ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) Multiplicative inverse of \(\left( \frac { -4 }{ 5 } \right) ^{ 2 }\) = ……..
(ii) The standard form of 0.000182 = ………
(iii) The standard form of ……….. is 0.00000003572.
(iv) Expanded form of 273.92 = ………..
(v) If (-7)^x × \(\left( \frac { 1 }{ -7 } \right) ^{ -3 }\) = 7⁸, then value of x is …….
(vi) If 3ⁿ = 729, then n = ……
(vii) The value of (7⁰ + 5⁰) is ……..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The value of (-3)^-2 is \(\frac { 1 }{ -9 }\).
(ii) For negative integers m and n, a^m × aⁿ = a^m+n (a ≠ 0).
(iii) 3⁰ × 4⁰ = 12⁰.
(iv) The value of 3⁷ – 2⁷ is 1⁷.
(v) The standard form of 0.0034 is 3.4 × 10³.
(vi) Multiplicative inverse of (-2)⁵ is \(\frac { 1 }{ -32 }\).
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 12):
Question 3.
\(\left( \frac { 1 }{ 2 } \right) ^{ -5 }\) is equal to
(a) 32
(b) \(\frac { 1 }{ 32 }\)
(c) -32
(d) \(\frac { -1 }{ 32 }\)
Solution:

Question 4.

Solution:

Question 5.
If 2⁴ × 4³ = 4^x, then the value of x is
(a) 5
(b) 7
(c) 4
(d) -5
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.
Standard form of 0.000000789 is
(a) 78.9 × 10^-8
(b) 789 × 10^-9
(c) 7.89 × 10^-7
(d) None
Solution:

Question 9.
The usual form of 3.67 × 10⁵ is
(a) 3670000
(b) 367000
(c) 36700
(d) 3670
Solution:

Question 10.
Multiplicative inverse of \(\left( \frac { -2 }{ 3 } \right) ^{ 4 }\) is
(a) \(\frac { 16 }{ 81 }\)
(b) \(\frac { -16 }{ 81 }\)
(c) \(\frac { 81 }{ 16 }\)
(d) \(\frac { -81 }{ 16 }\)
Solution:

Question 11.

Solution:

Question 12.

Solution:

Value Based Questions

Question 1.
Anaemia causes due to deficiency of Red Blood cells. The size of a red blood cell is 0.000000007 mm. Express it in standard form. Rahul is suffering from anemia, his doctor adviced him to take healthy food regularly and avoid junk food.
Why should we eat healthy food? What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
Find the multiplicative inverse of (5⁰ + 3⁰) (5⁰ – 3⁰).
Solution:

Question 2.

Solution:

Question 3.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Ex 2.2

Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.000000000000942
(iii) 6020000000000000
(iv) 0.00000000837
Solution:

Question 2.
Express the following numbers in the usual form:
(i) 3.02 × 10^-6
(ii) 1-007 × 10¹¹
(iii) 5.375 × 10¹⁴
(iv) 7.579 × 10^-14
Solution:

Question 3.
Express the number appearing in the following statements in standard form:
(i) The mass of a proton is 0.000000000000000000000001673 gram.
(ii) The thickness of a piece of paper is 0.0016 cm.
(iii) The diameter of a wire on a computer chip is 0.000003 m.
(iv) A helium atom has a diameter of \(\frac { 22 }{ 100000000000 }\) m
(v) Mass of a molecule of hydrogen gas is about 0.00000000000000000000334 tons.
(vi) The human body has 1 trillion cells which vary in shapes and sizes.
(vii) The distance from the Earth of the Sun is 149,600,000,000 m.
(viii) The speed of light is 300,000,000 m/sec.
(ix) Mass of the Earth is 5,970,000,000,000,000,000,000,000 kg.
(x) Express 3 years in seconds.
(xi) Express 7 hectares in cm².
(xii) A sugar factory has annual sales of 3 billion 720 million kilograms of sugar.
Solution:

Question 4.
Compare the following:
(i) Size of a plant cell to the thickness of a piece of paper.
(ii) Size of a plant cell to the diameter of a wire on a computer chip.
(iii) The thickness of a piece of paper to the diameter of a wire on a computer chip.
Given size of plant cell = 0.00001275 m
Thickness of a piece of paper = 0.0016 cm
Diameter of a wire on a computer chip = 0.000003 m
Solution:

