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Mathematics
List of top Mathematics Questions asked in CUET (PG)
The value of C in Rolle's theorem where
\(-\frac{π}{2}\)
<C<
\(\frac{π}{2}\)
and
\(f(x)=cos x\)
on
\([-\frac{π}{2},\frac{π}{2}]\)
is equal to :
CUET (PG) - 2023
CUET (PG)
Mathematics
Continuity and differentiability
Which one of the following is harmonic function
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of derivatives
Match List I with List II
LIST I
LIST II
A
.
A square matrix A is said to be symmetric if
I
.
A=A'
B
.
A square matrix A is said to be skew symmetric if
II
.
A= -A'
C
.
If A is any square matrix then
III
.
A+A' is a symmetric matrix
D
.
If A is any square matrix then
IV
.
A-A' is a skew symmetric matrix
Choose the correct answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Types of Matrices
The value of
\(∫_c \frac{3z^2+7z+1}{z+1} dz\)
, where C is the circle |z|=
\(\frac{1}{2}\)
is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Cauchy’s integral formula
Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II:
\(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)
convergent
In the light of the above statements, choose the correct answer from the options given below
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of Integrals
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
\(\int\int_R(x + y) dydx = A\)
, where R is the region bounded by x = 0, x = 2, y = x, y = x+2, then
\(\frac{A}{12}\)
is equal to:
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of Integrals
The volume generated by the revolution of the cardioid
\(r = a(1-\cosθ)\)
about its axis is:
CUET (PG) - 2023
CUET (PG)
Mathematics
Application of Integrals
Let f (x) be defined on [0, 3] by
\(f(x) = \begin{cases} x,\text{if x is a rational number} \\ 3-x\text{, if x is an irrational number} \end{cases}\)
Then f(x) is continuous in the interval at:
CUET (PG) - 2023
CUET (PG)
Mathematics
Relations and functions
Let f: G→H be a group homomorphism from group G into group H with kernel K. If the order of G, H and K are 50, 25 and 10 respectively then the order of f(G) is
CUET (PG) - 2023
CUET (PG)
Mathematics
Relations and functions
The solution of the differential equation
{x
4
+6x
2
+2(x+y)} dx-xdy=0
subject to the condition y(1)=0 is
CUET (PG) - 2023
CUET (PG)
Mathematics
Solution of Differential Equations
Which property is true for convolution integral?
A.$ h_1(t)*h_2(t)=h_2(t)*h_1(t) $
B. $[h_1(t)+h_2(t)]* h_3(t) = h_1(t)* h_3 (t) +h_2 (t) * h_3(t)$
C. $[h_!(t)+h_2(t)]*h_3(t) = h_1(t)h_3(t)+h_2(t)h_3(t) $
D. $h_1(t)*h_2(t)=h_2(t)h_1(t) $
Choose the correct answer from the options given below.
CUET (PG) - 2023
CUET (PG)
Mathematics
integral
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): If the equation x
2
+ px+q=0 has rational roots and p and q are integers, then the roots are integers.
Reasons (R): A quadratic equation has rational roots if and only if its discriminant is a perfect square of a rational number.
In the light of the above Statements, choose the most appropriate answer from the options given below :
CUET (PG) - 2023
CUET (PG)
Mathematics
Quadratic Equations
The value of
\(∫_0^{2\pi} sin^{2}nxdx\)
, where
\(n∈I\)
, is:
CUET (PG) - 2023
CUET (PG)
Mathematics
integral
If
\(\overrightarrow{r}=x_1\hat{a}_{x_1}+x_2\hat{a}_{x_2}+x_3\hat{a}_{x_3}\)
and
\(|\overrightarrow{r}|=r\)
then
\(div(r^2\nabla(In\;r))\)
is
CUET (PG) - 2023
CUET (PG)
Mathematics
Divergence theorem
Values of
\(K\)
for which the quadratic equation
\(2x^2 - Kx + K=0\)
has equal roots are:
CUET (PG) - 2023
CUET (PG)
Mathematics
Quadratic Equations
To evaluate the double integral
\(\int_0^8\left(\int\limits_{y/2}^{(y/2)+1}\left(\frac{2x-y}{2}\right)dx\right)dy\)
, we make the substitution
\(u=\frac{2x-y}{2}\)
and
\(v=\frac{y}{2}\)
. The integral will reduce to
CUET (PG) - 2023
CUET (PG)
Mathematics
Integration
Two pipes 'A' and 'B' can fill a cistern in 4 minutes and 6 minutes, respectively. If these pipes are turned on alternately for 1 minute each (pipe 'A' is opened first), then how long will it take for the cistern to fill?
CUET (PG) - 2023
CUET (PG)
Mathematics
Pipe and Cistern
Aman travels from P to Q at a speed of 40 km/hour and returns to P by increasing his speed by 50%. What is his average speed for the entire journey?
CUET (PG) - 2023
CUET (PG)
Mathematics
Speed Time and Distance
If an angle a is divided into two parts A and B such that A-B=x and tan A: tan B=k:1, then the value of sinx is
CUET (PG) - 2023
CUET (PG)
Mathematics
Angle between two lines
If
\(\Phi(z)=c_0+c_1z^{-1}\)
, then
\(\oint_{|z|=1}\frac{1+\Phi(z)}{z}dz\)
is
CUET (PG) - 2023
CUET (PG)
Mathematics
Integration
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The state transition matrix represents the free response of the system.
Reason R: The state transition matrix satisfies the homogeneous state equation
In the light of the above statements, choose the most appropriate answer from the options given below :
CUET (PG) - 2023
CUET (PG)
Mathematics
Matrix
The base of a tower is 80m away from a point A on the ground. If the angle of elevation of the top of the tower from A is 45. Calculate the height of the tower.
CUET (PG) - 2023
CUET (PG)
Mathematics
Heights and Distances
If the angle between the two lines 2x
2
+5xy +3y
2
+6x+7y+4=0 is represented by tan
-1
(m), then m is equal to
CUET (PG) - 2023
CUET (PG)
Mathematics
Angle between two lines
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): cos(x
2
), is a periodic function.
Reasons (R): If f(x) is periodic function with periods T and if a,b ∈ R such that a>0 then (ax+b) is periodic with period T/a.
In the light of the above Statements, choose the correct answer from the options given below:
CUET (PG) - 2023
CUET (PG)
Mathematics
Functions
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