Recent questions tagged engineering-mathematics

According to me both are inferencing each other, please someone suggest whether D is correct or B, if B is correct please provide a valid reason I could not understand wh...

Differentiate $f(x)=\sin x + e^x$.$\cos x + e^x$ $-\cos x + e^x$ $\sin x + e^x$ $\cos x - e^x$

$P(A)=0.3$, $P(B)=0.2$, $P(A \cup B)=0.5$. Which is true?$A$ and $B$ are mutually exclusive. $A$ and $B$ are independent. Such probabilities are not possible. Both A and ...

$P(A)=0.2$, $P(B)=0.3$, $P(A \cup B)=0.6$. Then A and B are?$A$ and $B$ are mutually exclusive $A$ and $B$ are independent Such probabilities are not possible Both A and ...

$P(A)=0.5$ and $P(B)=0.3$, $P(A \cap B)=?$(The answer depends on the relationship: Independent or Mutually Exclusive)

Find all number of ordered combinations of $3$ positive integers whose sum is $10$, where $(2,2,6)$ and $(6,2,2)$ are considered different combinations.$28$ $32$ $36$ $45...

Find the number of permutations of the numbers $\{1,2,3,4,5\}$ that generate $5$-digit numbers such that no two even numbers are adjacent to each other and the number for...

In a box, there are $4$ coins. One coin is biased with probability of head $0.8$, and the other $3$ coins are fair coins with probability of head $0.5$. If one coin is ch...

Find the rank of the matrix $A$ if $A^{-1}$ exists, where $A=\begin{bmatrix}1&2&a\\2&4&b\\3&c&6\end{bmatrix}$.$0$ $1$ $2$ $3$

Find the sum of eigenvalues of the given $4 \times 4$ matrix.$0$ $1$ $2$ $3$

If $P$ is of order $2 \times 2$, $Q$ is of order $3 \times 2$, and $R$ is of order $2 \times 1$, which one of the following matrix products is correct?$Q \times R \times ...

Which of the following scenarios is most likely to have the mean significantly less than the mode?Outcomes obtained from rolling a fair die, uniform distribution. Heights...

Let $A$ be a 5 x 5 matrix and $\lambda_1$ be one of the eigen value of $A$ such that $\text{rank}(A-\lambda_1I) = 2$, then geometric multiplicity of $\lambda_1$ is ______...

If matrix A has full rank, then what are the valid conclusions from the followingA is a full row rank matrixA is a full column rank matrixA is invertibleCan't say

If $A$ is a $2 \times 2$ matrix such that $\operatorname{trace}(A)=\operatorname{det}(A)=3$, then what is the $\operatorname{trace}\left(A^{-1}\right)$ ?$1$ $\left(\frac{...

Let $A$ be an $n \times n$ invertible matrix with real entries whose row sums are all equal to $c$. Consider the following statements:Every row in the matrix $2 A$ sums t...

Suppose the rank of the matrix $$ \left(\begin{array}{llll} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{array}\right) $$ is $2$ for some real numbers $a$ and $b$...

If B has eigenvalues $1,2,3, \mathrm{C}$ has eigenvalues $4,5,6$, and D has eigenvalues $7,8,9$, what are the eigenvalues of the $6 \times 6$ matrix $\mathrm{A}=\left[\be...

Consider the family of functions$$g(x)=a \ln (x)+\frac{b}{x}$$defined for $x>0,$ where $a$ and $b$ are positive constants.Any function $g(x)$ in this family has only one ...

Which of the following is/are TRUE?If $\lim _{x \rightarrow 5} f(x)=0$ and $\lim _{x \rightarrow 5} g(x)=0$, then $\lim _{x \rightarrow 5} \frac{f(x)}{g(x)}$ does not exi...

The derivative of $g(x)=e^{\sqrt{x}}$ is$\sqrt{x} e^{\sqrt{x}-1}$ $2 e^{\sqrt{x}} x^{-0.5}$ $\frac{0.5 e^{\sqrt{x}}}{\sqrt{x}}$ $e^{\sqrt{x}}$

Consider a $4 \times 4$ matrix $M$. Suppose that the following four entries of the matrix are known to be zero.For which of the following cases must the determinant of th...