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All questions of May Week 1 for Class 10 Exam

The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –
  • a)
    k = 2
  • b)
    k = 6
  • c)
    k = 6
  • d)
    k = 3
Correct answer is option 'A'. Can you explain this answer?

Naina Sharma answered
An equation has infinitely many solutions when the lines are coincident.
The lines are coincident when 
So 3x + 4y = k, 9x + 12y = 6 are coincident when

Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is –
  • a)
    28 years
  • b)
    30 years
  • c)
    32 years
  • d)
    34 years
Correct answer is option 'B'. Can you explain this answer?

Dr Manju Sen answered
Let the present age of man is x and of son is y.
Six years hence,
Man’s age =x+6
Son’s age=y+6
Man’s age is 3 times son’s age
x+6=3(y+6)
x+6=3y+18
x=3y+12    …...1
Three years ago,
Man’s age =x-3
Son’s age=y-3
Man’s age was 9 times as of son
x-3=9(y-3)
x-3=9y-27
x=9y-24   ….2
From 1 and 2
3y+12=9y-24
6y=36
y=6
x=3*6+12=18+12=30 years

What does the ‘Silk Route’ refer to?
  • a)
    Present-day West Asia 
  • b)
    West-bound Chinese silk cargoes 
  • c)
    Introduction of the humble potato
  • d)
    Both (a) and (b)
Correct answer is option 'B'. Can you explain this answer?

Arun Sharma answered
The Silk Route or Silk Road refers to a network of ancient trade routes connecting Asia, Europe and Africa. Extending more than 6,500 kms, the Silk Route was majorly used to transport Chinese Silk to Europe through Central Asia from 2nd Century BC.

The pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution if –
  • a)
    k ≠ -3
  • b)
    k = 3
  • c)
    k = 5
  • d)
    k = -5
Correct answer is option 'A'. Can you explain this answer?

Rohit Sharma answered
Given :
2 k x + 5 y – 7 = 0  ...( i )
6 x – 5 y – 1 = 0   ... ( ii )
Pair of linear equations has a unique solution.
We know for unique solution.
Comparing from ( i ) and ( ii ) we have
Put these values in formula.
Thus we get answer many values of k but leaving k ≠ -3.

The pair of linear equations 2x + 5y = k, kx + 15y = 18 has infinitely many solutions if –
  • a)
    k = 3
  • b)
    k = 6
  • c)
    k = 9
  • d)
    k = 18
Correct answer is option 'B'. Can you explain this answer?

Vivek Rana answered
An equation has infinitely many solutions when the lines are coincident.
The lines are coincident when 
So 2x + 5y = k, kx + 15y = 18 are coincident when

The group of powers collectively known as the Axis power during the Second World War were:
  • a)
    Germany, Italy, Japan
  • b)
    Austria, Germany, Italy
  • c)
    France, Japan, Italy
  • d)
    Japan, Germany, Turkey
Correct answer is option 'A'. Can you explain this answer?

In Second World War , there are two groups named as "Axis Powers" and "Allied Powers" . Allied Powers includes USA , France , Austria, Great Britain and Soviet Union. While Axis Powers includes Germany, Italy and Japan. Hence option A is correct as these three countries collective known as "Axis Powers".

Assertion: Corn Laws were scrapped in the 19th century.
Reason: Workers were against these laws.
  • a)
    Both A and R are true and R is the correct explanation of A
  • b)
    Both A and R are true but R is not the correct explanation of A
  • c)
    A is correct but R is wrong
  • d)
    A is wrong but R is correct
Correct answer is option 'C'. Can you explain this answer?

Amit Sharma answered
The corn laws were abolished by the government because:The laws raised the food prices and were meant to favour domestic producers.
The laws imposed steep import duties and hence,made import of grain from abroad very costly affair despite the shortage of food supply.

The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not have any solution if
  • a)
    k = 7
  • b)
    k = 14
  • c)
    k = 21
  • d)
    k = 28
Correct answer is option 'B'. Can you explain this answer?

Explanation:

Given pair of linear equations are:

3x - 7y = k ...(1)

12x - 2ky = 4k - 1 ...(2)

We need to find the value of k for which these equations do not have any solution.

Method:

If a pair of linear equations do not have any solution, it means they are inconsistent. Two linear equations are inconsistent if their slopes are equal but their y-intercepts are not equal.

We can rearrange the given equations into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Equation (1) can be rearranged as:

y = (3/7)x - (k/7) ...(3)

Equation (2) can be rearranged as:

y = (6/k)x - (2k-1)/(2k) ...(4)

Comparing equations (3) and (4), we get:

m1 = 3/7 and m2 = 6/k

For the pair of equations to be inconsistent, m1 = m2 and b1 ≠ b2.

