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We observe that it is difficult to stretch nylon, polyester, rayon thread than cotton thread. They are more strong. Therefore, we can say that synthetic fibres are strong and durable for long time.

Cotton gets wrinkled but nylon, polyester and rayon does not get wrinkled.

Radius of the circle = 28 cm

Area = πr²

= \(\frac {22}7\) × 28 × 28 = 2464 cm²

Circumference of the photo frame 2πr

= 2 x \(\frac {22}7\) × × 28 = 176 cm

∴ Cost of decorative piece at the rate of ₹ 3 per cm is 176 × 3 = ₹ 528

Given the radius of a park r = 40 m

Area of inner circle = πr²

= \(\frac {22}{7} \times 40 \times 40\)

^{= \(\frac{35200}{7}\)}

= Area of outer circle = πr²

= \(\frac{22}{7} \times 47\times47\)

^{=\(\frac {48,598} {7}\) = 6942.57 sq.m}

Area of the path = Outer circle area – Inner circle area

= 6942.57 – 5028.57 

∴  Area of circular path = 1914 sq.m

Radius of circular floor = 42 m 

Width around it = 7 m 

Radius of outer circle = 42 + 7 = 49 m 

Area of outside path = Area of outer circle – Area of inner circle 

Area of inner circle = πr² = \(\frac {22}7\) × 42 × 42 

Area of the outer circle = πr² = \(\frac {22}7\) × 49 × 49 

Area of floor = \(\frac {22}7\)(49 × 49 – 42× 42) 

= \(\frac {22}7\)(2401 – 1764) 

= \(\frac {22}7\)× 637 = 2002 m² 

∴ Cost of flooring at the rate of ₹ 150 per sq.m is 2002 × 150 = ₹ 300300

Given,

Side of the equilateral triangle = 6 cm

And,

The area of the equilateral triangle = √3/4(side)²

= √3/4(6)²

= √3/4(36)

= 9√3 cm²

Let us mark the center of the circle as O, OA and OB are the radii of the circle.

In triangle BOD,

sin 60^o = BD/ OB

√3/2 = 3/ OB

OB = 2√3 cm = r

Therefore,

The area of shaded region = Area of the circle – area of the equilateral triangle

= πr² – 9√3

= 3.14 x (2√3)² – 9√3

= 3.14 x 12 – 9 x 1.732

= 37.68 – 15.588

= 22.092 cm²

Correct option is  A) 7

According to the question,

AC = 6 cm and BC = 8 cm

A triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

Using Pythagoras theorem in right angled triangle ACB,

(AB)² = (AC)² + (CB)²

(AB)² = (6)² + (8)²

⇒(AB)² = 36 + 64

⇒(AB)² = 100 ⇒(AB)= 10

∴ Diameter of the circle = 10 cm

Thus, Radius of the circle = 5 cm

Area of circle = πr²

= π(5)²

= 25π cm²

= 25 × 3.14 cm²

= 78.5 cm²

We know that,

Area of the right angled triangle = ( ½ ) × Base × Height

= (½) × AC × CB

= (½) × 6 × 8

= 24 cm²

Now, Area of the shaded region = Area of the circle – Area of the triangle

= (78.5-24)cm²

= 54.5cm²

Correct option is  C) 154

The above reaction is a decomposition reaction.

According to the question,

Digits that can be used = 3,5,7,8,9

Since, no digits can be repeated,

The number of integers is ⁵P₅ = 5! = 120

For a four-digit integer to be greater than 7000,

The four-digit integer should begin with 7,8 or 9.

The number of such integer = 3 × ⁴P₃ =3 × ⁴P₃ = 3(24) =72

Therefore, the total no of ways = 120+72 = 192

We have to find the number of integers greater than 7000 with the digits 3,5, 7, 8 and 9. So, with these digits, we can make maximum five-digit numbers because repetition is not allowed.

Since all the five-digit numbers are greater than 7000, we have Number of five-digit integers = 5 x 4 x 3 x 2 x 1 = 120 A four-digit integer is greater than 7000 if thousandth place has any one of 7, 8 and 9.

Thus, thousandth place can be filled in 3 ways. The remaining three places can be filled from remaining four digits in ⁴P₃ ways.

So, total number of four-digit integers = 3x ⁴P₃ = 3 x 4 x 3 x 2 = 72 Total number of integers = 120 + 72 = 192

Returns to a Factor refers to change in output when only one input is Changed, other inputs remaining unchanged.

CVA_Fc = (ii x i) + (iv) - (v) + (vi) 

= [Units of Output x Price Per Unit] ] + Change in Stock - [Intermediate Cost] + Subsidy l

= [2,000 x 20] + [- 500] - [15,000] + [3,000] 

= [40,000- 500 15,000 + 3,000] 

= [43,000] - [15,500] 

CVA_Fc = Rs. 27,500 crore.

Total physical product is sum total of marginal product corresponding to all levels of employment of the variable factor.

TP = ∑MP

(i) MPP initially rises to its maximum.

(ii) MPP then decreases (Stays positive) to become zero.

(iii) MPP becomes negative.

Under diminishing returns to a factor, marginal product initially falls and remains positive but ultimately it becomes negative. Accordingly, total product increases at a diminishing rate and ultimately starts falling.

GVA_mp =[(ii) + (iv)] + (iii) - (v) 

= [200 + 10] + (-10) - 120 

= Rs.80 lakh,

Detailed Answer: GVA_MP = Sales + in stock- IC 

= [(ii) + (iv)] + (iii) - (v) 

= [200 + 10] + (-10) - 120 

= 80 lakh

NVA_FC  = (iv) + (ii) - (i) - (iii) - (v)

or 

= Sales f Change in stock - Intermediate consumption - Net direct taxes - Consumption of fixed capital

= 500 + 50 - 300 - 70 - 20

= 550 - 390

NVA_FC = Rs. 160 lakh.

NVA_MP = (iv x iii) + (ii) - (l) - (vi)

NVA_MP =[Output Sold x Price Per unit] + [Change in Stock] - Intermediate Cost - Consumption of Fixed Capital

= [750 x 40] + [1000] - [10,000] - [3,000] 

= 30,000 + 1,000 - 10,000 - 3,000

= 31,000 - 13,000

NVA_MP = Rs.18,000 crore.

NVA_MP = (i x ii) + (v) - (vii) , (vi) = [Output sold x Price Per Unit] + [Change in Stock] - [Intermediate Cost] - [Depreciation] 

= [800 x 20] + [- 500] - [8,000] - [1,000]  

= 16,000 - 500 - 8,000 - 1,000 

= 16,000 - 9,500 

NVA_MP = Rs.6, 500 crore

 NVA_Mp =(iii x ii) + (iv) - (v) - (vii) - (i)

= (40 x 900) + 1000 -800-2000-700

= 36000 +1000 -800-20000-700

= Rs.15500 crore

Hypermetropia; convex lens.

The correct option is A) Increases.

The resistivity of conductors increases with rise in temperature. As the temperature of the conductor increases, the average speed of the electrons acting as the current carriers increases. This in result increases the number of collisions and the average time of collisions decreases with temperature.

Refractive index of the denser medium = 1.245

The angle of incidence of ordinary light at which reflected light from transparent medium is completely plane polarised is called polarising angle.

Correct option is (A) unequal absorption of O-ray and E-ray takes place.

Angle of refraction is 37° and refractive index of water is 1.327

Given: R.I. of glass, μ = 1.55

To find: Angle of refraction (r)

Formula: tan i_p = μ

Calculation: From formula,

tan i_p = 1.55

\(\therefore\) i_p = tan^-1(1.55) = 57°10'

Since i_p + r = 90°,

\(\therefore\) r = 90° – i_p = 90°– (57°10')

\(\therefore\) r = 32°50' 

The angle of refraction of the ray of light is 32°50'.

Correct option is (C) double refraction does not take place

Angle of refraction is 30°

Correct option is (D) 60°

Given: μ = 1.633

To find: Polarising angle (i_p)

Formula: μ = tan i_p

Calculation: From formula we get,

i_p = tan_-1 (1.633)

\(\therefore\) i_p = 58°31' 

The angle of incidence at which light is polarised is 58°31'.

