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Controls the size of the pupil.

 Iris controls the size of pupil.

Ciliary muscles.

iv. (6x² + 7xy + 16y²) – (16x² – 17xy) 

= 6x² + 7xy + 16y² – 16x² + 17xy 

= (6x² – 16x²) + (7xy + 17xy) + 16y² 

= -10x² + 24xy + 16y²

v. (4x + 16z) – (19y - 14z + 16x) 

= 4x + 16z – 19y + 14z – 16x 

= (4x – 16x) – 19y + (16z + 14z) 

= -12x – 19y + 30z

i. 6x – 1 = 3x + 8

∴ 6x - 3x = 8 + 1

∴ 3x = 9

∴ x = 9/3

∴ x = 3

ii. 2(x - 4) = 4x + 2

∴ 2x - 8 = 4x + 2

∴ (-8 - 2) = 4x - 2x 

∴ (-10) = 2x 

∴ x = (-10/2)

∴ x = -5

iii. 5(x + 1) = 74

∴ 5x + 5 = 74

∴ 5x = 74 - 5

∴ 5x = 69

∴ x = 69/5

Let the numerator of the rational number be x. Therefore, its denominator will be x + 8.

The rational number will be x/x + 8.

According to the question,

x + 17/x + 8 - 1 = 3/2

⇒ x + 17/x + 7 = 3/2

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 − 21 = 3x − 2x

⇒13 = x

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

For the collision,

u₁ = 400 m s^-1, e = 0.75

For the firmly fixed hard surface, u₂ = v₂ = 0

e = 0.75 = \(\frac{v_1-v_2}{u_2-u_1}=\frac{v_1-0}{0-400}\)

∴ v₁ = -300 m/s.

Negative sign indicates that the bullet rebounds in exactly opposite direction. Change in momentum of each bullet = m(v₁ – u₁)

The same momentum is transferred to the surface per collision in opposite direction.

∴ Momentum transferred to the surface, per collision,

p = m (u₁ – v₁) = 0.04(400 – [-300]) = 28 Ns

The rate of collision is same as rate of firing.

∴ Momentum received by the surface per second, \(\frac{dp}{dt}\) = average force experienced by the surface = 28 × 5 = 140 N

This is the average force experienced by the surface of area A = 10 cm² = 10^-3 m²

∴ Average pressure experienced,

P = \(\frac{F}{A}=\frac{140}{10^{-3}}\) = 1.4 × 10⁵ N m^-2

∴ P ≈ 1.4 times the atmospheric pressure.

The average force and average pressure experienced by the surface due to the firing is 140 N and 1.4 × 10⁵ N m^-2 respectively.

a = F/m. On tripling the force, the acceleration will also be tripled.

If the wooden block is not properly supported, then it will be unable to offer suitable reaction.

Degree of polynomial

(i) 7x³ + 4x² -3x +12 is 3 

(ii) 12 - x + 2x³ is 3

(iii) 5y - √2 is 1

(iv) 7 = 7 x x^o is 0

(v) 0 is un defined.

The recoil speed of the gun is inversely proportional to its mass. Therefore, the recoil speed of heavy gun is less than that of light gun.

As Ft remains constant, so if t is reduced, then F will be increased and hence hurt our foot.

Correct option is: (a) position 

Correct option is: (a) Motion

Correct option is: (b) external unbalanced force

Correct option is: (b) a stone falls freely towards the earth

Correct option is: (d) rate of change of momentum

(i) x + x² + 4: It is a quadratic polynomial as its degree is 2. 

(ii) 3x – 2 : It is a linear polynomial as its degree is 1. 

(iii) 2x + x²: It is a quadratic polynomial as its degree is 2. 

(iv) 3y: It is a linear polynomial as its degree is 1. 

(v) t²+ 1: It is a quadratic polynomial as its degree is 2. 

(vi) 7t⁴ + 4t³ + 3t – 2: It is a biquadratic polynomial as its degree is 4.