Equating the slopes, we get:

3/7 = 6/k

Solving for k, we get:

k = 14

Now, substituting k = 14 in equations (1) and (2), we get:

3x - 7y = 14 ...(5)

12x - 28y = 55 ...(6)

Multiplying equation (5) by 4, we get:

12x - 28y = 56 ...(7)

Comparing equations (6) and (7), we see that the y-intercepts are not equal. Hence, the given pair of equations are consistent for k = 14.

Conclusion:

Thus, the given pair of linear equations 3x - 7y = k, 12x - 2ky = 4k - 1 do not have any solution if k = 14. Therefore, the correct option is (B).

The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
  • a)
    Unique solution
  • b)
    Exactly two solutions
  • c)
    No solution
  • d)
    Infinitely many solutions
Correct answer is option 'C'. Can you explain this answer?

Meera Rana answered
Given, 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 
a1/a2 = 9/18 = 1/2 
b1/b2 = 3/6 = 1/2 
c1/c2 = 12/26 = 6/13 
Since, a1/a2 = b1/b2 ≠ c1/c2 
So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

People livelihood and local economy of which one of the following was badly affected by the disease named Rinderpest
  • a)
    Asia
  • b)
    Europe
  • c)
    Africa
  • d)
    South America
Correct answer is option 'C'. Can you explain this answer?

Rinderpest arrived in Africa in the late 1880s. Within two years, it spread in the whole continent reaching Cape Town within five years. Rinderpest had a terrifying impact on people’s livelihoods and the local economy. It killed about 90 percent of the cattle. Planters, mine owners and colonial governments became successful to strengthen their power and to force Africans into the labour market.

8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.       
  • a)
    120, 130       
  • b)
    140,280       
  • c)
    240,280       
  • d)
    100,120
Correct answer is option 'B'. Can you explain this answer?

Vikas Kumar answered
Work done by 1 girl and 1 boy in x and y days respectively.
work done by 1 girl and 1 boy in 1 day is (1/x) and (1/y).
so, work done by 8 girls and 12 boys in 1 day is (8/x) + (12/y) = 1/10
let (1/x) = a and (1/y) = b
so, 8a + 12b = 1/10
→ 80a + 120b = 1 ---- (1)
work done by 6 girls and 8 boys in 1 day is (6/x) + (8/y) = 1/14
6a + 80 = 1/14
→ 84a + 112b = 1 ---- (2)
By elimination method, Multiple equation 1 by 21 on both sides, we get
1680a + 2520b = 21 ---- (3)
Multiply equation 2 by 20 on both sides, we get
1680a + 2240b = 20 ---- (4)
On solving equation 3 and 4, we get
2520 b - 2240b = 21 - 20
→ 280 b = 1
→ b = 1/280
b =1/y
→ 1/280 = 1/y
→ y = 280
80a + 120 x (1/280) = 1 (From 1)
→ 80a + (3/7) = 1
→ 80a = 1 - (3/7)
→ 80a = (7 - 3)/7
→ 80a = 4/7
→ a = 4/(7 × 80)
→ a = 1/140
→ a = 1/x
→ 1/140 = 1/x
→ x = 140
1 girl and 1 boy alone take 140 days and 280 days to complete a work.

Which of the following places was an important destination for indentured migrants?
  • a)
    Florida
  • b)
    Melbourne
  • c)
    Caribbean island
  • d)
    Mexico
Correct answer is option 'C'. Can you explain this answer?

Importance of Caribbean Islands for Indentured Migrants

Indentured migration was a system of labor migration that emerged in the 19th century to address labor shortages in various parts of the world. It involved the recruitment and transportation of workers from one country or region to another under a contractual agreement that bound them to work for a specific period in exchange for passage, food, clothing, and shelter. The Caribbean Islands were an important destination for indentured migrants, and here's why:

1. Historical Context

The Caribbean Islands were colonized by Europeans, primarily the British, French, and Spanish, who established sugar plantations that required a massive workforce. The indigenous population was decimated by diseases, and African slaves were brought in to work on the plantations. However, the abolition of slavery in the 19th century created a labor shortage, and the plantation owners turned to indentured labor to fill the gap.

2. Recruitment and Transportation

Indentured labor was recruited from various parts of the world, including India, China, and Africa. The recruitment process involved agents who traveled to different regions to sign up workers for the journey to the Caribbean Islands. The workers were promised a better life and higher wages than they could earn at home. They signed a contract that bound them to work for a specific period, usually five years, in exchange for passage, food, clothing, and shelter.

