List of top Mathematics Questions asked in CUET (PG)

If \(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\) and \(r=\sqrt{x^2+y^2+z^2}\), then grad \((\frac{1}{r})\) is equal to :
Which of the following set is convex?
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 x2+ y2+z2 = 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:
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:
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:
The function
\[f(x,y) =   \begin{cases} \frac{x^3-y^3}{x^2+y^2} ,when \space x≠0, y≠0.\\ k, when \space x = 0, y=0   \end{cases}\]
is continuous at (0,0), then k is equal to:
The set of all points, where the function \(f(x)=\frac{x}{(1+|x|)}\) is differentiable, is
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 :
The general solution of the differential equation \(2x^2 \frac{d^2y}{dx^2}=x\frac{dy}{dx}-6y=0\) is :
Which one of the following is harmonic function
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 ifII.A= -A'
C.If A is any square matrix thenIII.A+A' is a symmetric matrix
D.If A is any square matrix thenIV.A-A' is a skew symmetric matrix
Choose the correct answer from the options given below:
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
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:
The volume generated by the revolution of the cardioid \(r = a(1-\cosθ)\) about its axis is:
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:
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
The solution of the differential equation
{x4+6x2+2(x+y)} dx-xdy=0
subject to the condition y(1)=0 is
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.
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): If the equation x2+ 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 :
The value of \(∫_0^{2\pi} sin^{2}nxdx\), where \(n∈I\), is:
Values of \(K\) for which the quadratic equation \(2x^2 - Kx + K=0\) has equal roots are:
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?
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?
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
If the angle between the two lines 2x2+5xy +3y2 +6x+7y+4=0 is represented by tan-1(m), then m is equal to