List of top Mathematics Questions asked in CUET (PG)

If \(\overrightarrow F=2z\hat{i}-x\hat{j}+y\hat{k}\) and Vis the region bounded by the surface x=0,y=0,x=2,y=4,z=x2,z=2, then value of \(\iiint\limits_V\overrightarrow FdV\)is
Akhilesh and Javed started a business by investing 50,000 and 60,000 respectively. Akhilesh being an active partner receives 12.5% of the profit in addition to his share of profit. How much Akhilesh gets out of a profit of 8800?
Perimeter of a square is same as perimeter of a rectangle. If sides of rectangle are in the ratio 17:11, then find the ratio in the areas of the square and the rectangle.
Solution A Contains 12% water and the remaining is milk. Solution B contains 30% water and the remaining is milk. In what ratio should solutions A and B be mixed to obtain a mixture with 84% milk?
The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c1 and c2 are arbitrary constants)
Let F: R3 →R2 be the linear map defined by F(x, y, z) = (3x+2y-4z, x-5y+3z). The basis of R3 is S and basis of R2 is S', where S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and S' = {(1, 3), (2, 5)}. Then the matrix of F in the bases of R3 and R2 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:
The monthly income and expenditure of a person were ₹10,000 and ₹6,000 respectively. Next year, his income increased by 15% and his expenditure increased by 8%. Then the percentage increase in his savings is:
The surface area of the sphere x2 + y2 + z2 = 9 lying inside the cylinder x2 + y2 = 3y is
The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are
The volume of the cylindrical column standing on the area common to the parabolas \(y^2 = x\), \(x^2 = y\) and cut off by the surface \(z = 12+y-x^2\) is:
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
The orthogonal trajectory of the cardioid r = a(1+cos θ), a being the parameter 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?
The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.
Pipes A and B can fill a tank in 25 hours and 10 hours respectively. Pipe A was opened and after half an hour pipe B was also opened. In how much time the tank got filled?
Consider the linear mapping F: R2 →R2 defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R2: E= {e1, e2} = {(1, 0), (0, 1)} and S = {u1, u2} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:
The product of two numbers is 4840. If the first number is two fifth of the second number, then what is the first number?
The surface area of the cylinder \(x^2+z^2 = 4\) inside the cylinder \(x^2 + y^2 = 4\) is:
Find out the degree of the differential equation \(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)
The orthogonal trajectories of the family of curves y = \(ax^3\) is
The minimum distance of the point (3, 4, 12) from the sphere x2 + y2 + z2 = 1 is
The work done by the force \(\overrightarrow F = (x^2-y^2)\hat{i} + (x+y)\hat{j}\) in moving a particle along the closed path C containing the curves x + y = 0, x2+ y2 = 16 and y = x in the first and fourth quadrant is
If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t2. z=t3 is:
If the curl of vector \(\vec{A} = (2xy-3yz)\hat{i} +(x^2+axz −4z^2)\hat{j}-(3xy+byz)\hat{k}\) is zero, then a + b is equal to :