As we know, degree is the highest power in the polynomial 

(i) Degree of the polynomial 7x³ + 4x² – 3x + 12 is 3 

(ii) Degree of the polynomial 12 – x + 2x³ is 3 

(iii) Degree of the polynomial 5y – is 1 

(iv) Degree of the polynomial 7 is 0 

(v) Degree of the polynomial 0 is undefined.

(i) f(x) = 4x³ - x² - 3x + 7 is a polynomial.

(ii) g(x) = 2x³ - 3x²+\(\sqrt{x}\)-1is not a polynomial as exponent of x in \(\sqrt{x}\) is not a positive integer.

(iii) ) p(x) = \(\frac{2}{3}\)x² - \(\frac{7}{4}\) x + 9 is a polynomial as all the exponents are positive integer.

(iv) q(x) = 2x² - 3x + \(\frac{4}{x}\) + 2 is not a polynomial as the exponent of x in \(\frac{4}{x}\) is not a positive integer.

(v) h(x) = x⁴ - x\(\frac{3}{2}\)+ x - 1 is not a polynomial as the exponent of x in \(-x^{3/2}\) is not a positive integer.

(vi) f(x) = 2+ \(\frac{3}{x}\) + 4x is not a polynomial as the exponent of x in \(\frac{3}{x}\) is not a positive integer.

(i) 396 can be factorised as follows.

396 = 2 x 2 x 3 x 3 x 11

Here, prime factor 11 does not have its pair. If we divide this number by 11, then the number will become a perfect square. Therefore, 396 has to be divided by 11 to obtain a perfect square.

396 ÷11 = 36 is a perfect square.

36 = 2 x 2 x 3 x 3

∴ √36 = 2 x  3 = 6

(ii) 2645 can be factorised as follows.

2645 = 5 x 23 x 23

Here, prime factor 5 does not have its pair. If we divide this number by 5, then the number will become a perfect square. Therefore, 2645 has to be divided by 5 to obtain a perfect square.

2645 ÷5 = 529 is a perfect square

529 = 23 x 23

∴ √529 = 23

Coefficient of x² in:

(i) 17 – 2x + 7x² is 7

(ii) 9 - 12x + x³ is 0

(iii) \(\frac{\pi}{6}\) x² – 3x + 4 is \(\frac{\pi}{6}\)

(iv) \(\sqrt{3}\) x - 7 is

(i) 2800 can be factorised as follows.

2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

Here, prime factor 7 does not have its pair. If we divide this number by 7, then the number will become a perfect square. Therefore, 2800 has to be divided by 7 to obtain a perfect square.

2800 ÷7 = 400 is a perfect square

400 = 2 x 2 x 2 x2 x 5 x 5

∴ √ 400 = 2 x 2 x 5 = 20

(ii) 1620 can be factorised as follows.

1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5

Here, prime factor 5 does not have its pair. If we divide this number by 5, then the number will become a perfect square. Therefore, 1620 has to be divided by 5 to obtain a perfect square.

1620 ÷5 = 324 is a perfect square.

324 =  2 x 2 x 3 x 3 x 3 x 3 

∴ √324 = 2 x 3 x 3 = 18

(i) 252 can be factorised as follows.

252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 does not have its pair, If we divide this number by 7, then the number will become a perfect square. Therefore, 252 has to be divided by 7 to obtain a perfect square.

252 ÷7 = 36 is a perfect square.

36 = 2 x 2 x 3 x 3

∴ √36 = 2 x 3 = 6

(ii) 2925 can be factorised as follows.

2925 = 3 x 3 x 5 x 5 x 13

Here, prime factor 13 does not have its pair. If we divide this number by 13, then the number will become a perfect square. Therefore, 2925 has to be divided by 13 to obtain a perfect square.

2925 ÷13 = 225 is a perfect square.

225 = 3 x 3 x 5 x 5

∴ √225 = 3 x 5 = 15

‘Rajasthan Kesari’ newspaper’s publisher was Viiav Singh Pathik.

