Raju – Page 73 – MCQ Questions

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A

January 5, 2022July 17, 2018 by Raju

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A.

Other Exercises

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5B
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5C
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5D

Question 1.
Without solving, comment upon the nature of roots of each of the following equations:
(i) 7x² – 9x + 2 = 0
(ii) 6x² – 13x + 4 = 0
(iii) 25x² – 10x + 1 = 0
(iv) x² + 2√3 x – 9 = 0
(v) x² – ax – b² = 0
(vi) 2x² + 8x + 9 = 0
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A Q1.1

Question 2.
Find the value of ‘p’, if the following quadratic equations have equal roots :
(i) 4x² – (p – 2) x + 1 = 0
(ii) x² + (p – 3) x + p = 0
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A Q2.1

Question 3.
The equation 3x² – 12x + (n – 5) = 0 has equal roots. Find the value of n.
Solution:
3x² – 12x + (n – 5) = 0
Here a = 3, b = -12, c = (n – 5)
D = b² – 4ac
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A Q3.1

Question 4.
Find the value of ‘m’, if the following equation has equal roots :
(m – 2) x² – (5 + m) x + 16 = 0
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A Q4.1

Question 5.
Find the value of k for the which the equation 3x² – 6x + k = 0 has distinct and real root.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A Q5.1

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 5 Quadratic Equations Ex 5A are helpful to complete your math homework.

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Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B

January 5, 2022July 17, 2018 by Raju

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations (In one variable) Ex 4B

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B.

Other Exercises

Question 1.
Represent the following inequalities on real number lines:
(i) 2x – 1 < 5
(ii) 3x + 1 ≥ – 5
(iii) 2 (2x – 3) ≤ 6
(iv) -4 < x < 4
(v) -2 ≤ x < 5 (vi) 8 ≥ x > -3
(vii) -5 < x ≤ -1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 1.1

Question 2.
For each graph given below, write an inequation taking x as the variable :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 2.1
Solution:

Question 3.
For the following inequations, graph the solution set on the real number line :
(i) – 4 ≤ 3x – 1 < 8
(ii) x – 1 < 3 – x ≤ 5
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 3.

Question 4.
Represent the solution of each of the following inequalities on the real number line :
(i) 4x – 1 > x + 11
(ii) 7 – x ≤ 2 – 6x
(iii) x + 3 ≤ 2x + 9
(iv) 2 – 3x > 1 – 5x
(v) 1 + x ≥ 5x – 11
(vi) \(\frac { 2x + 5 }{ 2 }\) > 3x – 3
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 4.1

Question 5.
x ∈ {real numbers} and -1 < 3 – 2x ≤ 7, evaluate x and represent it on a number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 5.1

Question 6.
List the elements of the solution set of the inequation – 3 < x – 2 ≤ 9 -2x ; x ∈ N.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 6.1

Question 7.
Find the range of values of x which satisfies
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 7.1
Graph these values of x on the number line.
Solution:

Question 8.
Find the values of x, which satisfy the inequation:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 8.1
Graph the solution on the number line. (2007)
Solution:

Question 9.
Given x ∈ {real numbers}, find the range of values of x for which – 5 ≤ 2x – 3 < x + 2 and represent it on a real number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 9.1

Question 10.
If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.
Solution:
Here in, 5x – 3 ≤ 5 + 3x ≤ 4x + 2
⇒ 5x – 3 ≤ 5 + 3x and 5 + 3x ≤ 4x + 2
⇒ 5x – 3x ≤ 5 + 3 and 3x – 4x ≤ 2 – 5
⇒ 2x ≤ 8 and – x ≤ – 3
⇒ x ≤ 4 and x ≥ 3
Solution is 3 ≤ x ≤ 4
a = 3 and b = 4

Question 11.
Solve the following inequation and graph the solution set on the number line :
2x – 3 < x + 2 ≤ 3x + 5; x ∈ R.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 11.1

