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Correct option is (B) (ab)^m

\(a^m\times b^m=(a\times b)^m\)

= \((ab)^m\)

Correct option is  B) (ab)^m

(i) (3⁻⁷ ÷ 3⁻¹⁰) × 3⁻⁵ 

= (3^{−7 − (−10)}) × 3⁻⁵         (a^m ÷ aⁿ = a^{m − n})

= 33 × 3⁻⁵

= 3_{3 + (− 5)}                        (a_m × a_n = a_{m + n})

= 3−2 

= 1/3²                              ( a^-m = 1/a^m )

(ii) 2⁻³ × (−7)⁻³ = 1/2³ x 1/(-7)³

= 1/[ 2 x (-7) ]³              ( a^-m = 1/a^m )

= 1/(-14)³                      [ a^m x b^m= (ab)^m ]

The correct answer is 1/6

|z| < 4⇒ x² + y² < 16 which is the interior of circle with centre at origin and radius 4 units, and |z| > 3⇒ x² + y² > 9 which is exterior of circle with centre at origin and radius 3 units. Hence 3 < |z| < 4 is the portion between two circles x² + y² = 9 and x² + y² = 16.

Given details are,

Length of a cuboid = 10 cm

Breadth of a cuboid = 12 cm

Height of a cuboid = 14 cm

We know that,

Surface area of cuboid = 2 (lb + bh + hl) cm²

= 2 (10×12 + 12×14 + 14×10)

= 2 (120 + 168 + 140)

= 2 (428)

= 856 cm²

Given details are,

Side of cube = 75 cm = 7.5 dm

So, Volume of cube = 7.5³ 

= 421.875 dm³

Given details are,

Side of cube = 1.5 m = 15 dm

So, Volume of cube = 15³ 

= 3375 dm³

(i) 1 m³ = 1 × (100×100×100) = 10⁶cm³ (since 1m = 100cm)

(ii) 1 litre = 1000cm³ = 1000 × (0.1×0.1×0.1) dm³ = 1dm³ (since 1cm = 0.1dm)

(iii) 1 kl = 1000 litre = 1m³ (since 1m³ = 1000 litre)

(iv) The volume of a cube of side 8 cm is ……

We know that, side of a cube = 8cm

So, volume of cube = 8³ = 512cm³

(v) The volume of a wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm³. The height of the cuboid is …. cm.

Given, volume of cuboid = 4000 cm³

Length of cuboid = 10cm

Breadth of cuboid = 8cm

We know that volume = l × b × h

h = volume / (l × b)

= 4000 / (10×8)

= 50cm

(vi) 1 cu. dm = 1dm³ = 1× (10×10×10) = 10³cm³ (since 1dm = 10cm)

10³× (10×10×10) = 10⁶ mm³ (since 1cm = 10mm)

(vii) 1 cu. km = 1000×1000×1000 = 10⁹m³ (since 1km = 1000m)

(viii) 1 litre = 1000 cm³ = 10³cm³

(ix) 1 ml = 1/1000 litre = 1/1000 × 1000 = 1cm³ (since 1ml = 1/1000 litre)

(x) 1 kl = 1 × 1000 litre = 1m³ = 1 × (10×10×10) dm³ (since 1m = 10dm)

1 kl = 1000 dm³ 

= 10³ dm³ 

= 1000 × 1000 

= 10⁶ cm³

Given,

Volume of the gold sheet = \(\cfrac12\)m³

Area of sheet = 1 hectare = 10000 m²

So, thickness of gold sheet = \(\cfrac{volume\,of\,gold\,sheet}{area\,of\,gold\,sheet}\)

\(=\cfrac{\frac{1}2m^3}{10000m^2}\)= \(\cfrac{1}{200}\) cm

It is given that, 

Volume of the block = 0.5 m³ 

We know that, 

1 hectare = 10000 m² 

Therefore, 

Thickness of the sheet = volume/area 

= 0.5/10000 

= 0.00005 m 

= 0.005 cm 

= 0.05 mm

The area of outer surface of a cabinet except the bottom of the cabinet will be equal to its lateral surface area.

I = lm, b = 2m, h = 1.5m. 

A = 2h(l + b) 

= 2 × 1.5(1 + 2) 

= 3 × 3 = 9 m².

Convection--: It is the process by which heat is transmitted through a substance from one point to another due t_Q the bodily motion of the heated praticles of the substance.

(i) Trade winds --: The surface of the earth near the equator is heated by the sun. The are in contact with the surface of the earth becomes warmer and rises upwards. The are from the  colder polar regions rushes in towards the equatorial regions, thus producing northward wind in northern hemisphere and southward wind in southern hemisphere. Due to the rotation of the earth about its axis from west to east, the actual direction of the wind in the northern hemisphere is north -east and in the southern hemisphere, south-west. These winds are called trade winds.

(ii) Land and Sea Breezes --: Water has a high Specific heat.

Therefore, it is less readily heated by the sun than land. In other words, during the day the and land is heated by the sun to a higher temperature than water in the  sea. Air over the land is therefore heated, expands and rises while the cooler air from the sea blows towards land to take its place which constitutes the sea breeze.

At night the land is no longer heated by the sun. It therefore, cools, But land cools much faster than water due to high specific heat capacity of water. By comparison the sea is much warmer than land at night. So at night a current of air blows from the colder land to the warmer sea. This constitutes the land breeze.

Monsoons--: In Summer, the sun is in the Tropic of Cancer. During this time large parts of the earth situated in Central Asia are at a higher temperature than the surroundings oceans. Consequently, winds blow from the ocean to the land carrying moisture with hem. These winds cause widespread rains in India after they strike the mountain ranges.

In Winter, the sun is in the Tropic of Capricorn. During this time the land in the Central Asia is slightly cooler than the sea. Consequently, winds blow from the land to the sea. These winds take up moisture as they pass over the Bay of Bengal and cause rainfall in the coastal such as in Madras. These winds which bring rain are called monsoons.

Correct option is  D) all

Correct option is: (B) sea to land

Laws of refraction :

1. The incident ray, the refractive ray and the normal to interface of two transparent media at a point of incidence lie in the same plane.

2. During refraction light follows Snell’s law, i.e., the ratio of sine of angled of incidence to sine of angle of refraction is constant.

n₁ sin i = n₂ sin r (OR) sin i/ sin r = constant.

D) both B and C

B) the speed of light changes

1. Refractive index of diamond (2.42) is greater than that of vacuum (1). 

2. Speed of light is inversely proportional to refractive index of substances. 

3. Hence, light ray travel slowly in diamond when compared to vacuum.

Correct option is  A) less

Correct option is  B) i > r

Glass has higher refractive index

Refractive index = sine of the angle of incidence/sine of the angle of refraction.

Light travels in vacuum because it does not require medium for its propagation.

Refractive index.

1. Nature of material 

2. Wavelength of light used.

Correct option is (D) zero

The ratio of sine of angle of incidence and sine of angle of refraction gives refractive index.

Surface tension does not depend on gravity. [Note : The behaviour of liquids on board an orbiting spacecraft is mainly driven by surface tension phenomena. These make predicting their behaviour more difficult than under normal gravity conditions (i.e., on the Earth’s surface). New challenges appear when handling liquids on board a spacecraft, which are not usually present in terrestrial environments. The reason is that under the weightlessness (or almost weightlessness) conditions in an orbiting spacecraft, the different inertial forces acting on the bulk of the liquid are almost zero, causing the surface tension forces to be the dominant ones. 

In this ‘micro-gravity’ environment, the surface tension forms liquid drops into spheres to minimize surface area, causes liquid columns in a capillary rise up to its rim (without over flowing). Also, when a liquid drop impacts on a dry smooth surface on the Earth, a splash can be observed as the drop disintegrates into thousands of droplets. But no splash is observed as the drop hits dry smooth surface on the Moon. The difference is the atmosphere. As the Moon has no atmosphere, and therefore no gas surrounding a falling drop, the drop on the Moon does not splash.

There are more than 40 methods for determining equilibrium surface tension at the liquid-fluid and solid-fluid boundaries. Measuring the capillary rise (see Unit 2.4.7) is the laboratory method to determine surface tension.

Among the various techniques, equilibrium surface tension is most frequently measured with force tensiometers or optical (or the drop profile analysis) tensiometers in customized measurement setups

Wettability of a surface, and thus its propensity for penetration of water, depends upon the affinity between the water and the surface. A liquid wets a surface when its contact angle with the surface is acute. A waterproofing coating has angle of contact obtuse and thus makes the surface hydrophobic.

The poet says that everyone is important and each makes a difference. Since we are important we must not allow others to shame us or make us feel bad.

We should say ‘thank you

‘sad’ and ‘bad’ are the rhyming words.

Even the tiniest creature needs space in the world.

Planting a flower is compared to the blossoming of a friendship.

Every human being is unique. He/she deserves to be respected. When one is forgotten by the other, it makes him feel very sad. Every person makes a difference in life and his presence is needed. We must never put anyone to shame and no one has the authority to make others feel bad about themselves. We must respect and treat everyone well and be considerate towards others.

The poet compares planting flowers to maintaining friendship, because both need care, kindness and love to blossom. We must understand that as we move on this planet, every living thing, even the smallest needs its own space. Nothing is free of cost, either hard work, a lot of thought or money are involved in the gift. So we must learn to thank the person, who gives a gift and respect human beings.

Both friendship and planting flowers will bloom one day, when we show love, kindness and care every day.

1. He runs as fast as the wind.

2. They fought like cats and dogs.

3. As sweet as honey.

4. It means to be clever or cunning as a fox.

The figure of speech used in this line is “simile”.

In the poem Lessons in life the poets Daniel Ho and Bridgette Bryant bring out the importance of friendship in life and they add value to it by comparing it to the episode of planting flowers.

Just like making a flower bloom, friendship also blossoms only when there is constant care, love and kindness showered on them for a long period of time. Lessons that are taught by life come out of facing great difficulty. Similarly every small gift has a great deal of effort behind it. One should respect it and never forget to say ‘thank you’. We feel sad when we are forgotten by others and similarly others feel sad when they are forgotten. Everyone is unique and no one must be put to shame.

The poets repeat the values of gratitude, love and respect in the final stanza to make everyone understand that without these, no one can live happily. Hence happy friendship blossoms and planting flowers bloom only with love and kindness reciprocated.

1. (c) His words are pearls of wisdom.

2. The world is like a stage where all of us are merely actors.

3. Her hair is always a rat’s nest in the morning, a Hair is always a rat’s nest

4. He was a lion in the battle

Correct option is: (a) Robert Whittaker 

Criteria for classification of plants:

• If plants do not bear flowers, fruits and seeds, they are non-seed bearing plants. If they bear flowers, fruit and seeds, they are seed-bearing plants. 
• Presence or absence of conducting tissues Plants such as pteridophytes, gymnosperms and angiosperms which possess conducting tissues are included in vascular plants whereas thallophytes and bryophytes which do not possess conducting tissues are included under non-vascular plants.
• Depending upon whether the seeds are enclosed in fruit or not, plants are classified as gymnosperms (naked-seeds) and angiosperms (seeds covered by fruit)
• Depending upon the number of cotyledons in seeds, plants are classified into dicotyledons and monocotyledons

• Bryophyta group of plants are called the amphibians of the plant kingdom because they grow in moist soil but need water for reproduction.
• These plants are thalloid, multicellular and autotrophic.
• They reproduce by spore-formation. 
• Their plant body structure is flat, ribbon-like, long, without true roots, stem and leaves. 
• Instead, they have stem-like or leaf-like parts and root-like rhizoids. 
• They do not have specific tissues for the conduction of food and water. 
• Examples: Moss (Funaria), Anthoceros, Riccia etc.

Bryophyta: They grow in moist soil but need water for reproduction. Therefore, they are called ‘amphibians of plant kingdom’.

(1) Bryophyta 

(2) Pteridophyta 

(3) Thallophyta 

(4) Rhizoids 

(5) Covered seeds 

(6) Parallel venation 

(7) Disc like 

(8) Fibrous roots

Thallophyta: These plants grow mainly in water i.e. fresh water as well as in saline water, therefore they usually have a soft and fibre-like (filamentous) body.

Correct option is: (b) Rhizoids

B. Phytoene Synthase