NCERT

Find the(v) length of the latus rectum of each of the following ellipses.

Given: $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$…(i) Since, $25>9$ So, above equation is of the form, $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$…(ii)...

Express each of the following angles in radians – 36°

Answer: Formula: Angle in radians = $Angle\,in\,\deg \times \frac{\pi }{180}$ Therefore, Angle in radians =  $36\times \frac{\pi }{180}=\frac{\pi }{5}$

Find the equation of a line parallel to the y – axis at a distance of (i) 6 units to its right (ii) 3 units to its left

Answer : (i) Equation of line parallel to y - axis is given by x = constant, as the x - coordinate of every point on the line parallel to y - axis is 6 i.e. constant. Now the point lies to the right...

Arrange the bonds in order of increasing ionic character in the molecules: LiF, , and .

Solution: The difference in electronegativity between constituent atoms determines the ionic character of a molecule. As a result, the greater the difference, the greater the ionic character of a...

Explain with the help of suitable example polar covalent bond.

Solution: The bond pair of electrons are not shared equally when two unique atoms with different electronegativities join to form a covalent bond. The bond pair is attracted to the nucleus of an...

Define electronegativity. How does it differ from electron gain enthalpy?

Solution: "Electronegativity refers to an atom's ability to attract a bond pair of electrons towards itself in a chemical compound." Sr. No Electronegativity Electron affinity 1 A tendency to...

Write the significance/applications of dipole moment.

Solution: There is a difference in electro-negativities of constituents of the atom in a heteronuclear molecule, which causes polarisation. As a result, one end gains a positive charge, while the...

Although both and are triatomic molecules, the shape of the molecule is bent while that of is linear. Explain this on the basis of dipole moment.

Solution: $CO_2$ has a dipole moment of 0 according to experimental results. And it's only possible if the molecule's shape is linear, because the dipole moments of the C-O bond are equal and...

Use Lewis symbols to show electron transfer between the following atoms to form cations and anions :(iii) Al and N.

Solution: Below is a list of Lewis symbols. To form a cation, a metal atom loses one or more electrons, while a nonmetal atom gains one or more electrons. Ionic bonds are formed between cations and...

Use Lewis symbols to show electron transfer between the following atoms to form cations and anions : (i) K and S (ii) Ca and O

Solution: Below is a list of Lewis symbols. To form a cation, a metal atom loses one or more electrons, while a nonmetal atom gains one or more electrons. Ionic bonds are formed between cations and...

Temperature dependence of resistivity ρ(T) of semiconductors, insulators, and metals is significantly based on the following factors: a) number of charge carriers can change with temperature T b) time interval between two successive collisions can depend on T c) length of material can be a function of T d) mass of carriers is a function of T

The correct answer is a) number of charge carriers can change with temperature T b) time interval between two successive collisions can depend on T

Write the resonance structures for , and

Solution: Resonance is the phenomenon that allows a molecule to be expressed in multiple ways, none of which fully explain the molecule's properties. The molecule's structure is called a resonance...

can be represented by structures 1 and 2 shown below. Can these two structures be taken as the canonical forms of the resonance hybrid representing ? If not, give reasons for the same.

Solution: The positions of the atoms remain constant in canonical forms, but the positions of the electrons change. The positions of atoms change in the given canonical forms. As a result, they...

Explain the important aspects of resonance with reference to the ion.

Solution: However, while the carbonate ion cannot be represented by a single structure, the properties of the ion can be described by two or more different resonance structures. The actual structure...

Define Bond length.

Solution: Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule.

How do you express the bond strength in terms of bond order?

Solution: During the formation of a molecule, the extent of bonding that occurs between two atoms is represented by the bond strength of the molecule. As the bond strength increases, the bond...

Although geometries of and molecules are distorted tetrahedral, bond angle in water is less than that of Ammonia. Discuss.

Solution: Ammonia's central atom (N) has one lone pair and three bond pairs. In water, the central atom (O) has two lone pairs and two bond pairs. As a result, the two bond pairs repel the two lone...

