List of top Mathematics Questions asked in CUET (UG)

Let \(A = [a_{ij}]\) be a 2×2 matrix such that \(aij=\frac{|-3i + j|}{2}\)  then \(a_{21}\) is :

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

If, A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I-A)^3+A^2+I\) is:

If \(A=\begin{bmatrix} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\), \(B=\begin{bmatrix} 1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) and AB = I₃, where I₃ is the unit matrix of order 3 × 3, then x + y is equal to :

If \(A\)=\( \begin{vmatrix}  3  & 1  \\[0.1em]   -1 & 2  \end{vmatrix}\) then \(A^2-5A=\)

If \(A=\begin{pmatrix}     1 & -2 & 3  \\[0.3em]   4 & 2 &5 \end{pmatrix}\) and \(A=\begin{pmatrix}     1 & 3   \\[0.3em]   4 & 5  \\[0.3em]   2&1 \end{pmatrix}\)and \(BA=(b_{ij})\),then \(b_{21}+b_{32}=\)

The value of 2y-3x, if
\(2\begin {bmatrix}x &5\\ 7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\ 1&2\end{bmatrix}=\begin{bmatrix}7&6 \\15&14\end{bmatrix}\) is:

If \(\begin{bmatrix}3& 2x + 5y &-2 \\x + 4y  &7 &-5\end{bmatrix}=\begin{bmatrix}3 &10&-2\\ 2&7&-5\end{bmatrix}\) Then the values of x and y are:

If \(\begin{bmatrix} 4x & 5x-7 \\[0.3em] 4x & 2x+y\end{bmatrix}\)=\(\begin{bmatrix} x+6 & y \\[0.3em] 7y-13 & 7\end{bmatrix}\) then the value of 2x + y is:

If A=\(\begin{bmatrix} 2&3 \\ -1&1\end{bmatrix}\)and \(A^2-3A+kI = 0\) then the value of k is:

If \(A= \begin{bmatrix}1&√3&0 \\-√3&1&0 \\ 0&0&2 \end{bmatrix}\) and \(B=\begin{bmatrix}√3&1&0 \\-1&√3&0 \\ 0&0&2 \end{bmatrix}\) then AB is equal to :

For matrix \(A = \begin{bmatrix}3&1\\ 7&5\end{bmatrix}\), the values of x and y so that \(A^2+xI=yA\) are:

If A = \(\begin{bmatrix} 2 & 1 \\[0.3em] 1 & 4 \\[0.3em] -1 & 6 \\[0.3em] 0&7 \end{bmatrix}\) and B= \(\begin{bmatrix} 1 & 2&3&0 \\[0.3em] 2 & -1 & 6&7\end{bmatrix}\) then

If \(\begin{bmatrix}      1 & 2  \\[0.3em]    3  &4  \end{bmatrix}\)\(\begin{bmatrix}      3& 1  \\[0.3em]    2  &5  \end{bmatrix}\)\(=\begin{bmatrix}      7 & 11  \\[0.3em]    K&23  \end{bmatrix}\),then the value of k is

If \(\begin{bmatrix} a+2&3b+2c\\c+3&7d+6 \end{bmatrix}=\begin{bmatrix} 2&-3\\3c&-8 \end{bmatrix}\), then the values of a,b,c and d are.

If the matrix \(A=\begin{bmatrix} 5&4a+6\\a+12&a+3 \end{bmatrix} \)is a symmetric matrix, then the value of a is:

Match List - I with List - II.

List - I	List -II
(A) t-distribution	(I)sample size\(\geq30\)
(B) Sample mean	(II)\(X\)
(C) Population mean	(III)degree of freedom
(D)Z-distribution	(IV)\(\mu\)

Choose the correct answer from the options given below:

The index number of base yera is :

Match List I with List II:

List I		List II
A.	Marshall Edgeworth's Index Number	I.	\(\frac{\sum p_1q_0}{\sum p_0q_0}\times100\)
B.	Laspeyre's Index Number	II.	\(\sqrt{\frac{\sum p_1q_0}{\sum p_0q_0}\times\frac{\sum p_1q_1}{\sum p_0q_1}}\times100\)
C.	Fisher's Ideal Index Number	III.	\(\frac{\sum p_1q_1}{\sum p_0q_1}\times100\)
D.	Paasche's Index Number	IV.	\(\frac{\sum p_1(q_0+q_1)}{\sum p_0(q_0+q_1)}\times100\)

Consider the table below on the quantities of commodities alongside their prices in the year 2020 and 2022.

Commodity	Prices (₹)		Quantities
	In 2020 Year	In 2022 Year	In 2020 Year	In 2022 Year
A	1	2	5	6
B	3	4	3	4
C	5	6	2	5
D	4	5	1	3
E	3	4	4	6

The value of ∑p₁q₀ is :

Match List I with List II

LIST I		LIST II
A.	Weight is considered as quantity in base year in,	I.	Paasche's index number
B.	Weight is considered as quantity in current year in,	II.	Fisher's index number
C.	The index number which is called as ideal index number is,	III.	Marshall-Edgeworth's index number
D.	Weight is taken as the average of the base year quantity and current year quantity in	IV.	Laspeyre's index number

Choose the correct answer from the options given below:

The condition on a and b, such that for \(y = \frac{a}{x}-\frac{b}{x²}\), \(\frac{dy}{dx} =0\) at x=1 is:

For any two non zero vectors \(\vec{a}\) and \(\vec{b}\)
A. If \(|\vec{a}| = |\vec{b}|\)then \(\vec{a} = \vec{b}\)
B. If \(\vec{a} = \vec{b}\) then \(|\vec{a}| = |\vec{b}|\)
C. \(\vec{a} . \vec{b}=\vec{b} . \vec{a}\)
D. \(\vec{a} \times \vec{b}=\vec{b} \times \vec{a}\)
E. area of the parallelogram = \(\frac{1}{2} |\vec{a} \times \vec{b}|\). where \(\vec{a}\) and \(\vec{b}\) represent resent the diagonals of the parallelogram.
Choose the correct answer from the options given below:

In a \(\angle\)\(ABC\) right angled at A, if \(\triangle\)\(ABC=60°\) and\( AC=4\) units, then length of \(BC\) (in units) is :

If A is a symmetric matrix and n ∈ N, then Aⁿ is :