Question 12.
Solve and graph the solution set of:
(i) 2x – 9 < 7 and 3x + 9 ≤ 25; x ∈ R.
(ii) 2x – 9 ≤ 7 and 3x + 9 > 25; x ∈ I.
(iii) x + 5 ≥ 4 (x – 1) and 3 – 2x < -7; x ∈ R.
Solution:
(i) 2x – 9 < 7 and 3x + 9 ≤ 25; x ∈ R.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 12.1

Question 13.
Solve and graph the solution set of:
(i) 3x – 2 > 19 or 3 – 2x ≥ – 7; x ∈ R.
(ii) 5 > p – 1 > 2 or 7 ≤ 2p – 1 ≤ 17; p ∈ R.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 13.1

Question 14.
The diagram represents two inequations A and B on real number lines :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 14.1
(i) Write down A and B in set builder notation.
(ii) Represent A ∩ B and A ∩ B’ on two different number lines.
Solution:

Question 15.
Use real number line to find the range of values of x for which :
(i) x > 3 and 0 < x < 6
(ii) x < 0 and -3 ≤ x < 1
(iii) -1 < x ≤ 6 and -2 ≤ x ≤ 3
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 15.1

Question 16.
Illustrate the set {x : -3 ≤ x < 0 or x > 2 ; x ∈ R} on a real number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 16.1

Question 17.
Given A = {x : -1 < x < 5, x ∈ R} and B = {x : – 4 < x < 3, x ∈ R}
Represent on different number lines:
(i) A ∩ B
(ii) A’ ∩ B
(iii) A – B
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 17.1

Question 18.
P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5 (x – 5); where x ∈ R. Represent:
(i) P ∩ Q
(ii) P – Q
(iii) P ∩ Q’ on different number lines.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 18.1

Question 19.
If P = {x : 7x – 4 > 5x + 2, x ∈ R} and Q = {x : x – 19 ≥ 1 – 3x , x ∈ R}: find the range of set P ∩ Q and represent it on a number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 19.1

Question 20.
Find the range of values of x, which satisfy:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 20.1
Graph, in each of the following cases, the values of x on the different real number lines:
(i) x ∈ W
(ii) x ∈ Z
(iii) x ∈ R.
Solution:

Question 21.
Given A = {x : – 8 < 5x + 2 ≤ 17, x ∈ I}, B = {x : -2 ≤ 7 + 3x < 17, x ∈ R}
Where R = {real numbers} and I = {integers}
Represent A an B is on two different number lines. Write down the elements of A ∩ B.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 21.1

Question 22.
Solve the following inequation and represent the solution set on the number line 2x – 5 ≤ 5x + 4< 11, where x ∈ I.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 22.1

Question 23.
Given that x ∈ I, solve the inequation and graph the solution on the number line:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 23.1
Solution:

Question 24.
Given:
A = {x : 11x – 5 > 7x + 3, x ∈ R} and B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}.
Find the range of set A ∩ B and represent it on a number line. (2005)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 24.1

Question 25.
Find the set of values of x, satisfying:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 25.1
Solution:

Question 26.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 26.1
Solution:

Question 27.
Solve the inequation:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 27.1
Graph the solution set on the number line.
Solution:

Question 28.
Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is atmost 20.
Solution:
Let first positive integer = x
Then, second integer = x + 1
and third integer = x + 2
According to the condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 28.1

Question 29.
Solve the given inequation and graph the solution on the number line.
2y – 3 < y + 1 < 4y + 7; y ∈ R (2008)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 29.1

Question 30.
Solve the inequation:
3z – 5 ≤ z + 3 < 5z – 9; z ∈ R.
Graph the solution set on the number line.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 30.1

Question 31.
Solve the following inequation and represent the solution set on the number line.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 31.1
Solution:

Question 32.
Solve the following inequation and represent the solution set on the number line:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 32.1
Solution:

Question 33.
Solve the following inequation, write the solution set and represent it on the number
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 33.1
Solution:

Question 34.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 34.1
Solution:

Question 35.
Solve the following inequation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Represent the solution on a real number line. (2015)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 35.1

Question 36.
Solve the following inequation, write the solution set and represent it on the number line.
-3 (x – 7) ≥ 15 – 7x > \(\frac { x + 1 }{ 3 }\), x ∈ R. (2016)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B 36.1

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A

January 5, 2022July 17, 2018 by Raju

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations (In one variable) Ex 4A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A.

Other Exercises

Question 1.
State, true or false :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 1.1
Solution:

Question 2.
State whether the following statements are true or false:
(i) If a < b, then a – c < b – c (ii) If a > b, then a + c > b + c
(iii) If a < b, then ac > bc
(iv) If a > b, then \(\frac { a }{ b }\) < \(\frac { b }{ c }\) (v) If a – c > b – d; then a + d > b + c
(vi) If a < b, and c > 0, then a – c > b – c where a, b, c and d are real numbers and c ≠ 0.
Solution:
(i) True
(ii) True
(iii) False
(iv) False
(v) True
(vi) False

Question 3.
If x ∈ N, find the solution set of inequations,
(i) 5x + 3 ≤ 2x + 18
(ii) 3x – 2 < 19 – 4x
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 3.1
x = {1, 2}

Question 4.
If the replacement set is the set of whole numbers, Solve:
(i) x + 7 ≤ 11
(ii) 3x – 1 > 8
(iii) 8 – x > 5
(iv) 7 – 3x ≥ – \(\frac { 1 }{ 2 }\)
(v) x – \(\frac { 3 }{ 2 }\) < \(\frac { 3 }{ 2 }\) – x
(vi) 18 ≤ 3x – 2
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 4.1

Question 5.
Solve the inequation :
3 – 2x ≥ x – 12 given that x ∈ N. [1987]
Solution:
3 – 2x ≥ x – 12
⇒ – 2x – x ≥ – 12 – 3
⇒ – 3x ≥ -15
⇒ – x ≥ – 5
⇒ x ≤ 5
Solution Set= {1, 2, 3, 4, 5} or {x ∈ N : x ≤ 5}

Question 6.
If 25 – 4x ≤ 16, find:
(i) the smallest value of x, when x is a real number
(ii) the smallest value of x, when x is an integer.
Solution:
25 – 4x ≤ 16
⇒ – 4x ≤ 16 – 25
⇒ – 4x ≤ – 9
⇒ 4x ≥ 9
x ≥ \(\frac { 9 }{ 4 }\)
(i) The smallest value of x, when x is a real number \(\frac { 9 }{ 4 }\) or 2.25
(ii) The smallest value of x, when x is an integer 3.

Question 7.
If the replacement set is the set of real numbers, solve:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 7.1
Solution:

Question 8.
Find the smallest value of x for which 5 – 2x < 5\(\frac { 1 }{ 2 }\) – \(\frac { 5 }{ 3 }\) x, where x is an integer.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 8.1

Question 9.
Find the largest value of x for which 2 (x – 1) ≤ 9 – x and x ∈ W.
Solution:
2 (x – 1) ≤ 9 – x
⇒ 2x – 2 ≤ 9 – x
⇒ 2x + x ≤ 9 + 2
⇒ 3x ≤ 11
⇒ x ≤ \(\frac { 11 }{ 3 }\)
⇒ x ≤ 3\(\frac { 2 }{ 3 }\)
x ∈ W and value of x is largest x = 3

Question 10.
Solve the inequation:
12 + 1\(\frac { 5 }{ 6 }\) x ≤ 5 + 3x and x ∈ R. (1999)
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A 10.1

