CUET · MATHS · PYQ PAPER 2023

All positive integral powers of a symmetric matrix are:

A Skew-symmetric
B Diagonal
C Symmetric
D Identity matrix

Verified Solution

Answer & Solution

Correct Answer

(C) Symmetric

Step-by-step Solution

Detailed explanation

\( A^T = A \) \( (A^n)^T = (A^T)^n = A^n \) Symmetric

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Find the area of the region bounded by the two parabolas \(y=x^2\) and \(y^2=x\) :

CUET 2023 Easy
If \(e^y=\log x\), then which of the following is true?

CUET 2025 Easy
The points on the curve \(2 x=y^2\) which are nearest to the point \((5,0)\) lie in
A. I Quadrant
B. II Quadrant
C. III Quadrant
D. IV Quadrant
Choose the correct answer from the options given below:

CUET 2023 Medium
The set of value of \(x\) for which the angle between the \(\vec{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}\) and \(\vec{b}=7 \hat{i}-2 \hat{j}+x \hat{k}\) is obtuse is :

CUET 2023 Medium
The area of the region bounded by the curves \(y=x^2+2, y=-x, x=0\) and x = 1 is :

CUET 2023 Hard
If the matrix \(\left[\begin{array}{ccc}0 & 7 & -12 \\ -7 & 0 & -5 \\ 2 a & 5 & 3 b\end{array}\right]\) is skew-symmetric, then the value of \((4 a+3 b)\) is :

CUET 2025 Hard

Explore more questions on app

From CUET

Match List - I with List - II
List-I List-II
(A) Resonant frequency (I) \( \frac{\omega L}{R} \)
(B) Quality factor (II) \( 2\pi f L \)
(C) \( X_L \) (III) \( \frac{1}{2\pi\sqrt{LC}} \)
(D) \( X_C \) (IV) \( 1/2\pi f c \)

Choose the correct answer from the options given below :

CUET 2023 Medium
The general solution of the differential equation \(x\frac{d y}{d x}+2 y=x^2,x\neq 0\) is:

CUET 2023 Easy
The decomposition of N\(_2\)\(\mathrm{O}_5\) in CCl\(_4\) at 318K has been studied by monitoring the concentration of N\(_2\)\(\mathrm{O}_5\) in the solution. Initially, the concentration of N\(_2\)\(\mathrm{O}_5\) is 2.33 mol/L and after 184 minutes, it is reduced to 2.08 mol/L. The reaction takes place according to the equation
2N\(_2\)\(\mathrm{O}_5\)(g) \(\rightarrow\) 4NO\(_2\)(g) + O\(_2\)(g)
The average rate of this reaction in different units will be:

CUET 2025 Hard
If \(\vec{a}\) and \(\vec{b}\) are two unit vectors and \(\vec{a}+\vec{b}\) is also a unit vector, the magnitude of \(\vec{a}-\vec{b}\) is

CUET 2025 Hard
What is the full form of ELISA ?

CUET 2023 Easy
Observe the given diagram and answer the following question :

Genetically engineered insulin was made by Eli Lilly in 1983 by using :

CUET 2023 Medium

Explore more questions on app

List-I	List-II
(A) Resonant frequency	(I) \( \frac{\omega L}{R} \)
(B) Quality factor	(II) \( 2\pi f L \)
(C) \( X_L \)	(III) \( \frac{1}{2\pi\sqrt{LC}} \)
(D) \( X_C \)	(IV) \( 1/2\pi f c \)