrange the following cardinal points in ascending order on basis of their distance from second lens:
A. First Principal Point
B. First Focal Point
C. Second Focal Point
D. Second Nodal Point

Match the LIST-I with LIST-II

LIST-ILIST-II
A.Compton EffectIV.Scattering
B.Colors in thin filmII.Interference
C.Double RefractionIII.Polarization
D.Bragg's EquationI.Diffraction


Choose the correct answer from the options given below:

The resolving power of a grating:
A. increases with increase in total number of lines ruled on grating.
B. increases with increase in total width of grating.
C. increases with increasing the order of spectrum as in Echelon grating.
D. increases with decreasing the order of spectrum as in Echelon grating.
Choose the CORRECT answer from the options given below:
A 20g of cane sugar is dissolved in water to make 50 cc of solution. A 20 cm length of tube filled with this solution causes +53\(^{\circ}\)30' optical rotation. What will be the specific rotation?
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:

Match List-I with List-II for the index of refraction for yellow light of sodium (589 nm)

LIST-I (Materials)LIST-II (Refractive Indices)
A.IceI.1.309
B.Rock salt (NaCl)II.1.460
C.CCl₄III.1.544
D.DiamondIV.2.417


Choose the correct answer from the options given below:

Subtract (29.A)\(_{16}\) from (4F.B)\(_{16}\)

Match the LIST-I with LIST-II

LIST-I (Logic Gates)LIST-II (Expressions)
A.EX-ORI.\( A\bar{B} + \bar{A}B \)
B.NANDII.\( A + B \)
C.ORIII.\( AB \)
D.EX-NORIV.\( \bar{A}\bar{B} + AB \)

Choose the correct answer from the options given below:

Arrange the following numbers in ascending order:
A. (10110.011)\(_2\)
B. (32)\(_{10}\)
C. (5F.8)\(_{16}\)
D. F\(_{16}\)
Choose the Correct answer from the options given below:
As water flows from a faucet, stream of water becomes narrower as it descends. The guiding principle for this observation is:
In a semiconductor, intrinsic concentration of charge carriers varies with:
The molecular density of a gas is n and diameter of its molecule is d. The mean free path of molecule is:
Wavelength of X-rays having the largest penetrating power is:
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:
In an election between two candidates, a candidate who got 30% of the total votes is defeated by 15000 votes. The number of votes obtained by the winning candidate is:
In college B, each student participated in any one or both the sports, Hockey and Football. 36% of the students participated in both the sports. The number of students who participated in only Football is 120% more than those who participated in only Hockey. The total number of students who participated in only one of the sports is 960. Find the ratio of number of students who participated in hockey to those in only football?
In college B, each student participated in any one or both the sports, Hockey and Football. 36% of the students participated in both the sports. The number of students who participated in only Football is 120% more than those who participated in only Hockey. The total number of students who participated in only one of the sports is 960. What percentage of the students who participated in Hockey, participated in only Hockey?
The following pie-chart shows the amount collected by a shopkeeper by selling four different food items in degrees. The total amount collected is Rs.64,800. Find the average amount collected from the sales of Bengali dishes, Punjabi dishes and Gujarati dishes.
The following table shows the total number of people who were stuck in traffic jam while going to their office on working days of a week due to construction of a flyover. Table also shows the ratio of male to female among them. Find the average number of females who were stuck in traffic on working days.
Study the following table and answer the question that follows. The given table shows the percentage population of three states A, B and C below poverty line and the ratio of males and females as per poverty line. If the total population of state A is 51,00,000, then what is the number of females above the poverty line in state A?
Study the following table and answer the question that follows. If the population of state B is 42,00,000 and the population of state C is 32,00,000, then what is the sum of number of females below poverty line in state B and number of males below poverty line in state C?