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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

The negative of a matrix is obtained by multiplying it by ___.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t A b e a m a t r i x \\ ∴ - A = - 1 . A \\ H e n c e, n e g a t i v e o f a m a t r i x i s o b t a i n e d b y m u l t i p l y i n g i t b y - 1 . \end{array}$

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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

Sum of two skew symmetric matrices is always ___ matrix.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t A a n d B b e a n y t w o m a t r i c e s \\ ∴ F o r s k e w s y m m e t r i c m a t r i c e s \\ A = - A^{'} \dots (i) \\ a n d B = - B^{'} \dots (i i) \\ A d d i n g (i) a n d (i i) w e g e t \\ A + B = - A^{'} - B^{'} \\ \Rightarrow A + B = - (A^{'} + B^{'}), s o A + B i s s k e w s y m m e t r i c m a t r i x . \\ H e n c e, t h e s u m o f t w o s k e w s y m m e t r i c m a t r i c e s i s a l w a y s s k e w s y m m e t r i c m a t r i c e s . \end{array}$

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Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven

If the equilibrium constant for $A ⇌ B + C$ is $K_{(eq)}^{(1)}$ and that of $B + C ⇌ P$ is $K_{(eq)}^{(2)}$ , the equilibrium constant for $A ⇌ P$ is:

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alok kumar singh

Contributor-Level 10

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Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Six

The process that is NOT endothermic in nature is:

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alok kumar singh

Contributor-Level 10

Sol. $2 P b {({N O}_{3})}_{2} \overset{Δ}{?} 2 P b O + 2 {N O}_{2} + O_{2}$

$2 {N O}_{2} ? N_{2} O_{4}$ colourless

$N_{2} O_{4} + 2 N O ? 2 N_{2} O_{3}$

Oxidation state in $N_{2} O_{3}$ is +3

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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

___ matrix is both symmetric and skew symmetric matrix.

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Payal Gupta

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$N u l l m a t r i x i . e . [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] o r [\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}] i s b o t h s y m m e t r i c a n d s k e w s y m m e t r i c m a t r i x .$

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Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Twelve

Among the following compounds, which one has the shortest $C - C l$ bond?

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alok kumar singh

Contributor-Level 10

Sol. ${C r}^{2 +}$ and ${F e}^{2 +}$ both have 4 unpaired electrons.

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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

On using elementary row operation $R_{1} \to R_{1} - 3 R_{2}$ in the following matrix equation:

$[\begin{matrix} 4 & 2 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}],$ we have:

(A) $[\begin{matrix} - 5 & - 7 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}]$

(B) $[\begin{matrix} - 5 & - 7 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}] [\begin{matrix} - 1 & - 3 \\ 1 & 1 \end{matrix}]$

(C) $[\begin{matrix} - 5 & - 7 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & 2 \\ 1 & - 7 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 7 \end{matrix}]$

(D) $[\begin{matrix} 4 & 2 \\ - 5 & - 7 \end{matrix}] = [\begin{matrix} 1 & 2 \\ - 3 & - 3 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}]$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e h a v e, [\begin{matrix} 4 & 2 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}] \\ Using e l e m e n t a r y r o w t r a n s f o r m a t i o n R_{1} \to R_{1} - 3 R_{2}, w e g e t \\ [\begin{matrix} - 5 & - 7 \\ 3 & 3 \end{matrix}] = [\begin{matrix} 1 & - 7 \\ 0 & 3 \end{matrix}] [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}] \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

On using elementary column operations $C_{2} \to C_{2} - 2 C_{1}$ in the following matrix equation: $[\begin{matrix} 1 & - 3 \\ 2 & 4 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 4 \end{matrix}],$ we have:

(A) $[\begin{matrix} 1 & - 5 \\ 0 & 4 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ - 2 & 2 \end{matrix}] [\begin{matrix} 3 & - 5 \\ 2 & 0 \end{matrix}]$

(B) $[\begin{matrix} 1 & - 5 \\ 0 & 4 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & - 5 \\ 0 & 2 \end{matrix}]$

(C) $[\begin{matrix} 1 & - 5 \\ 2 & 0 \end{matrix}] = [\begin{matrix} 1 & - 3 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & 1 \\ - 2 & 4 \end{matrix}]$

(D) $[\begin{matrix} 1 & - 5 \\ 2 & 0 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & - 5 \\ 2 & 0 \end{matrix}]$

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n t h a t : [\begin{matrix} 1 & - 3 \\ 2 & 4 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 4 \end{matrix}] \\ Using C_{2} \to C_{2} - 2 C_{1}, w e g e t \\ [\begin{matrix} 1 & - 5 \\ 2 & 0 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 3 & - 5 \\ 2 & 0 \end{matrix}] \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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Class 12th Chemistry NCERT Exemplar Solutions Class 12th Chapter Three

$250 m L$ of a waste solution obtained from the workshop of a goldsmith contains $0.1 M$ ${A g N O}_{3}$ and $0.1 M A u C l$ . The solution was electrolyzed at $2 V$ by passing a current of $1 A$ for 15 minutes. The metal/metals electrodeposited will be : $(E_{{A g}^{+} / A g}^{o} = 0.8 V, E_{{A u}^{+} / A u}^{o} = 1.69 V)$

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alok kumar singh

Contributor-Level 10

Sol. Balmer series lies in the visible region.

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Class 12th Maths NCERT Exemplar Solutions Class 12th Chapter Three

For any two matrices $A$ and $B$ , we have

(A) AB = BA

(B) AB $AB \neq BA$ BA

(C) AB = O

(D) None of the above

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Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e k n o w t h a t f o r a n y t w o m t r i c e s A a n d B, w e m a y h a v e A B = B A, A B \neq B A a n d A B = 0, b u t \\ i t i s n o t a l w a y s t r u e . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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