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Given:

Ratio of speed of express train to superfast train = 1 ∶ 3

Time taken by superfast train to cross express train completely =  150 seconds

Time taken by passenger in superfast train to cross express train = 60 seconds

Formula used:

Distance = Speed × Time

Relative speed = S_a - S_b       (When both trains are moving in same direction and S_a > S_b)

Calculations:

Let the speed of express train and superfast train be 1x and 3x respectively.

In first case, when superfast train crossed express train completely

Distance covered = Length of express train(l_e)  + Length of superfast train(l_s)

Distance = Speed × Time

⇒ (l_e + l_s) = (3x - 1x) × 150

⇒ (le + ls) = 300x      ----(1)

In second case, when passenger in superfast train crossed express train

Distance covered = Length of express train(le)

Distance = Speed × Time

⇒ (le) = (3x - 1x) × 60

⇒ (le) = 120x      ----(2)

From (1) and (2),

⇒ ls = 180x 

⇒ (le ∶ ls) = 2 ∶ 3

∴ The ratio of the length of an express train to superfast train is 2 ∶ 3.

Given:

T = 45 minutes

Reduced speed = 54 km/hr

Percentage reduction in speed = 20%

80% Distance is covered in 45 minutes with reduced speed 

Formula used:

Distance = Speed × Time

Calculations:

Let the original speed be x km/hr

Reduced speed = 54 km/hr

x × (100 - 20)/100 = 54

⇒ x × (4/5) = 54

⇒ x = 54 × (5/4) = 135/2 km/hr

As time is 45 minutes = 45/60 = 3/4 hour

Distance = Speed × Time = (135/2) × (3/4) = 405/8

⇒ Distance = 50.625 km

∴ Required speed and distance is 18.75 m/s and 50.625 km

Calculation:

cube of negative number is always negative.

-11 × -11 × -11 = -1331

Calculation:

cube of negative numbers is always negative

-12 × -12 × -12 = -1728

Given ; 

4^x - 5(2^x) + 4 =  0

Calculation

(2^x)² - 5(2^x) + 4 = 0 

Let, 2^x = y

⇒ y² - 5y + 4 = 0

⇒ (y - 1) (y - 4) = 0

⇒ y = 1, 4 

⇒ 2^x = 1 and 2^x = 4

⇒ 2^x = 2⁰ and 2^x = 2²

∴ The required answer is x = 0, x = 2

Option changed check option and solution

Given:

The number = 24683B

Concept:

The divisibility rule of 16 = A number is divisible by 16 when it will divisible by both 2 and 8.

The number is divisible by 8 when the last three digits of the number are divisible by 8

The number is divisible by 2 when the last digit of the number is even

Calculation:

⇒ When the last three-digit is divisible by 8 = \({83B\over 8}\)

⇒ The possible value of B = 2

⇒ If the last digit is 2 then this number also divisible by 2

⇒ So, if B = 2 then the number is divisible by 16

⇒ 2B = 2 × 2 = 4

∴ The required result will be 4.

(√ 50 + 5)/(√ 32 + 4)

= {5(√ 2 + 1)}/{4(√ 2 + 1)}

= 5/4

Given:

When 15 is subtracted from 7 times of the number, the result is 10 more than twice of a number

Calculation:

Let the number be x

We know that

7 × x – 15 = (2 × x) + 10

⇒ 7x – 2x = 10 + 15

⇒ 5x = 25

⇒ x = 5

∴ The number is 5.

√ 1521 = 39 and √ 169 = 13

√ 784 = 28 and √ 196 = 14

Now, (√ 1521/√ 169) - (√ 784/√ 196)

= (39/13) - (28/14)

= 3 - 2

= 1

√ 196 = 14 and √ 144 = 12

√ 9 = 3 and √ 36 = 6

So, (√ 196/√ 144) - (√ 9/√ 36) = 14/12 - 3/6 = 8/12 = 2/3

Given:

A number when multiplied by 15 is increased by 196

Calculation:

Let the number be x

We know that

15 × x = x + 196

⇒ 15x – x = 196

⇒ 14x = 196

⇒ x = 14

∴ The number is 14.

