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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 22 Simple (Linear) Equations (Including Word Problems)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 22 Simple (Linear) Equations (Including Word Problems)

Simple (Linear) Equations Exercise 22A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve:


Solution:

Question 2.
Solve:

Solution:

Question 3.
Solve:

Solution:

Question 4.
Solve:

Solution:

Question 5.
Solve:

Solution:

Simple (Linear) Equations Exercise 22B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve:


Solution:

Question 2.
Solve:

Solution:

Question 3.
Solve:

Solution:

Simple (Linear) Equations Exercise 22C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
5 – x = 3
Solution:

Question 2.
2 – y = 8
Solution:

Question 3.
8.4 – x = -2
Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.
1.6z = 8
Solution:

Question 8.
3a = – 2.1
Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.
– 5x = 10
Solution:

Question 12.
2.4z = -4.8
Solution:

Question 13.
2y – 5 = -11
Solution:

Question 14.
2x + 4.6 = 8
Solution:

Question 15.
5y – 3.5 = 10
Solution:

Question 16.
3x + 2 = -2.2
Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.
-3y – 2 = 10
Solution:

Question 21.
4z – 5 = 3 – z
Solution:

Question 22.
7x – 3x + 2 =22
Solution:

Question 23.
6y + 3 = 2y + 11
Solution:

Question 24.
3 (x + 5) = 18
Solution:

Question 25.
5 (x – 2) – 2 (x + 2) = 3
Solution:

Question 26.
(5x – 3) 4 = 3
Solution:

Question 27.
3(2x + 1) – 2(x – 5) -5 (5 – 2x) = 16
Solution:

Simple (Linear) Equations Exercise 22D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A number increased by 17 becomes 54. Find the number.
Solution:

Question 2.
A number decreased by 8 equals 26, find the number.
Solution:

Question 3.
One-fourth of a number added to two- seventh of it gives 135; find the number.
Solution:

Question 4.
Two-fifths of a number subtracted from three-fourths of it gives 56, find the number.
Solution:

Question 5.
A number is increased by 12 and the new number obtained is multiplied by 5. If the resulting number is 95, find the original number.
Solution:

Question 6.
A number is increased by 26 and the new number obtained is divided by 3. If the resulting number is 18; find the original number.
Solution:

Question 7.
The age of a man is 27 years more than the age of his son. If the sum of their ages is 47 years, find the age of the son and his father.
Solution:

Question 8.
The difference between the ages of Gopal and his father is 26 years. If the sum of their ages is 56 years, find the ages of Gopal and his father.
Solution:

Question 9.
When two consecutive natural numbers are added, the sum is 31; find the numbers.
Solution:

Question 10.
When three consecutive natural numbers are added, the sum is 66, find the numbers.
Solution:

Question 11.
A natural number decreased by 7 is 12. Find the number.
Solution:

Question 12.
One fourth of a number added to one- sixth of itself is 15. Find the number.
Solution:

Question 13.
A whole number is increased by 7 and the new number so obtained is multiplied by 5; the result is 45. Find the number.
Solution:

Question 14.
The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.
Solution:

Question 15.
The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.
Solution:

Question 16.
Two natrual numbers differ by 6 and sum of them is 36. Find the larger number.
Solution:

Question 17.
The difference between two numbers is 15. Taking the smaller number as x; find:
(i) the expression for larger number.
(ii) the larger number, if the sum of these numbers is 71.
Solution:

Question 18.
The difference between two numbers is 23. Taking the larger number as x, find:
(i) the expression for smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.
Solution:

Question 19.
Find three consecutive integers such that their sum is 78.
Solution:

Question 20.
The sum of three consecutive numbers is 54. Taking the middle number as x, find:
(i) expression for the smallest number and the largest number.
(ii) the three numbers.
Solution:

Simple (Linear) Equations Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Solve each of the following equations :
Question i.
2x + 3 = 7
Solution:

Question ii.
2x – 3 = 7
Solution:

Question iii.
2x ÷ 3 = 7
Solution:

Question iv.
3x – 8 = 13
Solution:

Question v.
3y + 8 = 13
Solution:

Question vi.
3y ÷ 8 = 13
Solution:

Question vii.

Solution:

Question viii.

Solution:

Question ix.

Solution:

Question x.
5x – 2.4 = 4.9
Solution:

Question xi.
5y + 4.9 = 2.4
Solution:

Question xii.
48 z + 3.6 = 1.2
Solution:

Question xiii.

Solution:

Question xiv.

Solution:

Question xv.