Discuss the shape of the following molecules using the VSEPR model:

Solution: $BeCl_2$ The central atom does not have a lone pair, but it does have two bond pairs. As a result, its shape is AB2, or linear. $BCl_3$ The central atom has three bond pairs but no lone...

Write the favourable factors for the formation of an ionic bond.

Solution: Ionic bonds are formed when one or more electrons are transferred from one atom to another. As a result, the ability of neutral atoms to lose or gain electrons is required for the...

Define the octet rule. Write its significance and limitations

Solution: “Atoms can combine either by transferring valence electrons from one atom to another or by sharing their valence electrons in order to achieve the closest inert gas configuration by having...

Draw the Lewis structures for the following molecules and ions :

Solution: The lewis dot structures are:

Write Lewis symbols for the following atoms and ions: Sand and and

Solution: For S and S2- A sulphur atom has only 6 valence electrons, which is a very small number. As a result, the Lewis dot symbol for the letter S is       The presence of a...

Write Lewis dot symbols for atoms of the following elements :e) N f) Br

Solution: Nitrogen atoms have only five valence electrons in total. As a result, the Lewis dot symbol for N is     Bromine, because the atom has only seven valence electrons. As a result,...

Write Lewis dot symbols for atoms of the following elements :c) B d) O

Solution: Boron atoms have only three valence electrons, which is a very small number. As a result, the Lewis dot symbols for B are as follows:     The oxygen atom has only six valence...

Write Lewis dot symbols for atoms of the following elements : a) Mg b) Na

Solution: Only two valence electrons exist in the magnesium atom. As a result, the Lewis dot symbols for Mg are as follows:     Only one valence electron exists in the sodium atom. As a...

Explain the formation of a chemical bond.

Answer: "A chemical bond is an attractive force that holds a chemical species' constituents together." For chemical bond formation, many theories have been proposed, including valence shell electron...

Differentiate the following functions with respect to x:

As per the given question,

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Given there are total $9\;people$ Women occupies even places that means they will be sitting on ${{2}^{nd}},\text{ }{{4}^{th}},\text{ }{{6}^{th}}and\text{ }{{8}^{th}}$  place where as men will be...

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

We have a deck of cards has $4\;kings.$ The numbers of remaining cards are $52.$ Ways of selecting a king from the deck $\Rightarrow {{~}^{4}}{{C}_{1}}=$ Ways of selecting the remaining $4\;cards$...

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

The student can choose $3$ questions from $part\;I$ and $5$ from $part\;II$ Or $4\;questions$ from $part\;I$ and $4$ from $part \;II$ $5$ questions from $part\;I$ and $3$ from $part \;II$

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

We know that there are $5$ vowels and $21$ consonants in English alphabets. Choosing two vowels out of $5$ would be done in $^{5}{{C}_{2}}$ ways Choosing $2$ consonants out of $21$ can be done in...

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

As per the given question,

Evaluate: When (i) n = 6, r = 2 (ii) n = 9, r = 5

, Solution: As per the given question,

Find x. If

Solution: As per the given question,

Compute

Solution: As per the given question,

Is 3! + 4! = 7!?

Consider LHS 3! +4! Computing left hand side, we get $\begin{array}{l} 3 !+4 !=(3 \times 2 \times 1)+(4 \times 3 \times 2 \times 1) \\ =6+24 \\ =30 \end{array}$ Again consider RHS and computing we...

Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is A. 2 units B. 4 units C. 8 units D. 2/√29 units

Solution: It is known to us that the distance between two parallel planes $A x+B y+C z=d_{1}$ and $A x+B y+C z=d_{2}$ is given as...

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then

Solution: It is known to us that the distance of the point $\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)$ from the plane $\mathrm{Ax}+\mathrm{By}+\mathrm{Cz}$ $=\mathrm{D}$ is given...

Find the vector equation of the line passing through the point (1,2,-4) and perpendicular to the two lines: and

Solution: The vector eq. of a line passing through a point with position vector $\vec{a}$ and parallel to a vector $\overrightarrow{\mathrm{b}}$ is...

Find the vector equation of the line passing through and parallel to the planes and

Solution: The vector eq. of a line passing through a point with position vector $\vec{a}$ and parallel to a vector $\vec{b}$ is $\vec{r}=\vec{a}+\lambda \vec{b}$ It is given that the line passes...

Find the equation of the plane passing through (a, b, c) and parallel to the plane

Solution: The eq. of a plane passing through $\left(x_{1}, y_{1}, z_{1}\right)$ and perpendicular to a line with direction ratios $A, B, C$ is given as...

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane

Solution: The vector eq. of a line passing through a point with position vector $\vec{a}$ and parallel to vector $\vec{b}$ is given as...

If the lines are perpendicular, find the value of .

Solution: It is known to us that the two lines $\frac{x-1}{3 k}=\frac{y-2}{1}=\frac{z-3}{-5} \text { and }$ $\frac{\mathrm{x}-1}{3 \mathrm{k}}=\frac{\mathrm{y}-2}{1}=\frac{\mathrm{z}-3}{-5}$ are...

If and are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are

Solution: Let's consider $l, m, n$ be the direction cosines of the line perpendicular to each of the given lines. Therefore, $ll_{1}+m m_{1}+n n_{1}=0 \ldots(1)$ And...

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, –1), (4, 3, –1).

Solution: Let's consider $O A$ be the line joining the origin $(0,0,0)$ and the point $A(2,1,1)$. And let $B C$ be the line joining the points $B(3,5,-1)$ and $C(4,3,-1)$ Therefore the direction...

In the following cases, find the distance of each of the given points from the corresponding given plane. Point Plane (a) (2, 3, -5) x + 2y – 2z = 9 (b) (-6, 0, 0) 2x – 3y + 6z – 2 = 0

Solution: (a) The length of perpendicular from the point $(2,3,-5)$ on the plane $x+2 y-2 z=9 \Rightarrow x+2 y-2 z-9=0$ is $\frac{\left|a x_{1}+b y_{1}+c z_{1}+d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}}$...

Find the vector and Cartesian equations of the planes (a) that passes through the point and the normal to the plane is (b) that passes through the point and the normal vector to the plane is

Solution: (a) That passes through the point $(1,0,-2)$ and the normal to the plane is $\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ Let's say that the position vector of the point $(1,0,-2)$...

In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (a) 2x + 3y – z = 5 (b) 5y + 8 = 0

Solution: (a) $2 x+3 y-z=5$ It is given that The eq. of the plane, $2 x+3 y-z=5 \ldots$. (1) The direction ratio of the normal $(2,3,-1)$ Using the formula,...

Find the shortest distance between the lines whose vector equations are and

Solution: It is known to us that shortest distance between two lines $\vec{r}=\overrightarrow{a_{1}}+\lambda \overrightarrow{b_{1}}$ and $\vec{r}=\overrightarrow{a_{2}}+\mu \overrightarrow{b_{2}}$...

Find the shortest distance between the lines and

Solution: It is known to us that the shortest distance between two lines $\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}$ and $\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$ is given as:...

Find the shortest distance between the lines

Solution: It is known to us that the shortest distance between two lines $\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{1}}+\lambda \overrightarrow{\mathrm{b}_{1}}$ and...

Show that the lines and are perpendicular to each other.

Solution: The equations of the given lines are $\frac{\mathrm{x}-5}{7}=\frac{\mathrm{y}+2}{-5}=\frac{\mathrm{z}}{1}$ and $\frac{\mathrm{x}}{1}=\frac{\mathrm{y}}{2}=\frac{\mathrm{z}}{3}$ Two lines...

Find the values of p so that the lines and are at right angles.

Solution: The standard form of a pair of Cartesian lines is:...

Find the angle between the following pairs of lines: (i) and (ii) and

Solution: Let's consider $\theta$ be the angle between the given lines. If $\theta$ is the acute angle between $\vec{r}=\overrightarrow{a_{1}}+\lambda \overrightarrow{b_{1}}$ and...

Find the vector and the Cartesian equations of the line that passes through the points (3, –2, –5), (3, –2, 6).

Solution: It is given that Let's calculate the vector form: The vector eq. of as line which passes through two points whose position vectors are $\vec{a}$ and $\vec{b}$ is...

Find the vector and the Cartesian equations of the lines that passes through the origin and (5, –2, 3).

Solution: Given: The origin $(0,0,0)$ and the point $(5,-2,3)$ It is known to us that The vector eq. of as line which passes through two points whose position vectors are $\vec{a}$ and $\vec{b}$ is...

The Cartesian equation of a line is Write its vector form.

Solution: It is given that The Cartesian equation is $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2} \ldots \text { (1) }$ It is known to us that The Cartesian eq. of a line passing through a point...

Find the Cartesian equation of the line which passes through the point and parallel to the line given by

Solution: It is given that The points $(-2,4,-5)$ It is known that Now, the Cartesian equation of a line through a point $\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)$ and having...

Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and . is in the direction

Solution: Given: Vector equation of a line that passes through a given point whose position vector is $\vec{a}$ and parallel to a given vector $\vec{b}$ is $\vec{r}=\vec{a}+\lambda \vec{b}$ Let,...

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector

Solution: Given that, Line passes through the point $(1,2,3)$ and is parallel to the vector. It is known to us that Vector eq. of a line that passes through a given point whose position vector is...

Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5).

Solution: The points $(4,7,8),(2,3,4)$ and $(-1,-2,1),(1,2,5)$. Consider $A B$ be the line joining the points, $(4,7,8),(2,3,4)$ and $C D$ be the line through the points $(-1,-2$, 1), $(1,2,5)$. So...

Show that the line through the points (1, –1, 2), (3, 4, –2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Solution: Given that The points $(1,-1,2),(3,4,-2)$ and $(0,3,2),(3,5,6)$. Let's consider $A B$ be the line joining the points, $(1,-1,2)$ and $(3,4,-2)$, and $C D$ be the line through the points...

Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.

Solution: If the direction ratios of two lines segments are proportional, then the lines are collinear. It is given that $\mathrm{A}(2,3,4), \mathrm{B}(-1,-2,1), \mathrm{C}(5,8,7)$ The direction...

If a line has the direction ratios –18, 12, –4, then what are its direction cosines?

Solution: Given that, The direction ratios are $-18,12,-4$ Where, $a=-18, b=12, c=-4$ Consider the direction ratios of the line as $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ Direction cosines are...

Integrate the function in

As per the given question, Let I =  =  =  =  =  =  =  =  =

Solution:

Elements of group 14 (a) exhibit oxidation state of only (b) exhibit oxidation state of and (c) form and ion (d) form and ions

Solution: (b) Group 14 components have 4 valence electrons. Thus, bunch oxidation status is $+4$. In any case, the lower oxidation state turns out to be progressively steady because of the inactive...

An aqueous solution of borax is

Solution: (b) Borax is a strong base salt (NaOH) and a feeble corrosive $\left(\mathrm{H}_{3} \mathrm{BO}_{3}\right)$. In this way, it is essential thing in nature.

Give one method for industrial preparation and one for laboratory preparation of CO and each.

Solution: Carbon dioxide CO2 can be ready in the lab through the activity of weaken hydrochloric corrosive on calcium carbonate. Their response is as per the following: CO2 is industrially ready by...

Write balanced equations for: (ii) (iii) (iv) (v) (vi)

Solution: The balanced equations are as follow:

A certain salt gives the following results. (i) Its aqueous solution is alkaline to litmus. (ii) It swells up to a glassy material on strong heating. (iii) When conc. is added to a hot solution of , a white crystal of an acid separates out Write equations for all the above reactions and identify X, , and .

Solution: The salt given to litmus is antacid. $X$ is, subsequently, a salt with a solid base, and a feeble corrosive. When $X$ is warmed unnecessarily, it additionally enlarges to frame material...

When metal is treated with sodium hydroxide, a white precipitate (A) is obtained, which is soluble in excess of to give soluble complex (B). Compound (A) is soluble in dilute HCI to form compound (C). The compound (A) when heated strongly gives (D), which is used to extract the metal. Identify (X), (A), (B), (C) and (D). Write suitable equations to support their identities.

Solution: The given metal $X$ gives sodium hydroxide to a white accelerate, and the encourage breaks up surpassing sodium hydroxide. $X$ must, consequently, be made of aluminum. The acquired white...

(a) Classify the following oxides as neutral, acidic, basic or amphoteric. (B) Write suitable equations to show their nature.

Solution: $\rightarrow$ CO $=$ Neutral $\rightarrow \mathrm{B}_{2} \mathrm{O}_{3}=$ Acidic Being acidic, it responds with bases to frame salts. It responds with $\mathrm{NaOH}$ to frame sodium...

What are allotropes? Sketch the structure of two allotropes of carbon namely diamond and graphite. What is the impact of structure on the physical properties of two allotropes?

Solution: Allotropy is the presence of a component in more than one structure, having diverse actual properties however similar substance properties. Diamond's solid  3-D construction makes it a...

How would you explain the lower atomic radius of Ga as compared to Al?

Solution: A tomic sweep (in pm) Aluminum Gallium In spite of the fact that Ga has more than one shell than Al, it is more modest in size than Al. This is on the grounds that the $3 \mathrm{~d}$...

Explain why is there a phenomenal decrease in ionization enthalpy from carbon to silicon?

Solution: Carbon ionizing enthalpy (the primary component in bunch 14 ) is exceptionally high $(1086 \mathrm{~kJ}/\mathrm{mol})$. That is normal on account of its little size. Nonetheless, there is...

What sorts of informations can you draw from the following reaction?

Solution: The oxidation no. of $\mathrm{C}$ in $(C N)_{2}, C N^{-}$and $C N O^{-}$are $+3,+2$ and $+4$ separately. Let the oxidation no. of $\mathrm{C}$ be $\mathrm{y}$. $(C N)_{2}$ $2(y-3)=0$ Along...

Solution:

Why does the following reaction occur? What conclusion about the compound (of which is a part) can be drawn from the reaction?

Solution: $X e O_{6(a q)}^{4-}+2 F_{(a q)}^{-}+6 H_{(a q)}^{+} \rightarrow X e O_{3(g)}+F_{2(g)}+3 H_{2} O_{(l)}$ The oxidation no. of Xe decreases from $+8$ in $\mathrm{XeO}_{6}^{4-}$ to $+6$ in...

How do you count for the following observations? (a) Though alkaline potassium permanganate and acidic potassium permanganate both are used as oxidants, yet in the manufacture of benzoic acid from toluene we use alcoholic potassium permanganate as an oxidant. Why? Write a balanced redox equation for the reaction. (b) When concentrated sulphuric acid is added to an inorganic mixture containing chloride, we get colourless pungent smelling gas HCl, but if the mixture contains bromide then we get red vapour of bromine. Why?

Solution: (a) While producing benzoic corrosive from toluene, alcoholic potassium permanganate is utilized as an oxidant because of the given reasons. (I) In an impartial medium, $O H^{-}$ions are...

Whenever a reaction between an oxidisina adent and a reducina aqent is carried out, a compound of lower oxidation state is formed if the reducing agent is in excess and a compound of higher oxidation state is formed if the oxidising agent is in excess. J ustify this statement giving three illustrations. Justify the above statement with three examples.

Solution: When there is a response between lessening specialist and oxidizing specialist, a compound is framed which has lower oxidation number if the diminishing specialist is in abundance and a...

The compound is unstable compound. However, if formed, the compound acts as a very strong oxidising agent. Why?

Solution: The oxidation no. of $A g$ in $A g F_{2}$ is $+2$. Be that as it may, $+2$ is entirely unsound oxidation no. of Ag. Consequently, when $A g F_{2}$ is framed, silver acknowledges an...