List of top Mathematics Questions asked in CUET (PG)

The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

Let \(F: R^4 → R^3\) be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals

If W is a subspace of R³, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to

The area of region bounded by the curve y²=x, the y-axis and between y = 2 and y = 4 is

Which one of the following statements is wrong.

The equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0

Which one of the following is wrong?

If income of A is 20% more than that of B, then income of B is how much percent less than that of A?

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

A beam is supported at its ends by supporters which are 12 meters apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is

The tangent to the hyperbola x²-y² = 3 are parallel to the straight line 2x + y +8=0 points are

Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x₇} where x₇ denotes multiplication moduls 7?

The integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}\)is

The number of common tangents that can be drawn to the circle x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0 is

In a group G, if a⁵ = e, aba^-1 = b² for a, b ∈ G then o(b) is equal to:

If log₃2,log₃(2^x-5) and log₃(2^x-7/2) are in A.P., then x is equal to

The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)

The volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is

With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:

If \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is

If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is

if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are three non-coplanar vectors, then \((\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]\) equal to

The variance of a series of numbers 2, 3, 11 and x is 12.25. Find the value of x.