CUET · MATHS · PYQ PAPER 2023
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:
- A \(0\)
- B \(I\)
- C \(2I\)
- D \(4I\)
Answer & Solution
Correct Answer
(C) \(2I\)
Step-by-step Solution
Detailed explanation
\((I - A)^3 = I^3 - 3I^2A + 3IA^2 - A^3 = I - 3A + 3A^2 - A^3\) \(A^2 = A \implies A^3 = A^2 \cdot A = A \cdot A = A^2 = A\) \((I - A)^3 = I - 3A + 3A - A = I - A\) \((I - A)^3 + A^2 + I = (I - A) + A + I\) \(= I - A + A + I = 2I\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- Let y be a discrete random variable, taking values \(y_1, y_2, y_3, ..., y_n\) with probabilities \(p_1, p_2, p_3, ..., p_n\) respectively. Then the standard deviation of y is given by:CUET 2023 Easy
- A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is:
[Given that (1.6) \({ }^{\frac{1}{5}}=1.098\) ]CUET 2025 Easy - \(\int\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x\) is equal toCUET 2025 Easy
- The maximum value of the objective function \(Z=2 x+y\) of an LPP, subject to the constraints \(x \leq 6, y \leq 2, x-y \leq 0\), \(x \geq 0, y \geq 0\), is:CUET 2025 Hard
- For \(x>1, \int \frac{e^{7 \log x}-e^{5 \log x}}{e^{5 \log x}-e^{4 \log x}} d x\) equals.CUET 2025 Easy
- Match List-I with List-II
Choose the correct answer from the options given below :List-I (Example) List-II (Time-series component) (A) Labour strike (I) Secular-trend (B) Continuous decline in death rate (II) Seasonal (C) Rise in prices before Diwali (III) Cyclical (D) Rise and fall of the share-market (IV) Irregular CUET 2025 Medium
More PYQs from CUET
- Genetically modified organisms have been useful in many ways. Which one
of the following statements is not correct in the case of GMO plants?CUET 2025 Medium - On prolonged heating with HI , glucose formsCUET 2023 Medium
- A symmetric double convex lens of power 4D is cut in two halves by plane perpendicular to the principal axis. The power of each half is :CUET 2023 Easy
- When a steady current flows in a metalic conductor of non-uniform cross section. Which of these quantities is constant along the conductor?
A. Current
B. Electric field
C. Drift speed
D. Current density
E. Potential gradient
Choose the correct answer from the options given below:CUET 2023 Hard - The general solution of the differential equation \(\left(x^2-y x^2\right) d y+\left(y^2+x^2 y^2\right) d x=0\) is :CUET 2025 Easy
- If \(\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k},|\vec{b}|=5\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{6}\), then the area of the triangle formed by these two vectors as two sides is :CUET 2023 Easy