A determinant is chosen at random from the se | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) determinant of order $2$ is of the form $\Delta = \begin{vmatrix} a & b \ c & d \end{vmatrix}$.It is equal to $ad - bc$.The total number of ways

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(B) determinant of order $2$ is of the form $\Delta = \begin{vmatrix} a & b \ c & d \end{vmatrix}$.It is equal to $ad - bc$.The total number of ways of choosing $a, b, c,$ and $d$ is $2 	imes 2 	imes 2 	imes 2 = 16$.Now,$\Delta 
eq 0$ if and only if $ad - bc 
eq 0$,which means $ad 
eq bc$.Since $a, b, c, d \in \{0, 1\}$,the possible values for $ad$ and $bc$ are $0$ or $1$.We have $\Delta 
eq 0$ in the following cases:$1$. If $ad = 1$ and $bc = 0$: This happens when $a=1, d=1$ and $(b, c) \in \{(0, 0), (0, 1), (1, 0)\}$. ($3$ cases)$2$. If $ad = 0$ and $bc = 1$: This happens when $(a, d) \in \{(0, 0), (0, 1), (1, 0)\}$ and $b=1, c=1$. ($3$ cases)Total favorable cases = $3 + 3 = 6$.Therefore,the required probability = $\frac{6}{16} = \frac{3}{8}$.

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is

Similar Questions

Which of the following oxides is different from the other three oxides?

Which one of the following reactions is an example of oxidative decarboxylation?

Which one of the following correctly represents the variation of electronegativity $(EN)$ with atomic number $(Z)$ of group $13$ elements?

The pressure of an ideal gas varies with volume as $P = \alpha V$,where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes $m$ times its initial volume. The work done by the gas in the process is

$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

Vedclass Test Series

Exam Paper Generator

Online Exam Module