3. Living and Working Conditions

The living and working conditions of indentured laborers in the Caribbean Islands were harsh. They were housed in barracks and subjected to long hours of work in the sugar fields. The work was grueling, and the climate was hot and humid. Many workers died from disease, malnutrition, and overwork.

4. Legacy of Indentured Migration

Indentured migration to the Caribbean Islands lasted from the mid-19th century to the early 20th century. It brought millions of workers to the region, who contributed to the development of the sugar industry and the economy. However, it also created a legacy of exploitation, inequality, and discrimination that persists to this day.

Conclusion

In conclusion, the Caribbean Islands were an important destination for indentured migrants because of the labor shortages created by the abolition of slavery. The system of indentured migration brought millions of workers to the region, who contributed to the development of the sugar industry and the economy. However, it also created a legacy of exploitation and discrimination that continues to affect the region.

What does the "p" in the pH scale stand for, and what does the scale measure?
  • a)
    Potential; measures temperature variations.
  • b)
    Power; measures the hydrogen ion concentration in a solution.
  • c)
    Percentage; measures the basic nature of a solution.
  • d)
    Pressure; measures the acidity of a liquid.
Correct answer is option 'B'. Can you explain this answer?

Ankita Basak answered
What Does the "p" in pH Stand For?
The "p" in pH stands for "power." This designation is derived from the German word "Potenz," which translates to "power" or "potential."
Understanding pH Scale
The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution. It ranges from 0 to 14, where:
- A pH of 7 is considered neutral (pure water).
- A pH less than 7 indicates acidity (higher hydrogen ion concentration).
- A pH greater than 7 indicates basicity (lower hydrogen ion concentration).
Measurement of Hydrogen Ion Concentration
The pH scale specifically measures the concentration of hydrogen ions (H+) in a solution. This is crucial because:
- Acidic Solutions: Higher concentrations of H+ ions lead to lower pH values. For example, lemon juice has a pH of around 2, indicating high acidity.
- Basic Solutions: Lower concentrations of H+ ions correspond to higher pH values. For instance, bleach has a pH of around 12, indicating it is basic.
Importance of pH
Understanding pH is essential in various fields, including:
- Chemistry: It helps in determining the nature of chemical reactions.
- Biology: Enzyme activity and metabolic processes are pH-dependent.
- Environmental Science: pH affects aquatic life and soil health.
In summary, the correct answer is option 'B' because the pH scale effectively measures the hydrogen ion concentration in a solution, which determines its acidity or basicity.

Assertion: The pre-modern world shrank greatly in the 16th century.
Reason: European sailors found new sea routes to Asia and successfully crossed the western ocean to America.
  • a)
    Both A and R are true and R is the correct explanation of A
  • b)
    Both A and R are true but R is not the correct explanation of A
  • c)
    A is correct but R is wrong
  • d)
    A is wrong but R is correct
Correct answer is option 'A'. Can you explain this answer?

Rohit Sharma answered
During the 16th century, European sailors found sea routes, that linked the furthermost parts of the world. They crossed the western ocean and reached America and also many other regions of the world.Hence, we can say that the world was shrinking at that time mainly because of the European Sailors.

What ‘technology’ helped in transporting perishable goods?
  • a)
    Refrigerated aircrafts 
  • b)
    Refrigerated railways 
  • c)
    Refrigerated ships
  • d)
    Both (a) and (b)
Correct answer is option 'C'. Can you explain this answer?

Goods are transported in refrigerated ships that are fully equipped with a system to circulate air properly. You can also ship in refrigerated containers.
Nowadays, markets and consumers are more demanding of quality services in all areas, include transportation and merchandise. Transporting goods is a complicated endeavor and more so when it comes to products that are sensitive, that are perishable  goods

Solve : 5x/2+3x/4>39/4, x ∈ R :
  • a)
    (-3, ∞)
  • b)
    (3,3)
  • c)
    (-∞,3)
  • d)
    (3,∞)
Correct answer is option 'D'. Can you explain this answer?

It is not clear what the expression is asking. Please provide more information or clarify the expression.

The pairs of equations x + 2y - 5 = 0 and -4x - 8y + 20 = 0 have:
  • a)
    Unique solution
  • b)
    Exactly two solutions
  • c)
    Infinitely many solutions
  • d)
    No solution
Correct answer is option 'C'. Can you explain this answer?

