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Sodium sulphate is dissolved in water and barium chloride solution is added, an insoluble white precipitate of barium sulphate is obtained.

Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl(White ppt)

Sodium sulphite is warmed with dilute sulphuric acid, a colourless gas with a pungent and suffocating smell is evolved. When this gas is bubbled through acidified solution of potassium dichromate, it turns its colour from orange to green.

Na₂SO₃ + H₂SO₄ → Na₂SO₄ + H₂O + SO₂

K₂Cr₂O₇ + H₂SO₄ + 3SO₂ → K₂SO₄ + Cr₂(SO₄)₃ + H₂O

(1) → B

(2) → A

(3) → C

(4) → E

(5) → D

(a) Brown (anhydrous)

(b) Black (anhydrous)

(c) Blue

(d) White

(e) White

(f) White

(a) Sulphuric acid(aq) + Zinc(s) ------> Zinc  sulphate(aq) + Hydrogen(g)
H₂SO₄(aq) + Zn(s)  -----> ZnSO₄(aq) + H₂(g)
(b) Hydrochloric acid(aq) + Magnesium(s) -----> Magnesiurn chloride(aq) + Hydrogen(g)
  2HCl(aq) + Mg(s )   -----> MgCI₂(ag) + Hr(g)
(c) Sulphuric acid(aq) + Aluminium(s) ----> Aluminium sulphate(aq) + Hydrogen(g)
  3H₂SO₄(aq) + 2Al(s) -----> AI₂(SO₄)₃(aq) + 3H₂(g)
(d) Hydrochloric acid(aq) + Iron(s) ----> lron chloride(aq) + Hydrogen (g)
  2HCl(aq) + Fe(s) -----> FeCl₂(aq) + H₂(g)

[A] Lead (II) oxide, when heated with powdered coke, reduced to metallic lead and carbon monoxide is formed.

PbO + C ⟶ Pb + CO

[B] Lead (II) oxide, when dissolved in the dilute nitric acid, lead nitrate is formed.

PbO  + 2HNO₃→ Pb(NO₃)₂ (Lead nitrate) + H₂O

[C] Lead (U) nitrate is dissolved in water and then sodium hydroxide solution is added, a white precipitate of lead hydroxide is obtained.

Pb(NO₃)₂  + 2NaOH→ Pb(OH)₂ + 2NaNO₃

[D] Lead (II) nitrate is dissolved in water and then concentrated solution of sodium carbonate is added, a white precipitate of lead (Il) carbonate is obtained. 

Pb(NO₃)₂  + Na₂CO₃ → PbCO₃ + 2NaNO₃

[A] Copper (II) oxide, when heated with coke powder is reduced to metallic copper.

CuO + C → Cu(Metallic copper) + CO

[B] Copper (II) oxide is dissolved in dilute sulphuric acid to form copper sulphate.

CuO + H₂SO₄ → CuSO₄(Copper sulphate)  + H₂O

[C] Copper sulphate is dissolved in water and hydrogen suiphide gas is passed, a black precipitate of copper suiphide is formed.

CuSO₄ + H₂S → CuS(Black ppt.)  + H₂SO₄

[D] Copper (II) oxide is dissolved in dilute hydrochloric acid to form copper chloride. To the solution of copper chloride, when a saturated solution of sodium carbonate is added, a light blue precipitate of copper (II) carbonate is formed.

CuCl₂ + Na₂CO₃ → CuCO₃ + 2NaCl

\(\frac{15m^3n^3}{5m^2n^2}\)= \((\frac{15}{5}m^{3-2}n^{3-2})\) = 3mn [Using aⁿ÷a^m = a^n-m]

\(\frac{6x^3y^3z^2}{3x^2yz}\) = \((\frac{6}{3}x^{3-2}y^{3-1}z^{2-1})\) = 2xy²z [Using aⁿ ÷ a^m = a^n-m]

(i) x² + 2x^-2

A polynomial never has negative or fractional power. In the given expression x has negative power.

Therefore it is not a polynomial.

(ii)  \(\sqrt{a}x\) + x² - x³

A polynomial always has positive power.

Therefore the given expression is a polynomial.

(iii) 3y³ - \(\sqrt{5}y\) + 9

A polynomial always has positive power.

Therefore the given expression is a polynomial.

(iv) ax^1/2 + ax + 9x² + 4

A polynomial never has negative or fractional power. In the given expression x has fractional power.

Therefore it is not a polynomial.

(v) 3x^-3 + 2x^-1 + 4x + 5

A polynomial never has negative or fractional power. In the given expression x has negative power.

Therefore it is not a polynomial.

(i) 2x³ + 5x² - 7

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 3.

Therefore degree of the polynomial is 3.

(ii) 5x² - 3x + 2

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 2.

Therefore degree of the polynomial is 2.

(iii) 2x - x² - 8

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 2.

Therefore degree of the polynomial is 2.

(iv) \(\frac{1}{2}\)y⁷ - 12y⁶ + 48y⁵ - 10

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 7.

Therefore degree of the polynomial is 7.

(v) 3x³ + 1

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 3.

Therefore degree of the polynomial is 3.

(vi) 5 

Degree is the highest power of the variable of a polynomial. In the given polynomial there is no variable term.

Therefore degree of the polynomial is 0.

(vii) 20x³ + 12x²y² + 20

Degree is the highest power of the variable of a polynomial. In the given polynomial highest power is 4.

Therefore degree of the polynomial is 4.

(i) x² + 2x^-2

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

(ii) √(ax) + x² – x³

The given expression is a polynomial.

Because the polynomial has positive powers.

(iii) 3y³ – √5y + 9

The given expression is a polynomial.

Because the polynomial has positive powers.

(iv) ax^1/2 + ax + 9x² + 4

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

(v) 3x^-3 + 2x^-1 + 4x + 5

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

(i) 2x³ + 5x² – 7

We know that in a polynomial, degree is the highest power of the variable.

The degree of the polynomial, 2x³ + 5x² – 7 is 3.

(ii) 5x² – 3x + 2

The degree of the polynomial, 5x² – 3x + 2 is 2.

(iii) 2x + x² – 8

The degree of the polynomial, 2x + x² – 8 is 2.

(iv) 1/2y⁷ – 12y⁶ + 48y⁵ – 10

The degree of the polynomial, 1/2y⁷ – 12y⁶ + 48y⁵ – 10 is 7.

(v) 3x³ + 1

The degree of the polynomial, 3x³ + 1 is 3

(vi) 5

The degree of the polynomial, 5 is 0 (since 5 is a constant number).

(vii) 20x³ + 12x²y² – 10y² + 20

The degree of the polynomial, 20x³ + 12x²y² – 10y² + 20 is 4.

To cover the shortest distance between Kolkata and Chicago, the aeroplane should move north west via Delhi.

i. Vatican City

ii. 180°

iii. Greenwich Meridian

iv. Greenwich Mean Time

v. plant, animal life

Centre of gravity is centre of it’s geometry or given structure but centre of mass is a point where whole mass of the body can be considered. When vertical height or geometric centre of object is very small and very near to earth’s surface comparison to earth’s radius. So, these objects are small, if it is larger, they are extended objects.

(a) Buildings (High) and ponds are small objects.

(b) Mountains and lakes are extended objects.

According to parallel axis theorem, M.I. of an axis (A’B’), parallel to an axis AB passing through centre of mass is given by I_A’B’ = M.I.+ MR² where M is mass of body and R is the perpendicular distance between AB and A’B’ )

∴ I_A’B’ > I_AB

∴ to minimize I, R = 0

Hence M.I. of a body is minimum about an axis passing through the centre of mass.

• Distribution of mass in the body. 
• Shape of the body 
• Inclination of the axis of rotation.
• The axis of rotation about which to M.I. is calculated.

The moment of inertia of a body plays the same role in rotational motion as the mass does in linear motion.

The moment of inertia is 25 kg m².

Correct option is A) Focus

Certain Sanskrit words which occur in the Bible as names of articles of export from Ophir make the writer think so. Only India could export ivory, apes, peacocks and sandalwood together.

संस्कृत के कुछ निश्चित शब्द, अउर्फर नामक स्थान से निर्यात की जाने वाली वस्तुओं के नामों के रूप में बाइबल में आते हैं। केवल भारत ही हाथीदांत की वस्तुएँ, लंगूर, मोर तथा चंदन एक साथ निर्यात कर सकता था।

(c) Buddhism

The study of mythology has assured an entirely new character chiefly owing to the light that has been thrown on it by the ancient Vedic Mythology of India.

पुराण विद्या के अध्ययन ने पूर्णरूपेण नया रूप अपना लिया है क्योंकि मुख्यतः इस पर भारत की प्राचीन वैदिक पुराण विद्या द्वारा प्रकाश डाला गया है।

Europeans have been nurtured on the thoughts of the Greeks, the Romans and the Jewish.

यूरोप के लोगों का पोषण ग्रीक, रोमन व यहूदियों के विचारों पर हुआ है।

The India of the towns and the India of the village communities are the two different Indias.

शहरों का भारत व ग्रामीण समुदायों का भारत, दो अलग-अलग भारत हैं।

Correct answer is (c) India

According to the author, Buddhism is the principal source of our legends and parables.

लेखक के अनुसार, हमारी पौराणिक कथाओं व नीति कथाओं का प्रधान स्रोत बौद्धवाद है।

In ‘What India can teach us’ the author looks to the India of the village communities.

इस पाठ में लेखक ग्रामीण समुदायों वाले भारत की ओर देखता है।

It’s so because India is endowed with all the wealth, power and beauty that nature can bestow.

ऐसा इसलिए है क्योंकि भारत को सभी संपदा, शक्ति व सौन्दर्य प्रदान किया गया है जो प्रकृति प्रदान कर सकती है।

The growth and decay of dialects, the possible mixture of languages, with regard not only towards but also to grammatical elements can be studied in India.

बोलियों की वृद्धि व क्षरण, भाषाओं का संभव मिश्रण, न केवल शब्दों से सम्बन्धित ही बल्कि व्याकरणीय तत्त्वों से सम्बन्धित भी, भारत में अध्ययन कर सकते हैं।

The Aryans of India are the framers of the most wonderful language, the Sanskrit. They are the fellow workers in the construction of our fundamental concepts. They are the fathers of the most natural of natural religions. They are the makers of the most transparent mythologies. They are the inventors of the most subtle philosophy. And they are the givers of the most elaborate laws.

भारत के आर्य लोग सर्वाधिक अद्भुत भाषा संस्कृत के रचनाकार हैं। वे हमारी आधारभूत अवधारणाओं के निर्माण में साथी कार्यकर्ता हैं। वे प्राकृतिक धर्मों में सर्वाधिक प्राकृतिक धर्म के जनक हैं। वे सर्वाधिक पारदर्शी पुराण विद्याओं के बनने वाले हैं। वे सर्वाधिक सूक्ष्म दर्शन के आविष्कारक हैं। और वे सर्वाधिक विस्तृत कानूनों के देने वाले हैं।

It is absolutely right that India is the only country in the world, which has been most richly endowed with all the wealth, powers and beauty that nature can bestow. India is rich in all kinds of wealth – human or physical. India has produced great scientists, doctors, litterateurs such as Aryabhatta, Charak and Tagore. India is rich in mineral wealth. All kinds of metallic and non-metallic minerals are found here. India has been a powerful country. It has military power, space power, weapon power, economic power and so on. India is rich in natural beauty. For greenery, we have huge forest cover. For snowy beauty, we have snow covered mountains. For watery beauty, we have streams, water-falls, rivers, seas and oceans Thus, nature has bestowed India with rare gifts.

i. I am growing (grow) a beard now.

ii. forgot (forget) to wind the clock last night.

iii. Every year hes pends (spend) his holidays in Kashmir.

iv. It is raining (rain), take your umbrella.

v. Keep quiet, we are listening (listen) to the music.

vi. That silly boy always makes (make) stupid remarks.

vii. She hates (hate) cats.

viii. My friend came (come) to see me yesterday.

ix. Who discovered (discover) America?

x. What a noise! What on earth is happening (happen).

The Comprehensive list of India’s contribution to the world:

 1. India is the father of literature-Vedas, Puranas etc.

 2. Human values travelled from India – visible in Indian villages.

3. Opportunities for intellectual work – space for various disciplines.

4. Vedic Mythology – a true science of mythology.

5. Legends and parables travelled from India.

6. Export of articles from India.

7. Framed the most wonderful language Sanskrit.

8. Constructed fundamental concepts – of zero.

9. The father of the most natural religion – Sanatan dharma.

10 Made the most transparent mythologies.

Invented the most subtle philosophy.

Gave the most elaborate laws.

1. True

2. True

3. False

4. True

5. False

Human mind has most deeply pondered on the greatest problems of life in India.

मानव-मस्तिष्क ने जीवन की गंभीरतम समस्याओं पर सर्वाधिक गहनतम विचार भारत में किया है।

Between F and C.

The Cheshire cat told him that it would see Alice later at the Queen’s croquet game.

1. She found a green bottle that said, “DRINK ME”.

2. Alice took the bottle because she was curious to know about it.

3. She began to shrink, until she was no bigger than a doll.

Negative sign of magnification indicates that image is real and inverted. Also size of image is enlarged. So, object must be positioned between F and 2F, i.e. C.

Yes the refractive index changes with the color of the light because refractive index changes with the change in the wavelength and different colors have different wavelength. Due to it refractive index of violet color is highest and of red color is lowest.

7, 4, 8,10,1, 3, 6, 2, 5, 9.

7. Everyone rushed into the courtroom. 

4. “Court is now in session” announced the white rabbit. 

8. “Will Alice please come to the stand?” 

10. Alice took the stand and looked at the jury box, where March Hare and the Mad Hatter were making noise. 

1. The Dormouse slept and the Cheshire cat smiled at her. 

3. “What’s going on?” asked Alice. 

6. “Your are guilty of stealing the delicious heartshaped tarts” accused the Queen. 

2. “And now you must be punished. Off with her head” yelled the Queen. 

5. “How silly” , replied Alice. ‘I did not have the slightest idea what you were talking about. I was only playing croquet.

9. Alice felt someone touch her shoulder, ‘wake up

The answer is (a) is less than one

• Convex mirror is used in rear view mirror. Convex mirror always give smaller image.
• Hence, magnification produced by rear view mirror is always less than 1

Given; 

Magnification (m) = 0.16; 

Size of object = 4cm; 

Size of image =? 

We know that; 

Magnificaiton = \(\frac{Size\,of\,image}{Size\,of\,object}\)

⇒ 0.16 = \(\frac{Size\,of\,image}{4}\)

⇒ Size of image = 0.16×4 = 0.64cm. 

Hence size of image is 0.64cm

When milk and water are mixed, together they look like the same colour and shape. So, friends should look similar in the same way and then only friendship can last for long time

All-pins do not sink in water is False.

Things weighed in kilogram are brought to my home are vegetables, pulses, besan, rice, wheat flour etc.

The glass in which sugar is stirred with water, there sugar is visible or not visible at all.

Gauss’s law states that ‘the electric flux through a closed surface is equal to times the charge enclosed by that surface’. 

Sugar dissolves quickly in hot water is True.