Question 11.
Given x ∈ (integers), find the solution set of: -5 ≤ 2x – 3 < x + 2.
Solution:
-5 ≤ 2x – 3 < x + 2
(i) -5 ≤ 2x – 3
⇒ -2x ≤ -3 + 5
⇒ -2x ≤ 2
⇒ x ≤ -1
⇒ -1 ≤ x
(ii) 2x – 3 < x + 2
⇒ 2x – x < 2 + 3
⇒ x < 5
From (i) and (ii),
-1 ≤ x < 5
x = {-1, 0, 1, 2, 3, 4}

Question 12.
Given x ∈ (whole numbers), find the solution set of: -1 ≤ 3 + 4x < 23.
Solution:
-1 ≤ 3 + 4x < 23
(i) -1 ≤ 3 + 4x
⇒ -1 – 3 ≤ 4x
⇒ -4 < 4x
⇒ -1 ≤ x
(ii) 3 + 4x < 23
⇒ 4x < 23 – 3
⇒ 4x < 20
⇒ x < 5
From (i) and (ii)
-1 ≤ x < 5 and x ∈ W
Solution set = {0, 1, 2, 3, 4}

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 4 Linear Inequations Ex 4A are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2

January 5, 2022July 11, 2018 by Raju

RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2

Other Exercises

Question 1.
In which of the following tables x and y vary inversely :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 1

Solution:

We see that it in 15 x 4 and 3 x 25 are not equal to 36 others are 72
In it x and y do not vary.

Question 2.
It x and y vary inversely, fill in the following blanks :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 6
Solution:

Question 3.
Which of the following quantities vary inversely as each other ?
(i) The number of x men hired to construct a wall and the time y taken to finish the job.
(ii) The length x of a journey by bus and price y of the ticket.
(iii) Journey (x km) undertaken by a car and the petrol (y litres) consumed by it.
Solution:
(i) Here x and’y var inversely
More men less time and more time less men.
(ii) More journey more price, less journey less price
x and y do not vary inversely.
(iii) More journey more petrol, less journey, less petrol
x and y do not vary inversely.
In (i) x and y, vary inversely.

Question 4.
It is known that for a given mass of gas, the volume v varies inversely as the pressure p. Fill in the missing entries in the following table :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 10
Solution:

Question 5.
If 36 men can do a piece of work in 25 days, in how many days will 15 men do it ?
Solution:
Here less men, more days.
Let in x days, 15 men can finish the work
Therefore.
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 14

Question 6.
A work force of 50 men with a contractor can finish a piece of work in 5 months. In how many months the same work can be completed by 125 men.
Solution:
Let in x months, the work will be completed by 125 men
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 15

Question 7.
A work-force of 420 men with contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months?
Solution:
Let total x men can finish the work in 7 months.
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 16

Total men = 540
Number of men already employed = 420
Extra men required = 540 – 420 = 120

Question 8.
1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days ?
Solution:
Let x men can finish the stock, then
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 18
Total men required = 1680
Already men working = 1200
More men required = 1680 – 1200 = 480

Question 9.
In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel. How long will these provisions last ?
Solution:
Number of girls in the beginning = 50
More girls joined = 30
Total number of girls = 50 + 30 = 80
Let the provisions last for x days.
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 19

Question 10.
A car can finish a certain journey in 10 hours at the speed of 48 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance ?
Solution:
Let x km/hr be the speed. Then
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 21
Speed required = 60 km/hr.
Already speed = 48 km/hr
Speed to be increase = 60 – 48 = 12 km/hr

Question 11.
1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted now for 32 more days. How many soldiers left the fort ?
Solution:
Period = 28 days
After 4 day, the remaining period = 28 – 4 = 24 days
In the beginning number of soldiers in the fort = 1200
Period for which the food lasted = 32 days
Let for x soldier, the food was sufficient, then
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 22

Question 12.
Three spraying machines working together can finish painting a house in 60 minutes. How long will it take 5 machines of the same capacity to do the same job ?
Solution:
Let in x minutes, 5 machines can do the work
Now
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 24

Question 13.
A group of 3 friends staying together, consume 54 kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How new many numbers are there in this group now ?
Solution:
Let x members can finish the wheat in 18 day.
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 25

5 member can consume the wheat
Number of members already = 3
5 – 3 = 2 more member joined them.

