List of top Mathematics Questions asked in CUET (PG)

$ \begin{vmatrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1=d  \end{vmatrix} $ is equal to
The area of surface of solid generated by the revolution of line segment y = 2x from x = 0 to x = 2 about x-axis is equal to:
A point P(7,9) is reflected about line x = y. The new point P1 after reflection is:
Given below are two statements
Statement-I :   \(f(x)=\begin{cases} \frac{3x-2}x \quad &\text{for  0≤x≤1}\\          \frac{sin(x-1)}{x-1} \quad &\text{for} \,\, x>1 \\      \end{cases}\)
Function is continuous at x=1
Statement-II: \(f(x)=\begin{cases} \frac{xe^\frac{1}x}{1+e^{\frac1{x}}} \quad &\ ; x\neq 0\\          0\quad &\text{; } \,\, x=0 \\      \end{cases}\)
Function is continuous at origin. 
In the light of the above statements, choose the correct answer from the options given below.
A, B, C and D entered into a partnership. 'A' contributed one-third of the capital, 'B' contributed one-fourth, 'C' contributed one-fifth and 'D' contributed the rest. All four of them agreed to share profit in the ratio of their capital. What is the share of 'D' when total profit is ₹6000?
Which one of the following rings is an integral domain?
To evaluate the double integral \(\int_0^8\left(\int\limits_{y/2}^{(y/2)+1}\left(\frac{2x-y}{2}\right)dx\right)dy\), we make the substitution \(u=\frac{2x-y}{2}\)and \(v=\frac{y}{2}\). The integral will reduce to
If \(\Phi(z)=c_0+c_1z^{-1}\), then \(\oint_{|z|=1}\frac{1+\Phi(z)}{z}dz\) is
Which of the following points lie in the convex set of points (2, 3) and (4, 1)?
A. (3.6, 1.4) 
B. (1.2, 3.8) 
C. (2.4, 2.6) 
D. (0.4, 4.6) 
Choose the most appropriate answer from the options given below:
Two trains each of legth 250 m start at the same time on two parallele tracks from point A and point B and approached each other with speed of 36 km/hr respectively. When they crossed each, it was found that one train has moved 40 km more than the other. The distance between A and B is
A train running at 90 km/h crosses a 400 m long another train running towards it on parallel tracks at 80 km/h in 18 seconds. How much time will it take to pass a 450 m long tunnel?
Find out the degree of the differential equation \(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)
The average age of three boys is 22 years. Eight times the age of the youngest of them is 3 times the sum of the ages of the other two boys. Find the age of the eldest of them if he is 8 years older to the youngest of them.
Three containers have their volumes in the ratio 3:4:5. They are full of mixture of milk and water in the ratio 4:1, 3:1 and 5:2 respectively. The mixtures from all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is:
Ayan borrowed Rs. 50,000 from Ayush on 25th April, 2022 at 12% p.a. simple interest. Ayan cleared his debt on 18th September, 2022. How much interest is paid by Ayan?
The difference between simple interest and compound interest on a certain sum at 5% per annum for 2 years is ₹25. What is the sum invested?
The speeds of A and B are in the ratio 3:4. A takes 20 minutes more than B to reach the destination. In what time does A reach the distination?
A window is in the form of a rectangle surmounted by a semicircle. Perimeter of the window is 4.6m and height of the rectangular portion is 0.5m, then find the radius of the semicircular portion. (Take \(\pi=\frac{22}{7}\))
A vegetable vendor buys 100kg tomatoes at the rate of Rs18 and spent Rs120 as cartage. He sells 80Kg tomatoes at Rs25/kg and 16kg tomatoes at Rs20/kg. Remaining tomatoes got rotten and could not be sold. Find his profit percentage (correct to one decimal place)
The average of 5 consecutive positive integers starting with m is n. What is the average of 6 consecutive positive integers starting with (m+2)?
Jayant invested a sum of Rs. 65,000 in two schemes and received Rs.7275 as interest after 2 years. In scheme I simple interest is payable at 6% per annum and in scheme II compound interest is payable at 5% per annum Find the ratio of sums he invested in scheme I and scheme II.
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time taken to fill the tank?
If \(m = 2\), \(n = 3\), then the value of \(12m^2n-3mn^2\) is:
A large cube is formed by melting three solid metallic cubes of sides 3cm, 4cm and 5cm respectively. What is the ratio of the sum of the surface areas of the given cubes and that of the new cube?
When a painted cube is cut into 125 small identical cubes, how many smaller cubes have no face painted?