(i) f(x) = 4x³ -x² -3x +7 is a polynomial.

(ii) g(x) = 2x³ -3x² + √x -1 is not a polynomial as exponent of x in √x is not a positive integer.

(iii) p(x) = 2/3 x² - 7/4x + 9 is a polynomial as all the exponents are positive integers.

(iv) q(x) = 2x² -3x + 4/x +2 is not a polynomial as exponent of x in 4/x is not a positive integer.

(v) h(x) = x⁴ - x^3/2 +x -1 is not a polynomial as exponent of x in -x^3/2 is not a positive integer.

(vi) f(x) = 2+3/x +4x is not a polynomial as exponent of x in 3/x is not a positive integer.

Given,

Radius of the sphere = 9/2 cm

So, its volume = 4/3 πr³ = 4/3 π(9/2)³

And, the radius of the wire = 2 mm = 0.2 cm

Let the length of the wire = h cm

So, the volume of wire = πr²h = π(0.2)²h

Then, according to the question we have

Volume of wire = Volume of sphere

π(0.2)²h = 4/3 π(9/2)³

h = 4 x 729/ (3 x 8 x 0.01) = 12150 cm

Therefore, the length of the wire = 12150 cm

The tent is made as a combination of right circular cylinder and right circular cone on top.

Height of cylindrical part of the tent = h = 3 m

Radius of its base = r = 14 m

Total height of the tent = 13.5 m

Curved surface area of cylindrical part of tent = 2πrh

= 2 × 22/7 × 14 × 3

= 264 m²

Height of conical part of the tent = total height of tent – height of cylindrical part

Height of conical part of the tent = 13.5 – 3 m =10.5 m

Let the slant height of the conical part be l.

l² = h² + r² (used cone height)

= 110.25 + 196

= 306.25

or l = 17.5 m

Curved surface area of conical part of tent = πrl

= 22/7 × 14 × 17.5

= 770

Total surface area of tent = Curved surface area of cylindrical part of tent + Curved surface area of conical part of tent.

Total Surface area of tent = 264 + 770

= 1034 m²

Cloth required = Total Surface area of tent = 1034 m²

Cost of cloth = Rs 80/m² (given)

Total cost of cloth required = Total surface area of tent × Cost of cloth

= 1034 × Rs. 80

= Rs. 82720

Cost of cloth required to make the tent is Rs. 82720

Her uncle Roshan wanted to like the rabbit to Mangaluru and eat meat.

Fertilised egg i.e., zygote divides and redivides and forms a ball of cells. This is a kind of embryo and it reaches the uterus and gets attached to the wall of the uterus. This fixing of embryo to the uterus is called implantation. Now the embryo undergoes a process “specialisation of cells’’. It leads to the formation of different parts of the body. This process is called differentiation. It leads to the formation of various tissues and other organs and thus organ systems are formed. Organ system lead to the formation of an individual. Thus the zygote forms an embryo, it forms a baby and it forms an adult.

At the Silver Jubilee of electric light the President of U.S.A. honoured Edison, and when Edison stood to thank the President he suddenly fell ill.

The President of the USA received Edison and honoured him in a big function: True.

As a child, Edison was fond of asking questions: True.

In the Silver Jubilee function when Edison got up to thank the President, he suddenly fell ill and died on the morning of 18th October, 1931. Thus the great and eventful life of Socrates ended.

Edison was a great American sailor: False.

Edison was fond of books and read a lot of them: True.

(b) he was stupid and naughty.

Edison was never satisfied till he got the right answer: True.

(b) an intelligent answer.

(b) an intelligent statement.

Edison said, “I shall never invent anything which will destroy life. I want to make people happy.”: True.

Edison invented electric light.

The life of Edison has been called great and eventful because he gave the world more laughter and more light by inventing gramophone and electric bulb.

Edison was brilliant scientist of his age. He is known for many useful inventions. But he is famous for the invention of electric bulb. Invention of electric bulb is boon for humankind. If he did not invent the electric bulb, then we live in darkness today.