Question 14.
55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days ?
Solution:
Let number of cows required = x
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 27

Question 15.
18 men can reap a field in 35 days. For reaping the same field in 15 days, how many men are required ?
Solution:
Let x men are required,
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 28

Question 16.
A person has money to buy 25 cycles worth Rs. 500 each. How many cycles he will be able to buy if each cycle is costing Rs. 125 more ?
Solution:
Price of one cycle = Rs. 500
Number of cycle purchased = 25
New price of the cycle = Rs. 500 + Rs. 125 = Rs. 625
Let number of cycle will be purchase = x
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 29

Question 17.
Raghu has enough money to buy 75 machines worth Rs. 200 each. How many machines can he buy if he gets a discount of Rs. 50 on each machine ?
Solution:
Price of each machine = Rs. 200
Price after given discount of Rs. 50 = Rs. 200 – 50 = Rs. 150
Let machine can be purchase = x
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 30
Number of machines can be purchased = 100

Question 18.
If x and y vary inversely as each other and
(i) x = 3 when y = 8, find y when x = 4
(ii) x = 5 when y = 15, find x when y = 12
(iii) x = 30, find y when constant of variation = 900.
(iv) y = 35, find x when constant of variation = 7.
Solution:
x and y vary inversely
x x y is constant of variation
(i) x = 3, y = 8
Constant = xy = 3 x 8 = 24
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 31

Hope given RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.2 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1

January 5, 2022July 11, 2018 by Raju

RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1

Other Exercises

Question 1.
Explain the concept of direct variation.
Solution:
If two quantifies a and b vary with each other in such a way that the ratio \(\frac { a }{ b }\) remains constant and is positive, then we say that a and b vary directly with each other or a and b are in direct variation.

Question 2.
Which of the following quantities vary directly with each other ?
(i) Number of articles (x) and their price (y).
(ii) Weight of articles (x) and their cost (y).
(iii) Distance x and time y, speed remaining the same.
(iv) Wages (y) and number of hours (x) of work.
(v) Speed (x) and time (y) (distance covered remaining the same).
(vi) Area of a land (x) and its cost (y).
Solution:
(i) It is direct variation because more articles more price and less articles, less price.
(ii) It is direct variation because, more weight more price, less weight, less price.
(iii) It is not direct variation. The distance and time vqry indirectly or inversely.
(iv) It is direct variation as more hours, more wages, less hours, less wages.
(v) It is not direct variation, as more speed, less time, less speed, more time.
(vi) It is direct variation, as more area more cost, less area, less cost.
Hence (i), (ii), (iv) and (vi) are in direct variation.

Question 3.
In which of the following tables x and y vary directly ?
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 1
Solution:

All are different.
It is not in direct variation.
Hence (i) and (ii) are in direct variation.

Question 4.
Fill in the blanks in each of the following so as to make the statement true :
(i) Two quantities are said to vary ……….. with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directly with each other if for some positive number k = k.
(iii) If u = 3v, then u and v vary ……….. with each other.
Solution:
(i) Two quantities are said to vary directly with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directly with each other if for some positive number k, \(\frac { x }{ y }\) = k.
(iii) If u = 3v, then u and v vary directly with each other.

