List of top Mathematics Questions asked in CUET (PG)

Find out the degree of the differential equation \(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)

The surface area of the sphere x² + y² + z² = 9 lying inside the cylinder x² + y² = 3y is

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

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:

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 :

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.

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

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:

Find the sum of following hexadecimal numbers (7CA)₁₆+ (4B2)₁₆ =?

The product of two numbers is 4840. If the first number is two fifth of the second number, then what is the first number?

\(\frac{108^2-104^2}{32^2-28^2} = \) _______ ?

What is the volume of a 6m deep tank having rectangular shaped top 6mx4m and bottom 4mx2m (compound through the use of prismoidal formula)

The all values of z, such that
√2 sin z = coshβ + isinħβ, where β is real, are

The general solution of the differential equation y"+y = 6sin x is:

In what time will a 640 m long train cross an electric pole if its speed is 96 km/h?

Let f : Z→ \(Z_2\), be a homomorphism of groups defined by
\(f(a) =   \begin{cases}    0,  & \quad \text{if } a \text{ is even}\\     1,  & \quad \text{if } a \text{ is odd}   \end{cases}\)

then Kerf is : 

The resultant vector of the cross product of the two vectors\( î+2j-k; 2i+j+k\) is

A man invests some money partly in 8% stock at 105 and partly in 12%, stock at 90. In what ratio should he invest the money to have equal dividends?

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?

Match List-I and List-II

LIST I		LIST II
A.	Singular Matrix	I.	Determinant is always one.
B.	Real Symmetric Matrix	II.	Digonal element are necessarily either purely imaginary or zero
C.	Skew-Hermitian Matrix	III.	Eigen values are always Real
D.	Orthogonal Matrix	IV.	Determinant is always zero

Choose the correct answer from the options given below:

The value of \(\frac {1+tan^2θ}{1+cot^2θ} \times (1-sin^2θ)\) is

The sum of two numbers is 40 and their HCF is 8. How many pairs of numbers satisfy both the conditions?