Given:

Dinesh is traveling on his bike. He will reach point P at 6 p.m. if he travels at 20 km/h. He will reach point P at 2 p.m. If he travelers at a speed of 30 km/h

Concept used:

Distance = Time × Speed

Calculation:

Let, when Dinesh reach point P at 4 p.m it took time t hours.

⇒ When Dinesh reach point P at 6 p.m it took time (t + 2) hours.

⇒ When Dinesh reach point P at 2 p.m it took time (t - 2) hours.

As per the question, equating the distance get,

⇒ (t - 2) × 30 = (t + 2) × 20

⇒ 3t - 6 = 2t + 4

⇒ t = 10

Distance = (10 - 2) × 30 = 8 × 30 = 240 km.

Now, 8 × 30 = 10 × speed

⇒ speed = 240/10

∴ speed = 24km/hr

Given:

Total distance = 540 kms

Delay due to reduction in speed = 9 hours

Formula used:

Time = Distance/Speed

Calculations:

Let the actual speed of Ram be s km/hr.

According to question,

Difference between usual time and delayed time = 9 hours

⇒ {(270/s) + (30% of 540)/(2s/3) + (20% of 540)/(s/3)} - (540/s) = 9

⇒ {(270/s) + (162 × 3)/(2s) + (108 × 3)/s} - (540/s) = 9

⇒ {(270/s) + (243)/(s) + (324)/s} - (540/s) = 9

⇒ (270 + 243 + 324 - 540)/s = 9

⇒ s = 33 km/hr

∴ The actual speed of Ram is 33 km/hr.

Given:

Sum of three numbers 264.

Calculation:

Let the first, second, third number be x, y, z.

According to the question;

⇒ x = 2y

⇒ z = 1/3x

Then, z = 1/3 × 2y = 2/3y

Now, Sum of three numbers 264.

⇒ x + y + z = 264

⇒ 2y + y + 2/3y = 264

⇒ 11/3y = 264

⇒ y = 72

∴ The second number is 72.

Given:

 Time taken by train to cross a man = 8 seconds 

Time taken by train to cross a platform = 18 seconds

Length of the train = 100 metres 

Formula Used :

Distance = Speed × Time

Calculation :

let the length of the platform be x 

Total distance covered by train in 18 sec = Lenght of train + length of the platform

⇒  D = (100 + x) metres

speed of the train = 100/8 m/s 

 Total distance covered by train= speed of train × total time taken

100 +x = (100/8) × 18

⇒ x = 225 - 100

⇒x = 125 m

∴ The length of the platform is 125 m

To find the LCM:

Concept used:

Prime factorization concept

Calculation:

8 = 2 × 2 × 2

9 = 3 × 3

12 = 2 × 2 × 3

Now we have to take factors which occur most often

LCM = 2³ × 3² 

⇒ LCM = 8 × 9

⇒ LCM = 72

∴ Required LCM is 72

Given:

We have to find the smallest fraction in \(\frac{7}{6},\frac{7}{9},\frac{4}{5},\frac{5}{7}\)

Calculation:

7/6 = 1.67, 7/9 = 0.78, 4/5 = 0.8, 5/7 = 0.71

By comparing the values we can see

⇒ 5/7 = 0.71 is the smallest

∴ The smallest fraction is (5/7).

Given:

The number in percentage is 4%.

Concept Used:

Value% = Value/100

Calculation:

The number in percentage is 4%.

⇒ 4% = 4/100 = 1/25

∴ The fraction of 4% is 1/25.

Given:

HCF = 15

LCM = 300

First number = 60

Concept used:

If 'a' and 'b' are two numbers, then LCM × HCF = a × b

Calculations:

Let the first number be 'a' and second number be 'b'.

LCM × HCF = a × b

⇒ 300 × 15 = 60 × b

⇒ 4500 = 60 × b

⇒ b = 75

∴ The second number is 75.

Formula used:

The LCM of the fraction number = (LCM of the numerator)/(HCF of the denominator)

Calculation:

LCM of the numerator (2, 3, 4, 9) is 36

HCF of the denominator (3, 5, 7, 13) is 1

The LCM of 2/3, 3/5, 4/7, 9/13 = 36/1 = 36

∴ The LCM of the given expression is 36

Given:

7129p465 is divisible by 9. We have to find the value of p

Concept Used:

If a number is divisible by 9, then the sum of its all digit will also be divisible by 9

Calculation:

Given number is 7129p465

The sum of all digits of the number is 7 + 1 + 2 + 9 + p + 4 + 6 + 5

⇒ (34 + p)

Now,

9 × 1 = 9

9 × 2 = 18

9 × 3 = 27

9 × 4 = 36

9 × 5 = 45 and so on...

Nearest number to (34 + p) which is a multiple of 9 is 36

Then, (34 + p) = 36

⇒ p = 2

∴ The value of p is 2

Given:

The product of two numbers = 1548

HCF of numbers = 12

Formula used:

Product of numbers (a and b) = HCF of (a, b) × LCM of (a, b)

Calculation:

Let the LCM of numbers be x.

∴ 1548 = x × 12

⇒ x = 129.

Given:

The ratio of the two numbers = 2 : 3

LCM of the two numbers = 48

Calculation:

Let the two numbers be 2y and 3y. 

LCM (2y, 3y) = 6y 

⇒ 6y = 48 

⇒ y = 8 

Now, The sum of numbers = (2y + 3y)

⇒ 5y 

⇒ 5y = 5 × 8

⇒ 40

∴ The sum of the number is 40.

Given:

LCM = 108

HCF = 18 

one of the numbers = 36.

Concept Used:

(a and b) = HCF of (a, b) × LCM of (a, b)

Calculation:

Let the other number be x.

36 × x = 108 × 18

⇒ x = 54

∴ The other number is 54

a) Coherent

The principle of professional communication in which the words should make sense and should be related to the main topic is known as Coherent.

ADTOI- Association of Domestic Tour Operators of India. They promote Domestic Tourism.

The third carnatic war came to an end 1763.

1749- 54 was the second carnatic war fought.

Tourism sector generates a number of employment, opportunities and also a good supporter of GDP.

The second carnatic war came to an end with the treaty of Pondicherry.

Correct option is B) turn indicators

Tourism increases employment opportunities.

Medical emergencies can cause serious havoc with one’s travel plans.

Pherozeshah Mehta was not an Extremist Leader.

The full form of GIT is Group Inclusive tour.

Gandhi went to England in September 1931 to attend the second round table conference.

It is full rate before discounts are given. It is generally printed in the tour brochures.

V.D. Savarkar formed the gadar party in the United States of America in 1913.

Answer is : Correct

Correct option: a. European Plan

Bombay the Quit India resolution passed.

The drama Keechakvadh enraged the audience about the imperialistic attitude of the British Government. 

Points: • metaphorical drama to denounce the British Government 

• drama was written by Krishnaji Prabhakar Khadilkar 

• based on certain events in Maharashtra. 

• Draupadi represents helpless mother India, Yudhishthir represents the moderates, Bheem represents the extremists and Keechaka insolent viceroy Lord Curzon. 

• Thus, it created discontent for British Government.

The first governor general of Bengal was Lord Warren Hastings.

Patel in charge of the integration of princely states.

The INA joined the Japanese army in its march on India from Burma.

A tour accompanied by qualified, trained and experienced tour managers or guides is called Escorted Tour.

We should conserve our Natural and Cultural Heritage. 

Points: • Cultural heritage - manmade : tangible, intangible 

• natural heritage - biodiversity 

• many traditions/heritage sites are endangered. 

• need of conservation for next generation 

• tourism opportunities  

• employment opportunities 

Jinnah the first governor general of Pakistan.

Only trained persons, who are duly qualified can take up the tasks involved in the work of conservation and preservation. 

Points: • Collection of historical sources, their record, manuscripts, lists, old texts, material sources - maintenance and presentation should be done carefully. 

• Only after completion of proper training, it is possible. 

• Thus, training is required to take up tasks involved in the work of conservation and preservation

India wins freedom was written by Azad.