Solution:

Question xvi.
-3x + 4 = 10
Solution:

Question xvii.
5 = x – 3
Solution:

Question xviii.
8y = 3- 3y
Solution:

Question xix.
4x = 4.9 = 6.5
Solution:

Question xx.
3z + 2 = -4
Solution:

Question xxi.
7y – 18 = 17
Solution:

Question xxii.

Solution:

Question xxiii.

Solution:

Question xxiv.

Solution:

Question xxv.
7x – 2 = 4x + 7
Solution:

Question xxvi.
3y -(y + 2) = 4
Solution:

Question xxvii.
3z – 18 = z – (12 – 4z)
Solution:

Question xxiii.

Solution:

Question xxix.

Solution:

Question xxx.

Solution:

Question xxxi.
5x – 2x + 15 = 27
Solution:

Question xxxii.
5y – 15 = 27 -2y
Solution:

Question xxxiii.
7z + 15 = 3z – 13
Solution:

Question xxxiv.
2 (x -3) – 3 (x-4) =12
Solution:

Question xxxv.
(7y + 8) + 7 = 8
Solution:

Question xxxvi.
2(z – 5) +3 (z + 2) -(3 – 5z) = 10
Solution:

Question 2.
A natural number decreased by 7 is 12. Find the number.
Solution:

Question 3.
One-fourth of a number added to one-sixth of It is 15. Find the number.
Solution:

Question 4.
A whole number is increased by 7 and the number so obtained is multiplied by 5; the result is 45. Find the whole number.
Solution:

Question 5.
The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.
Solution:

Question 6.
The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.
Solution:

Question 7.
Two natural numbers differ by 6 and their sum is 36. Find the larger number.
Solution:

Question 8.
The difference between two numbers is 15. Taking the smaller number as x; find :
(i) the expression for the larger number.
(ii) the larger number, if the sum of these numbers is 71.
Solution:

Question 9.
The difference between two numbers is 23. Taking the larger number as x, find :
(i) the expression for smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.
Solution:

Question 10.
Find the three consecutive integers whose sum is 78.
Solution:

Question 11.
The sum of three consecutive numbers is 54. Taking the middle number as x, find :
(i) the expressions for the smallest number and the largest number.
(ii) the three numbers.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 7 Unitary Method (Including Time and Work)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 7 Unitary Method (Including Time and Work)

Unitary Method Exercise 7A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Weight of 8 identical articles is 4.8 kg. What is the weight of 11 such articles ?
Answer:

Question 2.
6 books weigh 1 .260 kg. How many books will weigh 3.150 kg ?
Answer:

Question 3.
8 men complete a work in 6 hours. In how many hours will 12 men complete the same work ?
Answer:

Question 4.
If a 25 cm long candle burns for 45 minutes, how long will another candle of the same material and same thickness but 5 cm longer than the previous one, burn ?
Answer:

Question 5.
A typist takes 80 minutes to type 24 pages. How long will he take to type 87 pages ?
Answer:

Question 6.
Rs. 750 support a family for 15 days. For how many days will Rs. 2,500 support the same family ?
Answer:

Question 7.
400 men have provisions for 23 weeks. They are joined by 60 men. How long will the provisions last ?
Answer:

Question 8.
200 men have provisions for 30 days. If 50 men left, the same provisions would last for the remaining men, in how many days?
Answer:

Question 9.
8 men can finish a certain amount of provisions in 40 days. If 2 more men join with them, find for how many days the same amount of provisions be sufficient ?
Answer:

Question 10.
If interest on Rs. 200 be Rs. 25 in a certain time, what will be the interest on Rs 750 for the same time ?
Answer:

Question 11.
If 3 dozen eggs cost Rs. 90, find the cost of 3 scores of eggs. (1 score = 20)
Answer:

Question 12.
If the fare for 48 km is Rs. 288, what will be the fare for 36 km ?
Answer:

Question 13.
What will be the cost of 3.20 kg of an item, if 3 kg of it costs Rs. 360 ?
Answer:

Question 14.
If 9 lines of a print, in a column of a book contains 36 words. How many words will a column of 51 lines cqntain ?
Answer:

Question 15.
125 pupil have food sufficient for 18 days. If 25 more pupil join them, how long will the food last now ? What assumption have you made to come to your answer ?
Answer:

Question 16.
A carpenter prepares a new chair in 3 days, working 8 hours a day. Atleast how many hours per day must he work in order to make the same chair in 4 days ?
Answer:

Question 17.
A man earns ₹5,800 in 10 days. How much will he earn in the month of February of a leap year?
Answer:

Question 18.
A machine is used for making rubber balls and makes 500 balls in 30 minutes. How many balls will it make in 3 hours?
Answer:

Question 19.
In a school’s hostel mess, 20 children consume a certain quantity of ration in 6 days. However, 5 children did not return to the hostel after holidays. How long will the same amount of ration last now?
Answer:

Unitary Method Exercise 7B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.

