List of top Mathematics Questions asked in CUET (PG)

If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then \(\frac{A1+A2}{G1G2}\) is equal to
Renu speaks truth in 70% of the cases and Bina in 75% of the cases. The percentage of ceses they are likely to contradict each other in stating the same fact is
A boat goes 12 km in one hour along the stream and 6 km in one hour against the stream. The speed of the stream in km/h is:
If sin β is the GM between sin a and cos a, then cos 2β is equal to
If A = \(\begin{bmatrix}        2 & 3 & 1           \\[0.3em]        0 & -1           & 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 2 & -1  \\[0.3em]  0 & -1  & 3 \end{bmatrix}\), what is the value of (2A-3B)?
Given below are two statements:
If \(z_1\) and \(z_2\) are complex numbers
Statement-1 : \(arg(\frac{z_1} {z_2})=arg(z_1)-arg(z_2)\)
Statement-II : \(|z_1+z_2|^2=|z_1|^2+|z_2|^2-2Re(z_1\bar z_2)\)
In the light of the above statements, 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: An elevator starts with m passengers and stops at n floors (m \(\leq\) n). The probability that no two passengers alight at the same floor is \(\frac{^np_m}{m_n}\)
Reason R: If (n + 1) p is an integer, say m, then\(p(x=r)= ^nC_rp^Ω(1-p)^{n-Ω} \)is maximum when r = m or r = m -1
In the light of the above statements, choose the most appropriate answer from the options given below :
Match List-I and List-II
LIST I LIST II 
A.8 : 81 :: 64 : ?I.290
B.182 : ? :: 210 : 380II.132
C.42 : 56 :: 110 : ?III.342
D.48 : 122 :: 168 : ?IV.625

Choose the correct answer from the options given below:
The solution of (x2 -√2y) dx + (y2 - √2x) dy = 0 is given by
The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c1 and c2 are arbitrary constants)
The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c1 and c2 are arbitrary constants)
The orthogonal trajectories of the family of curves y = \(ax^3\) is
The solution x1 = 1, x2 = 1, x3 = 0 and z = 3 to the system of equations
x1+x2+x3=2
x1+x2-x3=2
x1,x2,x3≥0
which minimizes z = x1 + 2x2 + 3x3 is
The extreme points of the set \({(x, y); |x|≤2,|y|≤2}\) are
If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is
The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
The area of the region bounded by the curve x2=4y and the straight line x = 4y - 2 is
The area of region bounded by the curve y2=x, the y-axis and between y = 2 and y = 4 is
The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) is:
If P(x) is a polynomial of degree 10 with leading coefficient as 11 and having (x-1), (x-2), (x-3),...(x-10) as factor, then the coefficient of x9 in P(x) is
The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?
If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?
Function f(x)=(x+1)cotx is continuous at x = 0, then the value of f(0) is
Consider the linear mapping F: R2 →R2 defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R2: E= {e1, e2} = {(1, 0), (0, 1)} and S = {u1, u2} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is: