Explore topic-wise InterviewSolutions in .

% of nitrogen in NH₃

₌ \(\frac{Total\,weight\,of\,nitrogen}{Molecular\,weight\,of\,NH_3}\) x 100

= \(\frac{14}{17}\) x 100

= \(\frac{1400}{17}\) = 82.3%

Correct option: (A) u

u means unified mass.

Correct option: (D) 1.66 x 10^-27 kg

Correct option: (C) amount of substance

Correct option: (A) \(\frac{1}{12}\) of C – 12

Correct option: (A) Molecular mass

Molecular formula = n × empirical formula

Where n = \(\frac{Molar\,mass}{Empirical\,formula\,mass}\)

Number of oxygen atoms

= \(\frac{16\times6.022\times10^{23}}{48}\)

= 2.007 × 10²³

Correct option: (D) 6.022 x 10²³

1 atom of He = 4 u of He

\(\because\) 4 u of He = 1 atom of He

\(\therefore\) 32.0 u He = \(\frac{1}{32}\) x 4 = 8 atoms.

One mole is the amount of a substance that contains as many particles or entities as there are atoms in exactly 12 g of the ¹²C isotope. 1 mole = 6.022 x 10²³.

Number of atoms in 1.0 g Na 

= \(\frac{6.022\times10^{23}\times 1}{23}\)

= 2.618 × 10²² atoms

Number of atoms in 1.0 g Mg

= 2.509 × 10²² atoms

So, 1.0 g Na has more number of atoms.

Number of molecules = \(\frac{Mass\,of\,CO_2}{Molecular\,mass\,of\,CO_2}\) x 6.022 x 10²³

= \(\frac{22}{44}\) x 6.022 × 10²³

= 3.011 × 10²³ molecules

The number of molecules present in 0.5 moles of CO₂ is

6.022 x 10²³ x 0.5 = 3.011 x 10^23.

(a) HO 

Molecular formula of hydrogen peroxide = H₂O₂ 

H₂O₂ ÷ 2 = HO = Empirical formula

Given: Points are A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) 

To prove: the quadrilateral formed by these 4 points is a rhombus All sides of both square and rhombus are equal But diagonals of a rhombus are not equal whereas they are equal for square 

Formula used: The distance between any two points (a, b, c) and (m, n, o) is given by,

    \(\sqrt{(a−m)^2+(b−n)^2+(c−o)^2}\)

Therefore, 

Distance between A(5, -1, 1) and B(7, -4, 7) is AB

= \(\sqrt{(5-7)^2+(-1-(-4))^2+(1-7)^2}\) 

= \(\sqrt{(-2)^2+3^2+(-6)^2}\) 

= \(\sqrt{4+9+36}\) 

= \(\sqrt{49}\) 

= 7

Distance between B(7, -4, 7) and C(1, -6, 10) is BC

= \(\sqrt{(7-1)^2+(-4-(-6))^2+(7-10)^2}\) 

= \(\sqrt{6^2+2^2+(-3)^2}\) 

= \(\sqrt{36+4+9}\) 

= \(\sqrt{49}\)  

= 7

Distance between C(1, -6, 10) and D(-1, -3, 4) is CD,

= \(\sqrt{(1-(-1))^2+(-6-(-3))^2+(10-4)^2}\) 

= \(\sqrt{2^2+(-3)^2+6^2}\) 

= \(\sqrt{4+9+36}\) 

= \(\sqrt{49}\) 

= 7

Distance between A(5, -1, 1) and D(-1, -3, 4) is AD,

= \(\sqrt{(5-(-2))^2+(1-(3))^2+(1-4)^2}\) 

= \(\sqrt{6^2+2^2+(-3)^2}\) 

= \(\sqrt{36+4+9}\) 

= \(\sqrt{49}\)  

= 7

Clearly, 

AB = BC = CD = AD 

All sides are equal 

Now, we will find length of diagonals 

Distance between A(5, -1, 1) and C(1, -6, 10) is AC,

= \(\sqrt{(5-1)^2+(-1-(-6))^2+(1-10)^2}\) 

= \(\sqrt{6^2+5^2+(-9)^2}\) 

= \(\sqrt{36+25+81}\) 

= \(\sqrt{142}\) 

Distance between B(7, -4, 7) and D(-1, -3, 4) is BD,

= \(\sqrt{(7-(-1))^2+(-4-(-3))^2+(7-4)^2}\) 

= \(\sqrt{8^2+(-1)^2+3^2}\) 

= \(\sqrt{64+1+9}\) 

= \(\sqrt{74}\) 

Clearly, 

AC ≠ BD 

The diagonals are not equal, but all sides are equal 

Thus, Quadrilateral formed by ABCD is a rhombus 

Hence Proved

Reflector depth = OD = 5 cm

Diameter of the mirror = BC = 20 cm

Consider the equation of the parabola is y² = 4ax

To find : Length of a, which is distance of the focus from the vertex.

Since parabolic reflector is 5 cm deep, which shows x-coordinate of the points B and C is 5.

Again, BD = CD = 10 cm

[D is the middle point of BC]

Therefore, coordinate of B is (5, 10)

Point B lies on the parabolic reflector, which means it satisfy the equation y² = 4ax

100 = 20a

or a = 5

Given coordinates are A (2, 3, 4) and B (4, 5, 8)

Now, the coordinates of the mid-point C are (2+4/2, 3+5/2, 4+8/2) = (3, 4, 6)

And, the direction ratios of the normal to the plane = direction ratios of AB

= 4 – 2, 5 – 3, 8 – 4 = (2, 2, 4)

Equation of the plane is

a(x – x₁) + b(y – y₁) + c(z – z₁) = 0

2(x – 3) + 2(y – 4) + 4(z – 6) = 0

2x – 6 + 2y – 8 + 4z – 24 = 0

2x + 2y + 4z = 38

x + y + 2z = 19

Thus, the required equation of plane is x + y + 2z = 19.

Two features seen in boys at puberty are: 

(i) Growth of facial hairs 

(ii) Voice becomes hoarse. 

Two features seen in girls at puberty are: 

(i) Development of breasts. 

(ii) Region below the waist becomes wider.

Given unit vector along normal 

\(\hat{n}\) =  i 

and distance from origin (0, 0, 0) = 7 units 

∴ from vector equation of plane

\(\vec{r} .\hat{n} = d\)

\(\vec{r}.\hat{i} = 7\)

Changes at puberty: 

 Sudden increase in height. 

 Broadening of shoulders and widening of chest in boys. In girls, the region below waist becomes wider. 

 At puberty, the voice box or the larynx begins to grow. Boys develop larger voice boxes. The growing voice box in boys can be seen as a protruding part of the throat called Adam’s apple. In girls, the larynx is hardly visible from the outside because of its small size. Generally, girls have a high pitched voice, whereas boys have a deep voice. 

 In girls, breasts begin to develop at puberty and boys begin to grow facial hair, that is, moustaches and beard. Boys also develop hair on their chest. In both, boys and girls, hair grows under the arms and in the region above the thighs or the pubic region. 

 Appearance of acne as a because of the increased activity of sweat glands and sebaceous glands in the skin. 

 Testis grows and starts producing sperms in males, whereas in females, the ovary enlarges and starts producing matured eggs.

Equation of plane passing through (3, 2, 4) 

a (x – 3) + b(y – 2) + c(z – 4) = 0 …..(1) 

∵ Plane passes through X-axis 

∴ a = 0,d = 0 ⇒ by + cz = 0 …..(2) 

From (1), a = 0 so b (y – 2) + c(z – 4) = 0 …..(3) 

⇒ by – 2b + cz – 4c = 0 

⇒ by + cz – 2b – 4c = 0 

⇒ – 2b = c [∵ by + cz = 0 from (2)] 

⇒ b = -2c 

∴ Equation of plane passing through (3,2,4) and X-axis b(y- 2) + c(z – 4) = 0 

⇒ – 2c(y – 2) + c(z – 4) = 0 

⇒ -2y + 4 + z – 4 = 0 

⇒ 2y – z = 0

\(\vec{a} \) = - 2i + 4j - 5k and

 \(\vec{b} \) = 3i + 5j + 6k 

equation of a line through (-2, 4, - 5) 

and is parallel to the vector 3i + 5j + 6k

\(\frac{x + 3}{3} = \frac{y - 4}{5} = \frac{z + 5}{6}\)

Given, points (–2, – 1, – 3) and (1, – 3, 3)

Direction ratios of the normal to the plane are (1 + 2, -3 + 1, 3 + 3) = (3, -2, 6)

Now, the equation of plane passing through one point (x₁, y₁, z₁) is

a(x – x₁) + b(y – y₁) + c(z – z₁) = 0

3(x – 1) – 2(y + 3) + 6(z – 3) = 0

3x – 3 – 2y – 6 + 6z – 18 = 0

3x – 2y + 6z – 27 = 0 ⇒ 3x – 2y + 6z = 27

Thus, the required equation of plane is 3x – 2y + 6z = 27.

Equation of plane passing through point (2,-1,3) a(x – 2) + b(y + 1) + c(z – 3) = 0 

∵ Plane is perpendicular to T-axis. 

∴ b = 0, c = 0 

Hence required equation of plane a(x – 2) + 0(y + 1) + 0(z – 3) = 0 

⇒ a(x – 2) = 0 

⇒ x – 2 = 0 (∵a ≠ 0)

Testosterone is a hormone found in human Males only.

Given points are (2, 1, 0), (3, –2, –2) and (3, 1, 7)

As the equation of the plane passing through the points (x₁, y₁, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃) is

(x – 2) (-21) – (y – 1)(7 + 2) + z (3) = 0

-21 (x – 2) – 9(y – 1) + 3z = 0

-21x + 42 – 9y + 9 + 3z = 0

-21x – 9y + 3z + 51 = 0 ⇒ 7x + 3y – z – 17 = 0

Thus, the required equation of plane is 7x + 3y – z – 17 = 0.

Menstruation is the process of the shedding of the uterine lining on a regular monthly basis in women. During menstruation the uterus wall along with blood vessels break off. This causes blood to come out and a new wall of uterus is formed. Menstruation lasts generally lasts for 4 to 5 days.

The period of life, when the body undergoes changes, leading to reproductive maturity, is called adolescence.

(a) fertilised egg. 

(b) blood stream, target site. 

(c) Testosterone, estrogen, secondary sexual. 

(d) pituitary gland.

Adolescence is the period of life, when the body undergoes changes, leading to reproductive maturity. It begins around the age of 11 and lasts till 18 or 19 years of age. The period of adolescence may vary from person to person.

The human body undergoes several changes during adolescence. These changes mark the onset of puberty.

(b) LH hormone

No, this thickening of the uterine wall is not permanent. 

If the egg gets fertilised, it starts developing and gets embedded in the uterine wall resulting in pregnancy. During pregnancy no more eggs are released and the thickened lining is discharged only when the baby is born. However, if fertilisation does not occur, the released egg and the thickened lining are shed off resulting in menstruation.

Hormones are chemical substances which are secreted by endocrine glands. They are responsible for changes taking place in the body.

In our country, the legal age for marriage is 18 years for girls and 21 years for boys. This is because teenage mothers are not prepared mentally or physically for motherhood. Early marriage and motherhood causes health problems in both mother and the child. It also curtails employment opportunities for the young woman and may cause mental agony as she is not ready to shoulder responsibilities of motherhood. 

Also, the boys before that age may not be mentally matured and financially secure enough to take on the responsibilities of a family.

Parents and teachers play an important role to develop the adolescents in to healthy, productive young ones to the nation. Parents feel to develop their children in to better ones than themselves. They must have good courage, confidence, boldness, and free to solve the problems. They should not be tense and worse. Parent is to be a friend and guide towards adolescents. Teacher is not only a master is to be a captain or a leader. Every adolescent needs mental support. Teacher is the only people who give suitable suggestions to make them free from all mental stress.

(a) Hormones

Larynx is also called Voice box.

Sex hormones are the hormones that control the development of secondary sexual characteristics and also regulate the proper functioning of the sex organs. They are named so because they are produced in both males and females by the respective sex organs under the influence of the pituitary gland. Functions of sex hormones: 

→ Testosterone: This hormone secreted by the testes brings about secondary sex characters in boys such as the growth of a beard, the voice becoming hoarse, development of reproductive organs, etc. 

→ Oestrogen: This hormone secreted by the ovaries is responsible for the development of secondary sexual characters in females such as the enlargement of breasts, development of female reproductive organs, etc.

The changes which occur at adolescence are controlled by hormones. Hormones chemical substances.These are secretions from endocrine glands or endocrine system. The male hormone or testosterone begins to be released by the testes at the onset of puberty. For example, the growth of facial hair. Once puberty is reached in girls, ovaries begin to produce the female hormone or estrogen which makes the breasts develop. Milk secreting glands or mammary glands develop inside the breasts. The production of thes​​​​​​​e hormones is under the control of another hormones secreted from an endocrine gland called pituitary gland. 

(c) gets one sex chromosome from the mother and the other from the father. 

The suggestion is to take nutritious food and to do body exercise regularly to improve his height.

At the age of 13 – 19 years, some changes like voice becomes hoarse, not caring to follow the suggestions and advises of parents, shows restlessness and growing tall. Because at this age children will be entering into a period which is called as Adolescence, where some changes in the behaviour is seen.

The sex organs by which children are identified as boys and girls at birth represent primary sexual characters.

If I have chance to talk with a doctor, I would ask about

1. How to develop positive emotions like bravery, self confidence, happiness, satisfaction, appreciation gratitude, concern and forgiveness.

2. And also how to over come the negative emotions like anger, bitterness, dissatisfaction, sadness, anxiety, fear, shame and guilt; which are needed in adolescence.