Answer:

Question 2.
3m of cloth costs Rs. 168 ; find the cost of 4m of the same cloth.
Answer:

Question 3.
A wrist watch loses 10 sec in every 8 hours; in how much time will it lose 15 sec. ?
Answer:

Question 4.
In 2 days and 20 hours, a watch gains 20 sec ; find how much time will the watch take to gain 35 sec. ?
Answer:

Question 5.
50 men mow 32 hectares of land in 3 days. How many days will 15 men take to mow it?
Answer:

Question 6.
The wages of 10 workers for a six days week are Rs, 1,200. What are the one day wages: (i) of one worker ? (ii) of 4 workers?
Answer:

Question 7.
If 32 apples weigh 2 kg 800 g. How many apples will there be in a box, containing 35 kg of apples ?
Answer:

Question 8.
A truck uses 20 litres of diesel for 240 km. How many litres will be needed for 1200 km?
Answer:

Question 9.
A garrison of 1200 men has provisions for 15 days. How long will the provisions last if the garrison be increased by 600 men ?
Answer:

Question 10.
A camp has provisions for 60 pupil for 18 days. In how many days, the same provisions will finish off if the strength of the camp is increased to 72 pupil ?
Answer:

EXERCISE 7 (C)

Question 1.
A can do a piece of work in 6 days and B can do it in 8 days. How long will they take to complete it together ?
Answer:

Question 2.
A and B working together can do a piece of work in 10 days B alone can do the same work in 15 days. How long will A alone take to do the same work ?
Answer:

Question 3.
A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in : (i) one day (ii) 2 days.
What part of work will be left, after they have worked together for 2 days ?
Answer:

Question 4.
A and B take 6 hours and 9 hours respectively to complete a work. A works for 1 hour and then B works for two hours.
(i) How much work is done in these 3 hours ?
(ii) How much work is still left ?
Answer:

Question 5.
A, B and C can do a piece of work in 12, 15 and 20 days respectively. How long will they take to do it working together ?
Answer:

Question 6.
Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together ?
Answer:

Question 7.
Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days.
Find:
(i) work done by Mohit in 20 days.
(ii) work left after Mohit has worked on it for 20 days.
(iii) time taken by Anuj to complete the remaining work.
Answer:

Question 8.
Joseph and Peter can complete a work in 20 hours and 25 hours respectively.
Find :
(i) work done by both together in 4 hrs.
(ii) work left after both worked together for 4 hrs.
(iii) time taken by Peter to complete the remaining work.
Answer:

Question 9.
A is able to complete of a certain work in 10 hrs and B is able to complete of the same work in 12 hrs.
Find:
(i) how much work can A do in 1 hour ?
(ii) how much work can B do in 1 hour ?
(iii) in how much time will the work be completed, if both work together.
Answer:

Question 10.
Shaheed can prepare one wooden chair in 3 days and Shaif can prepare the same chair in 4 days. If they work together, in how many days will they prepare :
(i) one chair ?
(ii)14 chairs of the same kind?
Answer:

Question 11.
A, B and C together finish a work in 4 days. If A alone can finish the same work in 8 days and B in 12 days, find how long will C take to finish the work.
Answer:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Framing Algebraic Expressions Exercise 21 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write in the form of an algebraic expression :
(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).
(ii) Perimeter (P) of a square is four times its side.
(iii) Area of a square is square of its side.
(iv) Surface area of a cube is six times the square of its edge.
Solution:

Question 2.
Express each of the following as an algebraic expression :
(i) The sum of x and y minus m.
(ii) The product of x and y divided by m.
(iii) The subtraction of 5m from 3n and then adding 9p to it.
(iv) The product of 12, x, y and z minus the product of 5, m and n.
(v) Sum of p and 2r – s minus sum of a and 3n + 4x.
Solution:

Question 3.
Construct a formula for the following :
Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.
Solution:

Question 4.
If x = 4, evaluate :
(i) 3x + 8
(ii) x² – 2x
(iii)
Solution:

Question 5.
If m – 6, evaluate :
(i) 5m – 6
(ii) 2m² + 3m
(iii) (2m)²
Solution:

Question 6.
If x = 4, evaluate :
(i) 12x + 7
(ii) 5x² + 4x
(iii)
Solution:

Question 7.
If m = 2, evaluate :
(i) 16m – 7
(ii) 15m² – 10m
(iii)
Solution:

Question 8.
If x = 10, evaluate :
(i) 100x + 225
(ii) 6x² – 25x
(iii)
Solution:

Question 9.
If a = – 10, evaluate :
(i) 5a
(ii) a²
(iii) a³
Solution:

Question 10.
If x = – 6, evaluate :
(i) 11x
(ii) 4x²
(iii) 2x³
Solution:

Question 11.
If m = – 7, evaluate :
(i) 12m
(ii) 2m²
(iii) 2m³
Solution:

Question 12.
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.
Solution:

Question 13.
If a = 5 and b = 6, evaluate :
(i) 3ab
(ii) 6a²b
(iii) 2b²
Solution:

Question 14.
If x = 8 and y = 2, evaluate :
(i) 9xy
(ii) 5x²y
(iii) (4y)²
Solution:

Question 15.
If x = 5 and y = 4, evaluate :
(i) 8xy
(ii) 3x²y
(iii) 3y²
Solution:

Question 16.
If y = 5 and z = 2, evaluate :
(i) 100yz
(ii) 9y²z
(iii) 5y²
(iv) (5z)³
Solution:

Question 17.
If x = 2 and y = 10, evaluate :
(i) 30xy
(ii) 50xy²
(iii) (10x)²
(iv) 5y²
Solution:

Question 18.
If m = 3 and n = 7, evaluate :
(i) 12mn
(ii) 5mn²
(iii) (10m)²
(iv) 4n²
Solution:

Question 19.
If a = -10, evaluate :
(i) 3a – 2
(ii) a² + 8a
(iii) x a2
Solution:

Question 20.
If x = -6, evaluate :
(i) 4x – 9
(ii) 3x² + 8x
(iii)
Solution:

Question 21.
If m = -8, evaluate :
(i) 2m + 21
(ii) m² + 9m
(iii)
Solution:

Question 22.
If p = -10, evaluate :
(i) 6p + 50
(ii) 3p² – 20p
(iii)
Solution:

Question 23.
If y = -8, evaluate :
(i) 6y + 53
(ii) y² + 12y
(iii)
Solution:

Question 24.
If x = 2 and 7 = -4, evaluate :
(i) 11xy
(ii) 5x²y
(iii) (5y)²
(iv) 8x²
Solution:

Question 25.
If m = 9 and n = -2, evaluate
(i) 4mn
(ii) 2m²n
(iii) (2n)³
Solution:

Question 26.
If m = -8 and n = -2, evaluate :
(i) 12mn
(ii) 3m²n
(iii) (4n)²
Solution:

Question 27.
If x = -5 and y = -8, evaluate :
(i) 4xy
(ii) 2xy²
(iii) 4x²
(iv) 3y²
Solution:

Question 28.
Find T, if T = 2a – b, a = 7 and b = 3.
Solution:

Question 29.
From the formula B = 2a² – b², calculate the value of B when a = 3 and b = -1.
Solution:

Question 30.
The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.
Solution:

Question 31.
The temperature in Fahrenheit scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = x C + 32, find F when C = 40.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Ratio and Proportion Exercise 6A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Express each of the given ratio in its simplest form :

Solution:

Question 2.
Divide 64 cm long string into two parts in the ratio 5 : 3.
Solution:

Question 3.
Rs. 720 is divided between x and y in the ratio 4:5. How many rupees will each get?
Solution:

Question 4.
The angles of a triangle are in the ratio 3 :2 : 7. Find each angle.
Solution:

Question 5.
A rectangular field is 100 m by 80 m. Find the ratio of
(i) length to its breadth
(ii) breadth to its perimeter.
Solution:

Question 6.
The sum of three numbers, whose ratios are 3 : 4 : 6 is 4917.Find the numbers.
Solution:

Question 7.
The ratio between two quantities is 3 : the first is Rs. 810, find the second.
Solution:

Question 8.
Two numbers are in the ratio 5 : 7. Their difference is 10. Find the numbers.
Solution:

Question 9.
Two numbers are in the ratio 10 : 11. Their sum is 168. Find the numbers.
Solution:

Question 10.
A line is divided in two parts in the ratio 2.5 : 1.3. If the smaller one is 35T cm, find the length of the line.
Solution:

Question 11.
In a class, the ratio of boys to the girls is 7:8. What part of the whole class are girls.
Solution:

Question 12.
The population of a town is ’ 50,000, out of which males are of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population.
Solution:

Question 13.
Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Find the ratio between :
(i) the weights of metals A and B in the alloy.
(ii) the weight of metal B and the weight of the alloy.
Solution:

Question 14.
The ages of two boys A and B are 6 years 8 months and 7 years 4 months respectively. Divide Rs. 3,150 in the ratio of their ages.
Solution:

Question 15.
Three persons start a business and spend Rs. 25,000; Rs. 15,000 atid Rs. 40,000 respectively. Find the share of each out of a profit of Rs. 14,400 in a year.
Solution:

Question 16.
A plot of land, 600 sq m in area, is divided between two persons such that the first person gets three-fifth of what the second gets. Find the share of each.
Solution:

Question 17.
Two poles of different heights are standing vertically on a horizontal field. At a particular time, the ratio between the lengths of their shadows is 2 :3. If the height of the smaller pole is 7.5 m, find the height of the other pole.
Solution:

Question 18.
Two numbers are in the ratio 4 : 7. If their L.C.M. is 168, find the numbers.
Solution:

Question 19.
is divided between A and B in such a way that A gets half of B. Find :
(i) the ratio between the shares of A and B.
(ii) the share of A and the share of B.
Solution:

Question 20.
The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.
Solution:

Question 21.
A bag contains ₹ 1,600 in the form of ₹10 and ₹20 notes. If the ratio between the numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all.
Solution:

Question 22.
The ratio between the prices of a scooter and a refrigerator is 4 : 1. If the scooter costs ₹45,000 more than the refrigerator, find the price of the refrigerator.
Solution:

Ratio and Proportion Exercise 6B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Check whether the following quantities form a proportion or not ?

Solution:

Question 2.
Find the fourth proportional of

Solution:

Question 3.
Find the third proportional of

Solution:

Question 4.
Find the mean proportional between

Solution:

Question 5.


Solution:

Question 6.
If x: y – 5 :4 and 2 : x = 3 :8, find the value of y.
Solution:

Question 7.
Find the value of x, when 2.5 : 4 = x : 7.5.
Solution:

Question 8.
Show that 2, 12 and 72 are in continued proportion.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Exponents Exercise 5A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the value of:
(i) 6²
(ii) 7³
(iii) 4⁴
(iv) 5⁵
(v) 8³
(vi) 7⁵
Solution:

Question 2.
Evaluate:
(i) 2³ x 4²
(ii) 2³ x 5²
(iii) 3³ x 5²
(iv) 2² x 3³
(v) 3² x 5²
(vi) 5³ x 2⁴
(vii) 3² x 4²
(ix) (5 x 4)²
Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Which is greater :
(i) 2³ or 3²
(ii) 2⁵ or 5²
(iii) 4³ or 3⁴
(iv) 5⁴ or 4⁵
Solution:

Question 6.
Express each of the following in exponential form :
(i) 512
(ii) 1250
(iii) 1458
(iv) 3600
(v) 1350
(vi) 1176
Solution:

Question 7.
If a = 2 and b = 3, find the value of:
(i) (a + b)²
(ii) (b – a)³
(iii) (a x b)^a
(iv) (a x b)^b
Solution:

Question 8.
Express:
(i) 1024 as a power of 2.
(ii) 343 as a power of 7.
(iii) 729 as a power of 3.
Solution:

Question 9.
If 27 x 32 = 3^x x 2^y; find the values of x and y.

Solution:

Question 10.
If 64 x 625 = 2^a x 5^b; find :
(i) the values of a and b.
(ii) 2^b x 5^a
Solution:

Exponents Exercise 5B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Fill in the blanks:
In 5² = 25, base = ……… and index = ……….
If index = 3x and base = 2y, the number = ………
Solution:

Question 2.
Evaluate:
(i) 2⁸ ÷ 2³
(ii) 2^3÷ 2⁸
(iii) (2⁶)⁰
(iv) (3^o)⁶
(v) 8³ x 8^-5 x 8⁴
(vi) 5⁴  x 5³ + 5⁵
(vii) 5⁴ ÷ 5³ x 5⁵
(viii) 4⁴ ÷ 4³ x 4⁰
(ix) (3⁵ x 4⁷ x 5⁸)⁰
Solution:

Question 3.
Simplify, giving Solutions with positive index:


Solution:

Question 4.
Simplify and express the Solution in the positive exponent form :


Solution:

Question 5.
Evaluate

Solution:

Question 6.
If m² = -2 and n = 2; find the values of:
(i) m + r² – 2mn
(ii) mⁿ + n^m
(iii) 6m^-3 + 4n²
(iv) 2n³ – 3m
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions