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(a) 25 cm, (b) Infinity (∞).

(d) will bend with steel on concave side

Coefficient of linear expansion of copper is greater than that of iron. Therefor, when bimetallic strip made up of copper and iron is heated. Copper the expands more than the iron strip. Since the two are rivetted together, the bimetallic strip bends so as to allow more expansion in the Copper strip. As a result, the copper strip forms the outer i. e., convex side of the bent metallic strip.

(i) rises 

(ii) come 

(ii) was 

(iv) refused

(i) who 

(ii) which 

(iii) that 

(iv) which/who 

(v) that 

(vi) who

• cite : Can you cite a few lines from Milton? s
• sight : Milton lost his eye sight in the middle of his age.
• Imaid: There is a maid servant in my house.
• made : He made me happy.

1. The name of the lesson is ‘Plants Also Breathe and Feel’. The author of the lesson is Sir Jagdish Chandra Bose.

2. Mr. Bose had a deep faith in the intelligence of his country men.

3. Mr. Bose addressed at a convocation of Mysore University in November, 1927.

4. Mr. Bose wanted his countrymen to have undying hope and faith in future.

5. (i) Glory-Glorious 

(i) Action—Active 

(i) 693 

We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7. 

Here last digit is 3. 

∴ Number to be tested = 69 – 2 × 3 = 63, which is divisible by 7. 

Hence, 693 is divisible by 7.

(ii) 7896 

We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7. 

Here last digit is 6. 

∴ Number to be tested = 789 – 2 × 6 = 777, which is divisible by 7. 

Hence, 7896 is divisible by 7.

(iii) 3467

We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.

Here last digit is 7.

∴ Number to be tested = 346 – 2 × 7 = 332.

Again repeating the process, taking last digit 2 for number 332,

Number to be tested = 33 – 2 × 4 = 19, which is not divisible by 7.

Hence, 3467 is not divisible by 7.

(iv) 12873

We know that if number formed by removing last digit is subtracted by double of removed digit, is divisible by 7, then our given number is divisible by 7.

Here last digit is 3.

∴ Number to be tested = 1287 – 2 × 3 = 1281.

Again repeating the process, taking last digit 1 for number 1281,

Number to be tested = 128 – 2 × 1 = 126, which is divisible by 7.

Hence, 12873 is divisible by 7.

(i) 44444 

We know that if number formed by last three digits of a given number is divisible by 8, then entire given number is divisible by 8. 

Here, number formed by last three digits is 444, which is not divisible by 8. 

Hence, 44444 is not divisible by 8.

(ii) 154360 

We know that if number formed by last three digits of a given number is divisible by 8, then entire given number is divisible by 8. 

Here, number formed by last three digits is 360, which is divisible by 8. 

Hence, 154360 is divisible by 8.

(iii) 998818 

We know that if number formed by last three digits of a given number is divisible by 8, then entire given number is divisible by 8. 

Here, number formed by last three digits is 818, which is not divisible by 8. 

Hence, 998818 is not divisible by 8.

(iv) 265472 

We know that if number formed by last three digits of a given number is divisible by 8, then entire given number is divisible by 8. 

Here, number formed by last three digits is 472, which is divisible by 8. 

Hence, 265472 is divisible by 8.

(v) 7350162 

We know that if number formed by last three digits of a given number is divisible by 8, then entire given number is divisible by 8. 

Here, number formed by last three digits is 162, which is not divisible by 8. 

Hence, 7350162 is not divisible by 8.

(i) 6543207 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 19 and sum of digits in even places = 8 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 6543207 is divisible by 11.

(ii) 818532 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 8 and sum of digits in even places = 19 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 818532 is divisible by 11.

(iii) 900163 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 4 and sum of digits in even places = 15 

∴ The difference of the sum of alternative digits of a number is 11, which is divisible by 11. 

Hence, 900163 is divisible by 11.

(iv) 7531622 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 18 and sum of digits in even places = 8 

∴ The difference of the sum of alternative digits of a number is 10, which is not divisible by 11. 

Hence, 7531622 is not divisible by 11.

(i) 22222 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 6 and sum of digits in even places = 4 

∴ The difference of the sum of alternative digits of a number is 2, which is not divisible by 11. 

Hence, 22222 is not divisible by 11.

(ii) 444444 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 12 and sum of digits in even places = 12 

∴ The difference of the sum of alternative digits of a number is 0, which is divisible by 11. 

Hence, 444444 is divisible by 11.

(iii) 379654 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 17 and sum of digits in even places = 17 

∴ The difference of the sum of alternative digits of a number is 0, which is divisible by 11. 

Hence, 379654 is divisible by 11.

(iv) 1057982 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 17 and sum of digits in even places = 15 

∴ The difference of the sum of alternative digits of a number is 2, which is not divisible by 11. 

Hence, 1057982 is not divisible by 11.

(i) 94 

We know that if units place digit is divisible by 2 then our given number is divisible by 2. 

Here units place is 4, which is divisible by 2. 

Hence, 94 is divisible by 2.

(ii) 570 

We know that if units place digit is divisible by 2 then our given number is divisible by 2. 

Here units place is 0, which is divisible by 2. 

Hence, 570 is divisible by 2.

(iii) 285 

We know that if units place digit is divisible by 2 then our given number is divisible by 2. 

Here units place is 5, which is not divisible by 2. 

Hence, 570 is not divisible by 2.

(iv) 2398 

We know that if units place digit is divisible by 2 then our given number is divisible by 2. 

Here units place is 8, which is divisible by 2. 

Hence, 2398 is divisible by 2.

(i) 134

We know that if number formed by last two digits of a given number is divisible by 4, then entire given number is divisible by 4.

Here, number formed by last two digits is 34, which is not divisible by 4.

Hence, 134 is not divisible by 4.

(ii) 618

We know that if number formed by last two digits of a given number is divisible by 4, then entire given number is divisible by 4.

Here, number formed by last two digits is 18, which is not divisible by 4.

Hence, 618 is not divisible by 4.

(iii) 3928

We know that if number formed by last two digits of a given number is divisible by 4, then entire given number is divisible by 4.

Here, number formed by last two digits is 28, which is divisible by 4.

Hence, 3928 is divisible by 4.

(iv) 50176

We know that if number formed by last two digits of a given number is divisible by 4, then entire given number is divisible by 4.

Here, number formed by last two digits is 76, which is divisible by 4.

Hence, 50176 is divisible by 4.

(v) 39392

We know that if number formed by last two digits of a given number is divisible by 4, then entire given number is divisible by 4.

Here, number formed by last two digits is 92, which is divisible by 4.

Hence, 39392 is divisible by 4.

Sediments which are deposited at the bottom of the sea are known as ocean deposits. These deposits can be biotic, abiotic, land, oceanic or cosmic.

Fault refers to the imbalance of the rocks due to cracks and fissures which occur in rocks caused due to stress and compression in the earth’s crust.

Epicenter is that central point on the surface of earth on the right angle to the seismic focus, where seismic waves are firstly experienced.

According to Monk house, “The transmission of elastic shock waves towards the outside in all the directions due to the activity of contraction and adjustment in the structure of the earth’s crust is known as earthquake.”

When concussion occurs on the seismic focus, shaking takes place in the rocks. The waves produced due to this are known as Seismic Waves.

S waves are also known as secondary waves. These waves reach the earth’s surface after the primary waves. Due to this reason, they are called secondary waves.

Correct Answer is : (b) Dormant

Correct Answer is : (a) P waves

(d) NAD – National Arithematic Division

When an earthquake originates in an oceanic region, such inter – oceanic earthquakes give rise to great destructive oceanic waves. These waves are known as Tsunami.

Volcanoes situated in Hawaiian Islands of Pacific Ocean, and in Mauritius, Comoro, Reunion, etc. islands situated in the Indian Ocean. All these volcanic regions are present in regions apart from Circum – Pacific Oceanic belt, Mid Continental belt, Mid-Atlantic Ridge belt, East African belt, etc.

Let P(n): 1 + 5 + 9 + … + (4n – 3) = n(2n – 1), for all natural numbers n.

P(1): 1 = 1(2 x 1 – 1) = 1, which is true.

Hence, P(1) is true.

Let us assume that P(n) is true for some natural number n = k.

∴ P(k) :1 + 5 + 9 +…+(4k -3) = k(2k - 1) .......(i)

Now, we have to prove that P(k + 1) is true.

P(k+ 1) : 1 + 5 + 9 + … + (4k - 3) + [4(k + 1) – 3]

= 2k² - k + 4k + 4 - 3

= 2k² + 3k + 1

= (k + 1)( 2k + 1)

= (k + 1)[2(k + 1) - 1]

Hence, P(k + 1) is true whenever P(k) is true.

So, by the principle of mathematical induction P(n) is true for any natural number n.

(c)  Gujarati

(c) H. Theil – Economic laws

(d)  Japanese

Answer is: (a) Sanskrit

(a) More that both ends of the magnet

No. of cuboids are formed using 64 unit cubes

 64 = 1 × 64 ……. (1) 

= 2 × 32 …….. (2) 

= 4 × 16 …….. (3) 

1) l = 64 cm, b = 1 cm, h = 1 cm. 

The total surface area of a cuboid, A = 2(lb + bh + lh) 

= 2 (64 × 1 + 1 × 1 + 1 × 64) 

= 2(64 + 1 + 64)

= 2 × 129 

= 258 Sq. cm.

2) l = 32 cm, b = 2 cm, h = 1 cm.

 A = 2(lb + bh + lh) 

= 2(32 × 2 + 2 × 1 + 32 × 1) 

= 2(64 + 2 + 32) 

= 2 × 98 

= 196 Sq. cm. 

3) l = 16 cm, b = 4 cm, h = 1 cm. 

A = 2(lb + bh + lh) 

= 2(16 × 4 + 4 × 1 + 16 × 1) 

= 2(64 + 4 + 16) 

= 2 × 84 

= 168 Sq. cm.

No, the volume of a cuboid is not same as the surface area of a cuboid.

i. poles

ii. independent

iii. separated

iv. magnet

v. magnet

1. B) 405 cm³

2. C) 405 cm²

3. D) 8

4. D) 4 : 9

R.I Refractive index = sini/sinr

R.I. = sin50/sin36

Refractive index of the water, μ_w = 4/3

Real depth at which the coin is places = 12 cm

Shift in the image = ?

Shift = real depth × (1 - 1/μ)

Shift = 12 × (1 - 3/4)

R = 12/4 = 3cm

Given,

Angle of prism, A = 60°

Angle of minimum deviation, = 36°

Angle of incidence, i =?

As δ_min = 2i – A

36° = 2i – 60

i = 48°

The light that bends the least is red colour and the light that bends the maximum is violet colour light.

Relation of refractive index μ wih real and apparent depths μ = Real depth/Apparent Depth

(b) refraction.

The correct ray is Ba

(a) reflected

If h₁ and h₂ are the sizes of the images formed in two conjugate positions, then, the size of object is given as h = √h₁h₂ = √9×1 = 3cm.

The size of the image in the two conjugate positions is 

In the first case, if the image is formed, the magnification is given as 

In the first case, if the image is formed, the magnification is given as \(\frac{v}{u} = \frac{9}{3}\)Such that, v = 3u

Also, v = 20+u, since “v” and “u” interchange the conjugate positions. 

∴ 3u = 20 + u 

Or 2u = 20 

Or u = 10 

And, v = 20+ u = 20+10 = 30 cm 

Now, focal length is calculated as

\(\frac1f=\frac1v+\frac1u\)

= \(\frac{1}{30} + \frac{1}{10}\)

= \(\frac{10+30}{300}\)

= \(\frac{40}{300} = 7.5\)

Thus, correct answer is option (d)

(b) At twice the focal length.

It is the line joining the centers of curvature of the two surfaces of the lens.

Four properties of an image formed by the given convex mirror are :

(i) Image is always erect.

(ii) Small in size

(iii) Virtual

(iv) Always from behind the mirror between focus and pol.

The angle of incidence is  zero. 

It is a concave.

Virtual and enlarged.

Explanation: When the object is kept between optical centre and focus of a convex lens, the image is formed on the same side, behind the object. The image thus formed is virtual, enlarged and erect.

Image is-

(i) Virtual

(ii) Erect

(iii) Diminished

(iv) Laterally invented

(a) The relation between speed of light in air c and in glass v is given by

c/v = =1.5

(b) The wavelength of light in glass (λ¹)

μ = λ/λ¹ = λ/1.5