A matrix P of order 2 × 3 with each entry 0 or 1 and α is a scalar which is 3 or 4. If R = αA, the number of matrices R formed is :
- 63
- 64
- 128
- 127
The Correct Option is B
Solution and Explanation
Top Questions on Matrices
Let $ A = \begin{bmatrix} \alpha & -1 \\6 & \beta \end{bmatrix},\ \alpha > 0 $, such that $ \det(A) = 0 $ and $ \alpha + \beta = 1 $. If $ I $ denotes the $ 2 \times 2 $ identity matrix, then the matrix $ (1 + A)^5 $ is:
Let $A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \end{bmatrix}$. If for some $\theta \in (0, \pi)$, $A^2 = A^T$, then the sum of the diagonal elements of the matrix $(A + I)^3 + (A - I)^3 - 6A$ is equal to
- If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:
Let $ A $ be a $ 3 \times 3 $ matrix such that $ | \text{adj} (\text{adj} A) | = 81.
$ If $ S = \left\{ n \in \mathbb{Z}: \left| \text{adj} (\text{adj} A) \right|^{\frac{(n - 1)^2}{2}} = |A|^{(3n^2 - 5n - 4)} \right\}, $ then the value of $ \sum_{n \in S} |A| (n^2 + n) $ is:- Let $ A $ be a matrix of order $ 3 \times 3 $ and $ |A| = 5 $. If $ |2 \, \text{adj}(3A \, \text{adj}(2A))| = 2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma}, \quad \alpha, \beta, \gamma \in \mathbb{N} $ then $ \alpha + \beta + \gamma $ is equal to
Questions Asked in CUET exam
- In the figure given below, APB is a curved surface of radius of curvature 10 cm separating air and a transparent material \((μ = \frac{4}{3} ).\) A point object O is placed in air on the principal axis of the surface 20 cm from P. The distance of the image of O from P will be _____.
Fill in the blank with the correct answer from the options given below - Match the words in List-I with their definitions in List-II :
List-I (Words) List-II (Definitions) (A) Theocracy (I) One who keeps drugs for sale and puts up prescriptions (B) Megalomania (II) One who collects and studies objects or artistic works from the distant past (C) Apothecary (III) A government by divine guidance or religious leaders (D) Antiquarian (IV) A morbid delusion of one’s power, importance or godliness Choose the correct answer from the options given below :- CUET (UG) - 2024
- Vocabulary
- Magnetic moment of a thin bar magnet is ‘M’. If it is bent into a semicircular form, its new magnetic moment will be________.
Fill in the blank with the correct answer from the options given below.- CUET (UG) - 2024
- Magnetic Effects of Current and Magnetism
- A metallic wire of uniform area of cross-section has a resistance \(R,\) resistivity \(ρ,\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity, and power rating at V volts are now denoted by \(R'\), \(ρ'\), and \(P' \)respectively. The corresponding values are correctly related as __________.
Fill in the blank with the correct answer from the options given below- CUET (UG) - 2024
- Current electricity
- The refractive index of the material of an equilateral prism is √2. The angle of minimum deviation of the prism is______.
Fill in the blank with the correct answer from the options given below.