Meera Rana answered
a1/a2 = 1/-4
b1/b2 = 2/-8 = 1/-4
c1/c2 = -5/20 = -¼
This shows:
a1/a2 = b1/b2 = c1/c2
Therefore, the pair of equations has infinitely many solutions.

Which was the fabled city of gold?
  • a)
    Peru
  • b)
    Mexico
  • c)
    El Dorado
  • d)
    Spain
Correct answer is option 'C'. Can you explain this answer?

Upsc Lover answered
El Dorado, the fabled city of gold that the Spanish believed was located somewhere in South America.

Solve : 2(x-1)/5<3(2+x)/7, x ∈ R :
  • a)
    (44, ∞)
  • b)
    (44,-∞)
  • c)
    (– 44,∞)
  • d)
    (+ 44,∞)
Correct answer is option 'C'. Can you explain this answer?

Drishti Kumari answered
2( x - 1 ) / 5 is less than 3 ( 2 + x ) / 7
2x - 2 / 5 is less than 6 + 3x / 7

Cross multiplication
14x - 14 is less than 30 + 15x
14 x - 15 x is less than 30 + 14
- x is less than 44
When we divide from negative no. to positive no. then inequality sign becomes change
So,
x is greater than - 44
On number line , it is ( - 44 , + infinity )
Hence, option (C) is correct .

What type of workers primarily manned ships transporting goods during this period?
  • a)
    Wealthy landowners
  • b)
    Low-paid workers from southern Europe, Asia, Africa, and the Caribbean
  • c)
    Highly paid industrialists
  • d)
    Farmers working on their own land
Correct answer is option 'B'. Can you explain this answer?

During the late 19th and early 20th centuries, the transportation of goods across vast distances, particularly by ships, was primarily carried out by low-paid workers from regions like southern Europe, Asia, Africa, and the Caribbean. These workers were often employed in harsh conditions and played a crucial role in the global trade network.
Topic in NCERT:  A World Economy Takes Shape
Line in NCERT: "It was transported by railway, built for that very purpose, and by ships which were increasingly manned in these decades by low-paid workers from southern Europe, Asia, Africa, and the Caribbean."

Solve : x/5R : <(3x-2)/4-(5x-3)/5, x ∈ R:
  • a)
    (2/7,∞)
  • b)
    (2/9,∞)
  • c)
    (-∞, 2/9)
  • d)
    (∞, 2/9)
Correct answer is option 'C'. Can you explain this answer?

Ram Mohith answered
I think the question is to solve for x, x/5 < (3x - 2)/4 - (5x - 3)/5
Now multiply throughout with 20,
4x < 5(3x - 2) - 4(5x - 3)
4x < 15x - 10 - 20x + 12
20x - 15x + 4x < 12 - 10
9x < 2
x < 2/9
So, x can be any real number in the interval (-infinity, 2/9) 

In Fig., ABCD is a rectangle. Find the values of x and y. 
  • a)
    22, 8 
  • b)
    20,10
  • c)
    15, 9
  • d)
    -22, -8
Correct answer is option 'A'. Can you explain this answer?

Kds Coaching answered
Since ABCD is a rectangle
⇒ AB = CD and BC = AD
x + y = 30 …………….. (i)
x – y = 14 ……………. (ii)
(i) + (ii) ⇒ 2x = 44
⇒ x = 22
Plug in x = 22 in (i)
⇒ 22 + y = 30
⇒ y = 8

The solution of the equations x - y = 2 and x + y = 4 is:
  • a)
    3 and 1
  • b)
    4 and 3
  • c)
    5 and 1
  • d)
    -1 and -3
Correct answer is option 'A'. Can you explain this answer?

Kds Coaching answered
To solve the equations, follow these steps:
  • Start with the first equation: x - y = 2.
  • Rearrange to express x in terms of yx = y + 2.
  • Substitute this expression for x into the second equation: x * y = 4.
  • This gives: (y + 2) * y = 4.
  • Expanding this results in: y^2 + 2y - 4 = 0.
  • Now, use the quadratic formula to solve for yy = (-b ± √(b² - 4ac)) / 2a, where a = 1b = 2, and c = -4.
  • Calculating the discriminant: b² - 4ac = 2² - 4(1)(-4) = 4 + 16 = 20.
  • Thus, y = (-2 ± √20) / 2.
  • Calculating the two possible values for y gives: y = 1 or y = -4.
  • Substituting y = 1 back into x = y + 2 yields: x = 3.
  • For y = -4, substituting gives: x = -2.
Therefore, the solutions are:
  • x = 3 and y = 1.
  • x = -2 and y = -4.

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