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Force acting on charge
F = q \(\overrightarrow{(v} \times \vec{B} )\)
\(|\vec F|\) = qvBsin 90°= qvB
The path of the particle will be circular.

Dimension of magnetic field = [M¹L⁰T^-2A^-1]
Unit- Tesla (7)

Moving charges produce both electric and magnetic field.

(a) By Income Method

Net Domestic Product at Factor Cost (NDP_FC) = Wages and Salaries + Social Security Contribution by Employers + Corporation Tax + Retained Earning of Private Corporations + Dividend +Rent + Interest 

= 2,000+ 100 + 30 + 10 + 60 + 300 + 300 

= Rs. 2,800 crore.

NI = (ii) + (vi) + (iii) + (vii) - (ix) - (viii)

= Private final consumption expenditure + Govt final consumption expenditure + Net domestic capital formation + Net exports - [Net factor income paid to abroad + Net indirect taxes]

= 400 + 200 + 100 + 40 - [10 + 80]

= 740 - 90

National income = Rs. 650 crore.

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

= 1,300 + 80 - 60 + 700 - (- 50)

= Rs. 2,070 lakh.

(i) Net National Product at Factor Cost (NNP_FC)

= Wages and salaries + social security contribution by employers + Rent and royalty + Profit + interest - Net factor income to abroad

=800+100+300+500+400-50

=2,100-50=2,050

=Rs. 2,050 Arab 

(ii) Gross National Disposable Income (GNDI)

= NNP_FC + Net indirect tax + Consumption of fixed capital - Net current transfer to abroad

=2,050+250+200-(-30)

=Rs. 2,500+30

=Rs. 2,530 Arab

National income = (iv) + (ii) + (i) + (vi) + (iii) - (vii)

= Private final consumption expenditure + Govt.final consumption expenditure + Net domestic capital formation + Net exports + [Net factor income from abroad - Net indirect taxes]

= 600 + 300 + 150 + 50 + (-20) - 90

= 1,100 - 110

N.I = Rs. 990 crore.

Sales = (i + ii + vi + iv) - iii

= 550 + 60 + 60 + I,000 - (-30)

= Rs. 1,710lakh

NNDI = (ii) + (iii) + (viii)

= 2,500 + 180 + 20

= 2,700 crore

P.I. = (ii) - (iv) + (vii) + (viii) + (x) - (ix) - (v)

= 2,500-500 + 100 + 20 + 30 - 70 - 80

= 2,000 crore

Income Method

NNP_FC= Profit + Compensation of Employees +

Interest + Rent - Net Factor Income to Abroad

= 200 + 350 + 50 + 70 - 50

=  Rs. 630 crore.

Expenditure Method

NNP_FC = Private Final Consumption Expenditure + Govt. Final Consumption Expenditure + Gross Domestic Capital Formation + Net Exports - Consumption of Fixed Capital - Net Factor Income to Abroad - Net Indirect Taxes 

= 440 + 250 + 90 + (-20) - 20 - (50) - 60 

= 780 - 20 - 20 + 50 - 60

= 780 - 100 + 50

= 780 - 150

NNP_FC=Rs.630 crore.

Correct option is (c) ₹ 50 lakh

1.True

2.False

Correct option is (D) Sole proprietorship

(d) “Ceteris paribus”

(c) The price of wheat determines its demand

It is a monetary measure of the income generated within the country plus net income received from abroad during a year.

Sum of factor incomes accruing to normal residents of a country during a year from their contribution to productions at home and abroad.

The total cost of producing 1001 unit is 10,04,000

(i) Private Final Consumption Expenditure (C): It refers to expenditure on final goods and services by the individuals, households and Non-profit Institution Serving Society.

(ii) Government Final Consumption Expenditure (G): It refers to expenditure on final goods and services by the government, like expenditure on the purchase of goods for consumption by the defence personnel.

(iii) Investment Expenditure (I): It refers to expenditure on the purchase of final goods by the producers.

(iv) Net Exports (X - M): It is the difference between exports and import during an accounting year.

It happens because when AVC falls, SMC is less than AVC. When AVC starts rising, SMC is more than AVC. So, it is only when AVC is constant and at its minimum point, that SMC is equal to AVC. Therefore, SMC curve cuts AVC curve at its minimum point.

False, the difference between AC and AVC is due to AFC. As output increase AFC falls, so the difference between AC and AVC falls.

Correct answer is (b) LAC

The cost curve which is a rectangular hyperbola is AFC

Yes, there is a shift in one sector’s dominance to other as the economy develops. As there is development, there is increased investment by the government in the education and health sector. This increases the knowledge of a person, and an educated individual prefers working in the manufacturing or service sector over agriculture. With time, the number of people employed in the agriculture sector will decrease, and there will be a subsequent increase in other sectors. This results in a shift of dominance from agriculture to other sectors.

NVA_FC of the two NVA_FC and NVA_MP is equal to sum of factor income.

Real Income=Norninal Income/Price Index x100

=600/100x100= Rs.600

• Sound requires a material medium for its propagation and travels in the form of a longitudinal wave. 
• The denser the medium, faster is the propagation of sound. 
• Hence, sound travels faster in iron than in air.

• A SONAR system determines the depth of the sea. 
• It locates underwater hills, valleys, icebergs, submarines and sunken ships. It also locates the positions of other ships or submarines. 
• Hence a SONAR system is installed in a ship.

1. Solid, liquid, gases.

2. External ear, the middle ear and the inner ear.

3. Pendulum, earthquake.

4. Bats, dolphins, mice.

In India landslides occur very after in hilly states.

The SI unit of magnetic induction is the tesla. We can define the unit from the velocity dependent part of the Lorentz force that acts on a charge in motion parallel to a magnetic field.

