List of top Mathematics Questions asked in CUET (PG)

If each observation of a Row data whose variance is σ² is multiplied by h, then the variance of the new set is

Which statistical method is best suitable for testing the goodness of fit between an observed and expected distribution?

A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)² + y² = 16 and x² + y² = 1. Then
A. Radius of S is 8
B. Radius of S is 7
C. Centre of S is (-7, 1)
D. Centre of S is (-8, 1)

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If two circles interesect at two points, then the line joining their centres is prependicular to the common chord.
Reason R: The perpendicular bisectors of two chords of a circle intersect at its centre.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following is true :
A. Two vectors are said to be identical if their difference is zero.
B. Velocity is not a vector quantity.
C. Projection of one vector on another is not an application of dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
Choose the most appropriate answer from the options given below :

Let E be the ellipse\(\frac{x^2}{9}+\frac{y^2}{4}=1\) and C be the circle x² + y² = 9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

Let \(a = cos\frac{2π}7 + isin\frac{2π}7\), a = a + a²+a⁴ and β = a³+ a⁵ +a⁶ then the equation whose root are α, β is

Given below are two statements:
Statement I: The angle between the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}-\hat{k}\) is \(\pi/2\)
Statement II: The vector \(\hat{a}\times(\hat{b}\times \hat{c})\) is coplanar with \(\hat{a}\) and \(\hat{b}\)
In the light of the above statements, choose the correct answer from the options given below:

If the unit vectors \(\vec{a}\) and \(\vec{b}\) are inclined at an angle 2θ such that \(|\vec{a}-\vec{b}|\lt 1\) and \(0 \leq \theta \leq \pi\), then θ lies in the interval.

Each of the angle between vectors \(\vec{a},\vec{b}\) and \(\vec{c}\) is equal to 60°. If \(|\vec{a}|= 4,|\vec{b}| = 2\; and\; |\vec{c}|=6\) then the modulus of \(\vec{a}+\vec{b}+\vec{c}\) is

If \(\vec{a}=2\vec{i}+2\vec{j}+3\vec{k},\vec{b}=\vec{i}+2\vec{j}+\vec{k}\;and\;\vec{c}=3\vec{i}+\vec{j}\) are such that \(\vec{a}+\gamma\vec{b}\) is perpendicular to \(\vec{c}\) then determine the value of \(\gamma\)?

Match List-I and List-II

LIST I		LIST II
A.	\(|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|\)	I.	45°
B.	\(|\vec{A}\times\vec{B}|=\vec{A}.\vec{B}\)	II.	30°
C.	\(|\vec{A}.\vec{B}|=\frac{AB}{2}\)	III.	90°
D.	\(|\vec{A}\times\vec{B}|=\frac{AB}{2}\)	IV.	60°

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Given below are two statements :
Statement I: \(\int\limits_{-a}^af(x)dx=\int\limits_{0}^a[f(x)+f(-x)]dx\)
Statement II : \(\int\limits_{0}^1\sqrt{(1+x)(1+x^3)}dx\) is less than or equal to \(\frac{15}{8}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
3 Assertion A: \(\int\limits_{-x}^{3}(x^3+5)dx=30\)
Reason R: f(x) = x³ +5 is an odd function
In the light of the above statements, choose the correct answer from the options given below:

If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)

If f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to

If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]²+[g(x)]² and h(5)=11, then h(10) =

The extreme points of the set \({(x, y); |x|≤2,|y|≤2}\) are

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

If the solution of \(x\frac{dy}{dx}+y=x^3y^6\) is \(\frac{1}{y^\alpha x^\beta}=\frac{\gamma}{2x^2}+C\), then value of \(\alpha+\beta+\gamma\) is

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 \(u=cos^{-1}\frac{x+y}{\sqrt{x}+\sqrt{y}}\), then the value of \(x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}\) 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 \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then