2 3 3 3 3-2 2 -3-2-1 3 3 4 3 3-3 2 -3-3-1 4 3 5 3 3-4 2 -3-4-1 is equal to

The correct option is A 0 2^ 3 amp; 3^ 3 amp; 3.2^ 2 +3.2+1 3^ 3 amp; 4^ 3 amp; 3.3^ 2 +3.3+1 4^ 3 amp; 5^ 3 amp; 3.4^ 2 ...

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Byju's Answer

Standard XII

Mathematics

Differentiation of a Determinant

2 3 3 3 3...

Question

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 2^{3} & 3^{3} & {3.2}^{2} + 3.2 + 1 3^{3} & 4^{3} & {3.3}^{2} + 3.3 + 1 4^{3} & 5^{3} & {3.4}^{2} + 3.4 + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is equal to

0

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Solution

The correct option is A $0$
$∣ ∣ ∣ ∣ ∣ \begin{matrix} 2^{3} & 3^{3} & {3.2}^{2} + 3.2 + 1 3^{3} & 4^{3} & {3.3}^{2} + 3.3 + 1 4^{3} & 5^{3} & {3.4}^{2} + 3.4 + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$C_{1} \to C_{1} + C_{2}$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2^{3} + {3.2}^{3} + 3.2 + 1 & 3^{3} & {3.2}^{2} + 3.2 + 1 3^{3} + {3.3}^{2} + 3.3 + 1 & 4^{3} & {3.3}^{2} + 3.3 + 1 4^{3} + {3.4}^{2} + 3.4 + 1 & 5^{3} & {3.4}^{2} + 3.4 + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} 3^{3} & 3^{3} & {3.2}^{2} + 3.2 + 1 4^{3} & 4^{3} & {3.3}^{2} + 3.3 + 1 5^{3} & 5^{3} & {3.4}^{2} + 3.4 + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$= 0$

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Similar questions

Q. A company manufactures car batteries of a particular type. The life (in years) of 40 batteries were recorded as follows:

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size

0.5

starting from the interval

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Q. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

\begin{matrix} 2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6 \end{matrix}

Construct a grouped frequency distribution table for this data, using class intervals of size

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starting from the interval

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Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{matrix} 2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6 \end{matrix}$
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{matrix} 2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6 \end{matrix}$
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{matrix} 2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6 \end{matrix}$

The number of batteries having a life of 3.5-4.0 years is:
(Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5)

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∣∣ ∣ ∣∣23333.22+3.2+133433.32+3.3+143533.42+3.4+1∣∣ ∣ ∣∣ is equal to

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 2^{3} & 3^{3} & {3.2}^{2} + 3.2 + 1 3^{3} & 4^{3} & {3.3}^{2} + 3.3 + 1 4^{3} & 5^{3} & {3.4}^{2} + 3.4 + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is equal to