Definition : The magnitude of magnetic induction is said to be 1 tesla when a charge of 1 coulomb experiences a force of 1 N when it moves at 1 m/s in a magnetic field in a direction perpendicular to the direction of the field.

1 tesla (T) = 1 N’s/Gm = 1 N/A-m.

[Notes : (1) Since the ampere and not the coulomb is the fundamental unit, the tesla is defined from the expression for the force on a current-carrying conductor in a magnetic field when placed perpendicular to the direction of the field The magnitude of magnetic induction is said to be 1 tesla when a conductor of length 1 metre and carrying a current of 1 ampere experiences a force oflN when it is placed with its length perpendicular to the direction of the magnetic field. (2) The unit is named after Nikola Tesla (1870 -1943), Croatia-born US electrical engineer, inventor of the AC induction motor.]

A) Given radius (r) = 7 cm 

Circumference of a circle C = 2πr (∵ π = \(\frac{22}{7}\)) = 2 x \(\frac{22}{7}\) x 7 = 44 cm 

∴ Circumference of a circle = 44 cm

B) Given radius (r) = 3.5 cm 

Circumference of a circle C = 2πr (∵ π = \(\frac{22}{7}\))

= 2 x \(\frac{22}{7}\) x 3.5 

∴ Circumference of a circle = 22 cm

C) Given radius (r) = 14 cm 

Circumference of a circle C = 2πr (∵ π = \(\frac{22}{7}\)) 

= 2 x \(\frac{22}{7}\) x 14 

∴ Circumference of a circle = 88 cm

(c) √10

Here b = 3

3x² + 3y² + 12x - 18y + 9 = 0 

(÷ 3) zz > x² + y² + 4x – 6y + 3 = 0

Comparing with general form

g = 2, f = -3, c = 3 

∴ radius = √(g² + f² - c) = √(4 + 9 - 3) = √10

(a) 2ab

Area of the greatest rectangle is (√2a) (√2b) 

= 2ab

(b) x = -1

When the tangents at drawns from a point on the directrix are at right angles. 

So equation of directrix to y² = 4x is x = -1

Equation of normal to y² = 4 at’ t’ is y + xt = 2at + at³. 

So equation of normal at ‘t₁’ is y + xt₁ = 2at₁ + at₁³ 

The normal meets the parabola y² = 4ax at ‘t₂’ 

(ie.,) at (at₂², 2at₂) 

⇒ 2at₂ + at₁t₂² = 2at₁ + at₁³ 

So 2a(t₂ – t₁) = at₁³ – at₁t₂² 

⇒ 2a(t₂ – t₁) = at₁(t₁² – t₂²) 

⇒ 2(t₂ – t₁) = t₁(t₁ + t₂)(t₁ – t₂) 

⇒ 2 = -t₁(t₁ + t₂) 

⇒ t₁ + t₂ = -2/t₁

⇒ t₂ = -t₁ - (2/t₁) = -(t₁ + (2/t₁))

(d) (-6, -4)

Given parabola is x² + 12x – 9y = 0 

⇒ (x² + 12x + 36) – 36 – 9y = 0

⇒ (x + 6)² = 9y + 36 ⇒ (x + 6)² = 9(y + 4) 

∴ Vertex = (-6, -4)

(d) 8

We have, 9x² + 16y² = 144 

⇒ (x²/16) + (y²/9) = 1 (Dividing both sides by 144) 

Here a² = 16, b² = 9 ⇒ a = 4, b = 3 

Length of major axis = 2a = 2(4) = 8 

Since the sum of the focal distances from any point on the ellipse is equal to its major axis 

∴ Required sum = 8

Comparing this equation with the general equation of the conic 

Ax² + Bxy + Cy² + Dx + Ey + F = 0 

We get A = 2, C = – 1 

Where A ≠ C also A and C are of opposite signs. 

So the conic is a hyperbola.

Comparing this equation with the general equation of the conic 

Ax² + Bxy + Cy² + Dx + Ey + F = 0 

We get A = 0 and B = 0 

So the conic is a parabola.

• Steps in the elimination method:
• First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal.
• Then add or subtract one equation from the other so that one variable gets eliminated. If you get an equation in one variable, go to Step 3. If in Step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions. If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.
• Solve the equation in one variable (x or y) so obtained to get its value.
• Substitute this value of x (or y) in either of the original equations to get the value of the other variable.

Comparing this equation with the general equation of the conic 

Ax² + Bxy + Cy² + Dx + Ey + F = 0 

We get A = C and B = 0 

So the given conic is a circle.

(i) (3, 4, 2):- A (3, 0, 0), B (0, 4, 0), C (0, 0, 2)

(ii) (–5, 3, 7):- A (−5, 0, 0), B (0, 3, 0), C (0, 0, 7)

(iii) (4, – 3, – 5):- A (4, 0, 0), B (0, −3, 0), C (0, 0, −5)

Since L is the foot of perpendicular from P on the x-axis, its y and z coordinates are zero. The coordinates of L is (3, 0, 0). Similarly, the coordinates of M and N are (0, 4, 0) and (0, 0, 5), respectively

From the given figure, we can write as

∠ACD + ∠ACB = 180° is a linear pair

On rearranging we get

∠ACB = 180° – 112° = 68°

Again from the figure we have,

∠BAE + ∠BAC = 180° is a linear pair

On rearranging we get,

∠BAC = 180°– 120° = 60°

We know that the sum of all angles of a triangle is 180°.

Therefore, for △ABC:

x + ∠BAC + ∠ACB = 180°

x = 180° – 60° – 68° = 52°

x = 52°