Question
The set of all points where the function $f(x)=x+|x|$ is differentiable, is
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Which of the following is correct?
- Determinant is a square matrix.
- Determinant is a number associated with a matrix.
- Determinant is a number associated with a square matrix.
- None of these.
If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a$:$
→Let $\text{X}=\begin{bmatrix}\text{x}_1\\\text{x}_2\\\text{x}_3\end{bmatrix},\text{A}=\begin{bmatrix}1&-1&2\\2&0&1\\3&2&1\end{bmatrix}\text{and }\text{B}=\begin{bmatrix}3\\1\\4\end{bmatrix}$. If $AX = B,$ then $X$ is equal to:
→Two persons $A$ and $B$ take turns in throwing a pair of dice.The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game is.
→Find the value of $\lambda$ for which the vectors $3 \hat{i}-6 \hat{j}+\hat{k}$ and $2 \hat{i}-4 \hat{j}+\lambda \hat{k}$ are parallel.
→If $\vec{\text{a}},\vec{\text{b}}$ represent the diagonals of a rhombus, then:
→- $\vec{\text{a}}\times\vec{\text{b}}=\vec{0}$
- $\vec{\text{a}}.\vec{\text{b}}=0$
- $\vec{\text{a}}.\vec{\text{b}}=1$
- $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{a}}$
The general solution of differention eqution $\frac{\text{y}\ \text{dx}-\text{x}\ \text{dy}}{\text{y}}=0$ is:
→$\text{A}^2=\text{I}\Rightarrow$
→- $|\text{A}|=0$
- $|\text{A}|=1$
- $|\text{A}|=-1$
- $|\text{A}|=\pm1$
The value of $\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+k \cdot(\hat{i} \times \hat{j})$ is:
→If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$, then the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$ is
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