Class 12th

This is a Short Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l}f(z)=\left|z\right|\forall z\in C\\ f(1)=\left|1\right|=1\\ f(-1)=\left|-1\right|=1\\ f(1)=f(-1)\\ But1\ne -1\\ Therefore,itisnotone-ono.\\ Now,letf(z)=y=\left|z\right|.\\ Here,thereisno;pre-imageofnegativenumbers.\\ Hence,itisnotonto.\end{array}$

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (i) and (iv)

(i) As₂O₃ < SiO₂ < P₂O₃ < SO₂ is the order of acid

(ii) AsH₃ <  PH₃ < NH₃ is the correct or enthalpy of vapourization

(iii) S < O < F < Cl is the correct order of more negative gain enthalpy

(iv)  H₂O > H₂Se > H₂Te is the order of thermal stability

This is a Short Answer Type Question as classified in NCERT Exemplar

Sol:

$Given that,$
$\begin{array}{l}f = \left\{\left(1,2\right),\left(3,5\right),\left(4,1\right)\right\}\hfill \end{array}$

$and$
$\begin{array}{l}g = \left\{\left(2,3\right),\left(5,1\right),\left(1,3\right)\right\}\hfill \end{array}$

$\begin{array}{l}Now, fog \left(2\right) = f \left\{g\left(2\right)\right\} = f \left(3\right) = 5\hfill \end{array}$

$\begin{array}{l}fog \left(5\right) = f \left\{g\left(5\right)\right\} = f \left(1\right) = 2\hfill \end{array}$

$\begin{array}{l}fog \left(1\right) = f \left\{g\left(1\right)\right\} = f \left(3\right) = 5\hfill \end{array}$

$\begin{array}{l}fog = \left\{\left(2,5\right),\left(5,2\right),\left(1,5\right)\right\}\hfill \end{array}$

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (iii) and (iv)

The P₄ molecule in white phosphorus has an angular strain, white phosphorus is very reactive.

PCl₅ is ionic in the solid state, with a tetrahedral cation and an octahedral anion.

This is a Short Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l}\left(i\right)Given set of ordered pair is \left\{\left(x,y\right):xisaperson,yisthemotherofx\right\}.\hfill \end{array}$$\begin{array}{l}It represents a function.\hfill \end{array}$

$\begin{array}{l}Here, the image of distinct elements of x under f are not distinct, so it is not an injective but it is a surjective.\hfill \end{array}$

$\begin{array}{l}\left(ii\right)Set of ordered pairs = \left\{\left(a,b\right):aisaperson,bisanancestorofa\right\}\hfill \end{array}$

$\begin{array}{ll}Here, each element of domain does not have a unique image.\hfill & \hfill \end{array}$

$\begin{array}{l}So, it does not represent function.\hfill \end{array}$

This is a Short Answer Type Question as classified in NCERT Exemplar

Sol:

Given that, g = { (1, 1), (2, 3), (3, 5), (4, 7)}.

Here, each element of domain has unique image. So, g is a function.

Now given that, g (x ) = $\alpha$ x + $\beta$

For (1,1) g (1) = $\alpha$ + $\beta$

$\alpha$ + $\beta$ = 1… (i)

For (2,3)   g (2) = 2 $\alpha$ + $\beta$

2 $\alpha$ + $\beta$ = 3 … (ii)

From Equations. (i) and (ii),

2 (1 - $\beta$ ) + $\beta$ = 3

2 - 2 $\beta$ + $\beta$ = 3

2 - $\beta$ = 3

$\beta$ = - 1

If $\beta$ = - 1, then $\alpha$ = 2

$\therefore$ $\alpha$ = 2,  $\beta$ = - 1

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (i) and (iii)

SO₂ is employed as an antichlor, disinfectant, and preservative in the bleaching of wool and silk.

This is a Short Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Given that\hfill \end{array}$$\hfill$$\begin{array}{l}f(x)=x^2- 3x+ 2\hfill \end{array}$ $\begin{array}{ll}f\left\{f(x)\right\} =f\left(x^2-3x+2\right)\hfill & \hfill \end{array}$

$\begin{array}{ll}= {\left(x^2-3x+2\right)}^2- 3\left(x^2-3x+2\right) + 2\hfill & \hfill \end{array}$

$\begin{array}{ll}=x^4+ 9x^2+ 4 - 6x^3- 12x+ 4x^2- 3x^2+ 9x- 6 + 2\hfill & \hfill \end{array}$

$\begin{array}{l}=x^4+ 10x^2- 6x^3- 3x\hfill \end{array}$

$\begin{array}{l}Hence f\left\{f(x)\right\} =x^4- 6x^3+ 10x^2- 3x\hfill \end{array}$

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (i)

Due to its high electronegativity and tiny size, F is the only interhalogen with weaker X-X' bonds and no X-X bonds.

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (ii) and (iv)

Tetrahedral geometry characterises the structure of a white phosphorus molecule.

Phosphorus has a valency of 5, and there are four phosphorus atoms in total. As a result, there will be a total of 4*5=20 valence electrons.

As a result, each P atom will have one lone pair of electrons, and each covalent bond (two electrons) will be established.

In a molecule of white phosphorus, there will be four lone pairs of electrons and six P-P single bonds in total.