If matrix
$A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$
and $A^2 = kA$, then the value of $k$ is:
Show Hint
- 1
- -2
- 2
- -1
The Correct Option is C
Solution and Explanation
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \). The determinant of \( A^3 \) is:
- Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.
- The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
- If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
- If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
Questions Asked in CBSE CLASS XII exam
- What type of cell is mercury cell? Why is it more advantageous than dry cell?
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Electrochemistry
The standard electrode potential for Ni²⁺/Ni couple is -0.25 V and for Ag⁺/Ag couple is 0.80 V. These two couples are connected to make an electrochemical cell. The redox reaction is spontaneous. The cell potential will be:
- CBSE Compartment XII - 2024
- Electrochemistry
- In a group activity class, there are 10 students whose ages are 16, 17, 15, 14, 19, 17, 16, 19, 16 and 15 years. One student is selected at random such that each has equal chance of being chosen and age of the student is recorded.
On the basis of the above information, answer the following questions : - Ahousing society wants to commission a swimming pool for its residents. For this, they have to purchase a square piece of land and dig this to such a depth that its capacity is 250 cubic metres. Cost of land is 500 per square metre. The cost of digging increases with the depth and cost for the whole pool is 4000 (depth)2. Suppose the side of the square plot is x metres and depth is h metres.
On the basis of the above information, answer the following questions
Given:- Square plot side = x metres
- Depth = h metres
- Volume = x2h = 250 cubic metres
- Cost of land: 500 per sq.metre
- Cost of digging: 4000 ×h- CBSE CLASS XII - 2023
- CBSE Compartment XII - 2023
- Applications of Derivatives
In an agricultural institute, scientists conduct experiments with varieties of seeds to grow them in different environments for producing healthy plants and obtaining higher yields.
A scientist observed that a particular seed grew very fast after germination. He recorded the growth of the plant from the time of germination and modeled its growth with the function:
Given:
\( f(x) = \frac{1}{3}x^3 - 4x^2 + 15x + 2 \), \( 0 \leq x \leq 10 \)
where \( x \) is the number of days the plant is exposed to sunlight.
On the basis of the above information, answer the following questions:- CBSE CLASS XII - 2023
- CBSE Compartment XII - 2023
- Applications of Derivatives