Question 5.
Complete the following tables given that x varies directly as y.
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 3
Solution:

Question 6.
Find the constant of variation from the table given below :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 9
Solution:

Set up a table and solve the following problems. Use unitary method to verify the answer.
Question 7.
Rohit bought 12 registers for Rs. 156, find the cost of 7 such registers.
Solution:
Price of 12 registers = Rs. 156
Let cost of 7 registers = Rs. x. Therefore
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 11

Question 8.
Anupama takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes.
Solution:
For walking 100 m, time is taken = 125 minutes
Let in 315 minutes, distance covered = m
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 12

Question 9.
If the cost of 93 m of a certain kind of plastic sheet is Rs. 1395, then what would it cost to buy 105 m of such plastic sheet.
Solution:
Cost of 93 m of plastic sheet = Rs. 1395
Let cost of 105 m of such sheet = Rs. x
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 14

Question 10.
Suneeta types 1080 words in one hour. What is GWAM (gross words a minute rate) ?
Solution:
1080 words were typed in = 1 hour = 60 minutes
Let x words will be typed in 1 minute
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 15

Question 11.
A car is travelling at the average speed of 50 km/hr. How much distance would it travel in 12 minutes.
Solution:
Speed of car = 50 km/hr = 50 km in 60 minutes
Let it travel x km in 12 minutes. Therefore
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 16

Question 12.
68 boxes of a certain commodity require a shelf length of 13.6 m. How many boxes of the same commodity would occupy a shelf of 20.4 m ?
Solution:
For 68 boxes of certain commodity is required a shelf length of 13.6 m
Let x boxes are require for 20.4 m shelf Then
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 17

Question 13.
In a library 136 copies of a certain book require a shelf length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 metres ?
Solution:
For 136 copies of books require a shelf of length = 3.4 m
For 5.1 m shelf, let books be required = x Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 18

Question 14.
The second class railway fare for 240 km of journey is Rs. 15.00. What would be the fare for a journey of 139.2 km ?
Solution:
Fare of second class for 240 km = Rs. 15.00
Let fare for 139.2 km journey = Rs. x
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 20

Question 15.
If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of a pile of 294 cardboards.
Solution:
Thickness of a pile of 12 cardboards = 35 mm.
Let the thickness of a pile of 294 cardboards = x mm
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 21

Question 16.
The cost of 97 metre of cloth is Rs. 242.50. What length of this can be purchased for Rs. 302.50 ?
Solution:
Cost of 97 m of cloth = Rs. 242.50
Let x m can be purchase for Rs. 302.50
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 22

Question 17.
men can dig 6\(\frac { 3 }{ 4 }\) metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day ?
Solution:
11 men can dig a trench = 6\(\frac { 3 }{ 4 }\) m long
Let x men will dig a trench 27 m long.
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 23

Question 18.
A worker is paid Rs. 210 for 6 days work. If his total income of the month is Rs. 875, for how many days did he work ?
Solution:
Payment for 6 day’s work = Rs. 210
Let payment for x day’s work = Rs. 875
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 24

Question 19.
A worker is paid Rs. 200 for 8 days work. If he works for 20 days, how much will he get ?
Solution:
Labour for 8 days work = Rs. 200
Let x be the labour for 20 days work, then
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 25

Question 20.
The amount of extension in an elastic string varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm ?
Solution:
150 gm of weight produces an extension = 2.9 cm
Let x gm of weight will produce an extension of 17.4 cm
Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 26

Question 21.
The amount of extension in an elastic spring varies directly with the weight hung on it. If a weight of 250 gm produces an extension of 3.5 cm, find the extension produced by the weight of 700 gm.
Solution:
A weight of 250 gm produces an extension of 3.5 cm.
Let a weight of 700 gm will produce an extension of x cm. Therefore :
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 28

Question 22.
In 10 days, the earth picks up 2.6 x 108 pounds of dust from the atmosphere. How much dust will it pick up in 45 days.
Solution:
In 10 days dust is picked up = 2.6 x 108 pounds
Let x pounds of dust is picked up in = 45 days
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 29

Question 23.
In 15 days, the earth picks up 1.2 x 108 kg of dust from the atmosphere. In how many days it will pick up 4.8 x 10s kg of dust ?
Solution:
Dust of 1.2 x 108 kg is picked up in = 15 days
Let the dust of 4.8 x 108 will be picked up in x days
Therefore,
RD Sharma Class 8 Solutions Chapter 10 Direct and Inverse variations Ex 10.1 30

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