हम जानते हैं कि फ्लिण्ट काँच, क्राउन काँच की तुलना में अधिक विक्षेपण उत्पन्न करता है। 

(a) बिना विक्षेपण के विचलन उत्पन्न करने हेतु क्राउन काँच का एक प्रिज्म लीजिए तथा एक फ्लिण्टे काँच का प्रिज्म लीजिए जिसका अपवर्तक कोण अपेक्षाकृत कम हो। अब इन्हें एक-दूसरे के सापेक्ष उल्टा रखते हुए सम्पर्क में रखिए। इस प्रकार बना संयोजन श्वेत प्रकाश को बिना अधिक परिक्षेपित किए विचलित कर देगा।

(b) पुराने संयोजन में लिए गए फ्लिण्ट काँच के प्रिज्म के अपवर्तक कोण में वृद्धि कीजिए (परन्तु अभी भी यह कोण दूसरे प्रिज्म की तुलना में कम ही रहेगा)। यह व्यवस्था पुंज को बिना अधिक विचलित किए परिक्षेपण उत्पन्न करेगी।

1. Material A has greater Young’s modulus as the slope of the graph of material A is greater than material B. 

Young’s Modulus = Y = Slope = \(\frac {stress}{strain}\)

∴ Material A has greater Young’s Modulus. 

2. From the graph it can be approximated that the stress at the fracture point for material A is higher than material B, thus material A is stronger.

(c) Material (ii) is elastic over a larger region of strain as compared to (i).

(d) Material (ii) is more brittle than material (i).

(d) The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre.

Data : λ = 5000 Å = 5000 × 10^-10 m

= 5 × 10^-7 m, v = 500 m/s

(i) speed (v) = \(\frac{distance(\lambda)}{time(T)}\)

∴ The time interval between successive collisions of a gas molecule, T = \(\frac{\lambda}v\)

= \(\frac{5\times10^{-7}m}{500\,m/s}\) = 10^-9 s

(ii) The collision frequency (number of collisions per unit time) of a gas molecule, f = \(\frac1T\) = \(\frac1{10^{-9}\,s}\) = 10⁹ collisions per second

It is the phenomenon of transfer of heat by actual mass motion of the medium. All liquids and gases are heated by convection.

1. If the temperature of the liquid is higher, more is the average kinetic energy.

2. This implies that the number of fast moving molecules is more.

3. Hence the rate of losing such molecules to atmosphere will be higher.

4. Thus, higher is the temperature of the liquid, greater is the rate of evaporation.

1. Molecules in a liquid are moving about randomly. 

2. The average kinetic energy of the molecules decides the temperature of the liquid. 

3. However, all molecules do not move with the same speed. 

4. Some with higher kinetic energy may escape from the surface region by overcoming the interatomic forces. 

5. This process can take place at any temperature and is termed as evaporation.

1. Drying of clothes:

• Clothes dry faster when hanged exposing more surface area than when kept folded.
• Due to more surface area, water in clothes gets evaporated faster, drying clothes quickly.

2. Using a spirit swab on skin before injecting gives cooling effect:

• Before giving an injection to a patient, normally a spirit swab is used to disinfect the region.
• A cooling effect is experienced by skin of patient due to evaporation of the spirit as explained before.

(i) Evaporation can take place at all the temperature, while boiling of a liquid occurs only at the boiling point of the liquid.

(ii) Evaporation takes place only at the surface of the liquid, while the boiling of a liquid takes place throughout the liquid.

The degree of hotness of a body is called temperature. All bodies in thermal contact with each other ultimately attain the same temperature. the flow of heat energy from one body to another due to temperature difference between the two is called heat. Two bodies in thermal equilibrium with each other may not have the same amount of heat, but they must have the same temperature.

β = 2α

and γ = 3α

∝ : β : γ = 1 : 2 : 3

where,

α → Coefficient of linear expansion,

β → Coefficient of superficial expansion,

γ → Coefficient of cubical or volume expansion

For making permanent magnet, the material must have high retentively and high coercively (e.g., steel).