Explore topic-wise InterviewSolutions in .

Thickness of the paper measured is by Screw Gauge.

parallactic angle , theta =57 '

=(57/60)^o

=(57/60 )x pi/180 rad 

b= Radius of earth =6.4 x 10⁶ m 

Distance of the moon from the earth ,

s= b/theta = 6.4 x10⁶ x 60 x180 / 57x pi 

s= 3.86 x 10⁸ m

distance of sun from the earth =1.5 x 10¹¹ m

angular diameter of sun ,

theta =1920''= (1920/60x60)^o =1920/3600 xpi/ 180 rad

diameter of sun , D = s x theta 

                             = 1.5 x 10¹¹ x 1920/3600 x pi /180 

                           D= 1.4 x 10⁹ m

y = Fx/AΔx,

y = Fx/πr²(0.01)  ...(1)

y' \(=\frac{Fx}{\pi(\frac r2)^2\;\Delta x}\)

y' \(=\frac{Fx\times4}{\pi r^2(\Delta x)}\)  ...(2)

y' = y

4/Δx = 1/0.01

Δx = 0.04 mm

D. the amount of charge that flows past a point in one second when the current is 1 A

E. tesla ·meter /ampere 

A. 0.25 A · m², in the positive z direction

A. in the same direction as the field

C. ampere· meter ²

B. in the positive y direction

A. one of the directions of the velocity when the magnetic force is zero

C. if the particle is moving across the field lines

E. none of the above 

When a steel blade is placed on water horizontally, the surface tension and the buoyancy will be able to balance the wight of the blade and it will oat on the water surface. You know the buoyancy is not sufficient to make the steel blade oat. Now if you add detergent to water, the surface tension of water immediately decreases. The surface tension no longer be able to balance the blade and it will sink.

Given f(x) = x² + 4

Since f is a second degree polynomial

∴ f is continuous on [–3, 3] and f is desivable on (–3, 3)

Also f(–3) = 9 + 4 = 13 f(3) = 9 + 4 = 13

∴ f(–3) = f(3)

∴ f satisfies all the conditions of Role's theorum.

∴ There exists c∈(–3, 3) such that f¹(c) = 0

But f¹(x) = 2x

f¹(c) = 2c

0 = 2c

⇒ c = 0 ∈ (–3, 3)

Hence Rolle's theorum is verified.

Given A = (2, 3) 

B = (2, –3) 

Let P(x, y) be any point on the locus. 

Given geometric condition is 

PA + PB = 8 ⇒ PA = 8 – PB 

⇒ PA² = (8 – PB)² 

⇒ PA² = 64 + PB² – 16PB

⇒ (x – 2)²+(y – 3)² = 64 + (x – 2)² + (y + 3)² - 16√((x - 2)² + (y + 3)²)

⇒ y² – 6y + 9 – y² – 6y – 9 – 64 = – 16√(x² - 4x + 4 + y² + 6y + 9)

⇒ (–12y – 64) = –16√(x² + y² - 4x + 6y + 13)

⇒ (3y + 16) = 4√(x² + y² - 4x + 6y + 13) 

S.O.B.S

⇒ (3y + 16)² = 16 (x² + y² – 4x + 6y + 13) 

⇒ 9y² + 256 + 96y = 16x² + 16y² – 64x + 96y + 208 

⇒ 16x² + 7y² – 64x – 48 = 0

∴ The locus of P is 16x² + 7y² – 64x – 48 = 0

Given y = ae^nx + be^{– nx} 

y¹ = ae^nx . n + be^{– nx} (–n) 

= ane^nx – bne^{– nx} 

y¹¹ = ane^nx . n – bne^{– nx}(–n) 

= an² e^nx + bn² e^{– nx}

= n² (ae^nx + be^{– nx}) 

= n²y 

∴ y¹¹ = n²y.

Given f(x) = x² + x, x = 10 and ∆x = 0.1

dy = f'(x) ∆x

= (2x + 1) ∆x

= [2(10) + 1] (0.1)

= (21) (0.1) = 2.1

∆y = f(x + ∆x) – f(x)

= (x + ∆x)² + (x + ∆x) – (x² + x)

= x² + 2x ∆x + (∆x)² + x + ∆x – x² – x

= 2x ∆x + (∆x)² + ∆x

= 2(10) (0.1) + (0.1)² + 0.1

= 2 + 0.01 + 0.1

= 2.11

Incomplete question.  What will come after cot^-1. 

The correct answer is To celebrate acts of courage of ordinary women who played extraordinary roles.

• About International Women's Day
  • International Women's Day is a global day celebrating the social, economic, cultural and political achievements of women.
  • The day also marks a call to action for accelerating gender parity. Significant activity is witnessed worldwide as groups come together to celebrate women's achievements or rally for women's equality. 
  • Marked annually on March 8th, International Women's Day (IWD) is one of the most important days of the year to:
    • celebrate women's achievements
    • raise awareness about women's equality
    • lobby for accelerated gender parity
    • fundraise for female-focused charities
    • To celebrate acts of courage of ordinary women who played extraordinary roles.

• What's the theme for International Women's Day?
  • The campaign theme for International Women's Day 2021 is 'Choose To Challenge'.
  • A challenging world is an alert world. And from challenge comes change.
• What colours symbolize International Women's Day?
  • Purple, green and white are the colours of International Women's Day.
  • Purple signifies justice and dignity. Green symbolizes hope.
  • White represents purity, albeit a controversial concept.
  • The colours originated from the Women's Social and Political Union (WSPU) in the UK in 1908.

Given:

Total mixture of spirit and water = 45 litres

Percentage of water in mixture = 20%

Calculation:

Let x litre of water must be added to make it 25% in the new mixture

Percentage of water in mixture = 20% of 45 litres

⇒ (20/100 × 45)

⇒ 9 litres

According to the question

⇒ (9 + x)/(45 + x) = 25/100

⇒ (9 + x)/(45 + x) = 1/4

⇒ 36 + 4x = 45 + x

⇒ 3x = 9

⇒ x = 3 litres

∴ Water should be added is 3 litres

Given:

D invested Rs. 1210 for 3 years and E invested 3450 for 9 years. D again invested Rs. 2410 for 7 years and E invested Rs. 1750 for 1 year.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Profit sharing ratio of D and E after 10 years

D                                                        :                         E

1210 × 3 + 2410 × 7                          :                         3450 × 9 +1750 × 1

3630 + 16870                                    :                         31050 + 1750

20500                                                :                         32800

Required ratio = 205 : 328 = 5 : 8

The ratio of cost price of two articles is 4 ∶ 9

⇒ Let the cost price of first article = 4x

The cost price of second article = 9x

The articles are marked up by 40% and 15% respectively

⇒ Marked price of first article = 4x × (140/100) = 5.6x

Marked price of second article = 9x × (115/100) = 10.35x

The ratio of their Marked price is 112 ∶ 207

⇒ Marked price of first article = 112y

Marked price of second article = 207y

∴ 5.6x = 112y

⇒ x = 20y

According to question,

Selling price of first article = 112y × (7/8) = 98y      ----(12.5% = 1/8)

Profit = 98y – 4x = 270

⇒ 98y – 80y = 270

⇒ 18y = 270

⇒ y = 15

∴ x = 20 × 15 = 300

⇒ Cost price of second article = 300 × 9 = 2700

Marked price of second article = 2700 × (115/100) = 3105

Selling price of second article = 3105 × (8/9) = 2760

∴ Profit earned = 2760 – 2700 = 60

∴ The profit earned on second article is Rs.60

Given:

Two brothers K and L invested Rs. 3900 and 4500 respectively. K invested for 8 months and L invested for 4 months. They then interchanged their amount and again invested for 4 months and 8 months respectively.

Formula:

Ratio of Profit = ratios of product of Amount invested and time

Calculation:

Given that two brothers invested 3900 and 4500 for 8 and 4 months respectively and they interchanged their amount and again invested for 4 months and 8 months respectively.

K                                           :                L

3900 × 8 + 4500 × 4             :               4500 × 4 + 3900 × 8

49200                                   :                49200

Required ratio = 1 : 1

Given:

Let cost price of a mobile and an earphone be Rs.a and Rs.b respectively.

⇒ a + b = 14000

⇒ b = a - 2500

Solving,

a = 8250 and b = 5750

⇒ Selling price of a mobile = 8250 × 110/100 = Rs.9075

⇒ Selling price of an earphone = 5750 × 115/100 = Rs.6612.5 ≈ 6612

∴ Required difference = 9075 - 6612 = Rs.2463

Given:

The new speed of the train = 7/11 × old speed of the train

With new speed, time taken to reach the place = 22 hours

Concept used:

When traveling the same distance,

Speed ∝ (1/time)

Calculation:

Let the old speed be S_O and the new speed be S_N

Let the old time taken be T_O and new time taken be T_N

SN = (7/11) × SO 

⇒ S_N ∶ S_O = 7 ∶ 11

⇒ T_N ∶ TO = 11 ∶ 7

With new speed, time taken to reach, T_N = 11x = 22 hrs

⇒ x = 2 hrs

The time that could be saved by him if the train runs on time = 11x – 7x = 4x

⇒ 4x = 4 × 2 = 8 hours.

∴ The time that can be saved by running with old speed is 8 hours.

Answer: probability

Converse = (q → P) = If the child is brave then maths is easy 

Inverse = (~ P → ~q) = If maths is not easy then the child is not brave.

Correct answer is: (c) 0 ≤ P(E) ≤1

0≤ P( E) ≤1

Option : (c)

adj A = \(\begin{bmatrix} 7& -5 \\[0.3em] -11 & 2 \end{bmatrix}\)

⇒ (adj A)' = \(\begin{bmatrix} 7& 11 \\[0.3em] -5 & 2 \end{bmatrix}\)

2((2x-1)/(x+3)) - 3((x+3)/(2x-1)) = 5, x ≠ - 3,1/2

⇒ \(\frac{2(2x-1)^2-3(x+3)^2}{(x+3)(2x-1)}\) = 5

⇒ 2(4x² − 4x + 1) − 3(x² + 6x + 9) = 5(x + 3)(2x − 1) 

⇒ 8x² − 3x² − 8x − 18x + 2 − 27 = 10x² + 25x − 15 

⇒ 5x² − 26x − 25 = 10x² + 25x − 15 

⇒ 10x² − 5x² + 25x + 26x − 15 + 25 = 0 

⇒ 5x² + 51x + 10 = 0 

⇒ 5x² + x + 50x + 10 = 0 

⇒ 5x(5x + 1) + 10(5x + 1) = 0 

⇒ 5(x + 10)(5x + 1) = 0 

⇒ x + 10 = 0 or 5x + 1 = 0

⇒ x = −10 or x = \(\frac{-1}{5}\).

Hence, 

The solutions of given equation are x = \(\frac{-1}{5}\),-10.

Given:

The vertices of the triangle A, B and C = (4, 6), (6, 3) and (5, 9)

Formula used:

[(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3]

where, x₁ = 4, x₂ = 6, x₃ = 5, y₁ = 6, y₂ = 3 and y₃ = 9

Calculation:

According to the question

[(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]

⇒ [(4 + 6 + 5)/3, (6 + 3 + 9)/3]

⇒ [(15/3), (18/3)]

⇒ (5, 6)

∴ The centroid of the triangle is (5, 6)

Given:

t_n = 4n – 9

Formula used:

Common difference (d) = t₂ – t₁

Calculation:

According to the question

⇒ t₁ = 4 × (1) – 9 = -5

⇒ t₁ = 4 – 9 

⇒ t₁ = -5

⇒ t₂ = 4 × (2) – 9

⇒ t₂ = 8 – 9

⇒ t₂ = -1

⇒ d = (-1) – (-5)

⇒ -1 + 5

⇒ 4

∴ Common difference is 4

We know that,

A number that is divisible by a number other than 1 and itself, is called a composite number. 

Now,

7 × 5 × 3 × 2 + 3 = 3(7 × 5 × 2 + 1) 

= 3(70 + 1) 

= 3 × 71. 

∵ The given number has two factors 3 and 71 other than 1 and itself. 

∴ The given number is a composite number.

Zeros of the polynomial P(x) are the points where the graph of P(x) intersect x-axis. There are two such points. Hence, total number of zeros of P(x) is 2.

The speech of Yaser Arafat, the leader of PLO in the UN Assembly in 1974.

Israel was formed in 1948. Following this, Israel seized Palestine, expelling the Palestinians from their homeland. The Palestinian refugees migrated to various Arab countries. It was in this context that the Palestine Liberation Organization (PLO) was formed with Yaser Arafat as President to establish a nation for the Palestinians. Yaser Arafat made such a speech in order to create a state for Palestinians through peaceful means.

The correct option is: (a) sec² θ