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Mathematics
List of top Mathematics Questions asked in CUET (PG)
If
\(u=sin^{-1}[\frac{x+y}{\sqrt{x}+\sqrt{y}}]\)
and
\(x^2u_{xx}+2xyu_{xy}+y^2u_{yy}=-\frac{sinucos2u}{m^2cos^3u}\)
then, m is equal to
CUET (PG) - 2023
CUET (PG)
Mathematics
Differential Equations
If there is no feasible region in LPP, then the problem has:
CUET (PG) - 2023
CUET (PG)
Mathematics
Linear Programmig Problem
The surface area of the cylinder
\(x^2+z^2 = 4\)
inside the cylinder
\(x^2 + y^2 = 4\)
is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of Integrals
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=t
2
. z=t
3
is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of Integrals
The rank of matrix A =
\(\begin{bmatrix} 1&3&1&-2&-3\\1&4&3&-1&-4\\2&3&-4&-7&-3\\3&8&1&-7&-8 \end{bmatrix}\)
CUET (PG) - 2023
CUET (PG)
Mathematics
Matrices
If
\(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\)
where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
Let A =
\(\begin{bmatrix}2&3\\4&-1\end{bmatrix}\)
then the matrix B that represents the linear operator A relative to the basis
S = {
\(u_1,u_2\)
}=
\({[1, 3]^T, [2, 5]^T}\)
, is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Matrices
Double integral
\(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\)
equals:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
The value of double integal
\(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\)
is equal to:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
Which one of the following is a cyclic group?
CUET (PG) - 2023
CUET (PG)
Mathematics
Matrices
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral
\(\int \int \int (x^2+y^2+z^2)dxdydz\)
taken over the volume enclosed by the sphere x
2
+ y
2
+z
2
= 1 is
\(\frac{4\pi}{5}\)
Reason R:
\(\int^{1}_{0}\int^{1}_{0}x\ dxdy=\frac{1}{2}\)
In the light of the above statements, choose the most appropriate answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
Given below are two statements
Statement I: In cylindrical co-ordinates,
\(Volume = \int \int\limits_{V} \int rdrdødz \)
Statement II: In spherical polar Co-ordinates,
\(Volume = \int \int\limits_{V} \int r^2\ \cos\theta\ drd\theta d\phi\)
In the light of the above statements, choose the correct answer from the options given below :
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
The integral
\(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\)
is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
Match List I with List II
Homogeneous function
Degree
A
.
\(f(x,y)=\frac{x^\frac{1}{3}+y^\frac{1}{3}}{x^\frac{1}{2}+y^\frac{1}{2}}\)
I
.
3
B
.
\(f(x,y)=\frac{x+y}{\sqrt{x}+\sqrt{y}}\)
II
.
\(\frac{1}{2}\)
C
.
\(f(x,y)=\frac{x^4+y^4}{x+y}\)
III
.
1
D
.
\(f(x,y)=\frac{\sqrt{x^3+y^3}}{\sqrt{x}+\sqrt{y}}\)
IV
.
\(-\frac{1}{6}\)
Choose the correct answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Differential Equations
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The given vector
\(\vec{F}=(y^2-z^2+3yz-2x)\hat{i} +(3xz+2xy)\hat{j}+(3xy-2xz+2z)\hat{k}\)
is solenoidal
Reason R: A vector
\(\vec{F}\)
is said to be solenoidal if div
\(\vec{F}\)
= 0
In the light of the above statements, choose the correct answer from the options given below :
CUET (PG) - 2023
CUET (PG)
Mathematics
Vector Algebra
Given below are two statements
Statement I: If
\(x=\frac{1}{3}(2u + v)\)
and
\(y =\frac{1}{3}(u − v)\)
, then
\(dxdy=\frac{-1}{3}\ dudv\)
Statement II: Area in Polar Co-ordinater
\(\int\limits^{\theta_1}_{\theta_1} \int\limits^{r_2}_{r_1} rd\theta dr\)
In the light of the above statements, choose the correct answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Double and triple integrals
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 :
CUET (PG) - 2023
CUET (PG)
Mathematics
Vector Algebra
For what value(s) of k the set of vectors {(1, k, 5), (1, -3, 2), (2, -1, 1)} form a basis in R
3
?
CUET (PG) - 2023
CUET (PG)
Mathematics
Vector Algebra
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, x
2
+ y
2
= 16 and y = x in the first and fourth quadrant is
CUET (PG) - 2023
CUET (PG)
Mathematics
Vector Algebra
The value of the integral
\(∮_c \frac{dz}{3-\bar z}, C:|z|=1\)
is
CUET (PG) - 2023
CUET (PG)
Mathematics
Cauchy’s integral formula
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A given family of curves is said to be 'self- orthogonal' if the family of orthogonal trajectory is the same as the given family of curves.
Reason R: For finding orthogonal trajectory, replace
\(\frac{dy}{dx}by-\frac{dx}{dy}\)
in
\(f(x,y,\frac{dy}{dx})=0\)
In the light of the above statements, choose the correct answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Differential Equations
Given below are two statements :
Statement I: Mdx+Ndy = 0 is said to be an exact differential equation if it satisfies the following condition
\(\frac{∂M}{∂x}=\frac{∂N}{∂y}\)
Statement II: If Mdx + Ndy = 0 is not an exact differential equation and
\(\frac{1}{N}(\frac{∂M}{∂y}-\frac{∂N}{∂x})=f(x)\)
, then
\(I.F.=e^{\int f(x)dx}\)
In the light of the above statements, choose the correct answer from the options given below :
CUET (PG) - 2023
CUET (PG)
Mathematics
Differential Equations
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:
CUET (PG) - 2023
CUET (PG)
Mathematics
Parabola
The general solution of the differential equation
\(2x^2 \frac{d^2y}{dx^2}=x\frac{dy}{dx}-6y=0\)
is :
CUET (PG) - 2023
CUET (PG)
Mathematics
Solutions of Differential Equations
The solution of the Linear Programming Problem
maximize Z = 107x + y
subject to constraints x + y ≤2
-3x + y ≥ 3
x, y ≥ 0 is
CUET (PG) - 2023
CUET (PG)
Mathematics
Linear Programmig Problem
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