Question 5.
The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cell in the body? (1 litre = 1,00,000 mm³)
Solution:

Question 6.
Mass of Mars is 6.42 × 10²⁹ kg and the mass of the sun is 1.99 × 10³⁰ kg. What is the total mass?
Solution:

Question 7.
A particular star is at a distance of about 8.1 × 10¹³ km from the Earth. Assuming that the light travels at 3 × 10⁸ m/sec, find how long does light take from that star to reach the Earth.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Ex 2.1

Question 1.
Evaluate:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Find the multiplicative inverse of the following:

Solution:

Question 4.
(i) Express 16^-2 as a power with base 2.
(ii) Express 125^-4 as a power with base 5.
Solution:

Question 5.
Write the following numbers in expanded form using exponents:
(i) 2789.453
(ii) 3007.805
Solution:

Question 6.
Simplify and write in exponential form with positive exponent:

Solution:

Question 7.
Simplify and write the following in exponential form:

Solution:

Question 8.
Simplify and write in exponential form with negative exponent:

Solution:

Question 9.
Simplify:

Solution:

Question 10.
By what number should \(\left( \frac { 3 }{ -2 } \right) ^{ -3 }\) be divided to get \(\left( \frac { 2 }{ 3 } \right) ^{ 2 }\) ?
Solution:

Question 11.
Find the value of m for which 9^m ÷ 3^-2 = 9⁴.
Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Check Your Progress

Question 1.
Evaluate the following:

Solution:

Question 2.
What number should be added to \(\frac { -4 }{ 11 }\) to get \(\frac { -3 }{ 8 }\)?
Solution:

Question 3.
What rational number should be subtracted from the sum of \(\frac { 3 }{ 14 }\) and \(\frac { -4 }{ 7 }\) to get \(\frac { 13 }{ 21 }\)?
Solution:

Question 4.
If the product of two rational numbers is \(\frac { 25 }{ 42 }\) and one of them -2\(\frac { 6 }{ 7 }\), find the other.
Solution:

Question 5.
Divide the sum of \(\frac { 4 }{ 13 }\) and \(\frac { -3 }{ 2 }\) by their product.
Solution:

Question 6.
Using the appropriate properties of operations of rational numbers, evaluate the following:

Solution:

Question 7.
Find the additive inverse of the following:
(i) -13\(\frac { 7 }{ 8 }\)
(ii) 4\(\frac { 3 }{ 6 }\)
Solution:

Question 8.
Find the multiplicative inverse of the following:
(i) \(\frac { -23 }{ 46 }\)
(ii) 0
Solution:

Question 9.
Represent the following rational numbers on the number line:
(i) \(\frac { -3 }{ 11 }\)
(ii) \(\frac { 5 }{ 17 }\)
Solution:

Question 10.
Insert five rational numbers between \(\frac { -3 }{ 7 }\) and \(\frac { 2 }{ 5 }\)
Solution:

Question 11.
If p = \(\frac { -4 }{ 9 }\) , q = \(\frac { 2 }{ 3 }\) and r = \(\frac { -8 }{ 11 }\), then verily the foflowing:
(i) p + (q + r) = (p + q) + r
(ii) p × q = q × p
(iii) p × (q + r) = p × q + p × r
(iv) (p + q) ÷ r = p ÷ r + q ÷ r.
Solution:

Question 12.
A wedding cake weighed 8 kg. If \(\frac { 2 }{ 5 }\) th of its weight was flour, \(\frac { 5 }{ 16 }\) th was sugar, \(\frac { 1 }{ 4 }\) thwas cream and the rest were nuts, find the weight of nuts.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) The product of two rational numbers is a ……….
(ii) Subtraction of rational numbers is …….. commutative.
(iii) The rational number \(\frac { -7 }{ 4 }\) lies ……. of zero on the number line.
(iv) Division of rational numbers is ……… associative.
(v) \(\frac { p }{ q }\) ÷ 0 is ……..
(vi) Negative of a rational number is called its ………
(vii) Multiplicative identity of rational numbers is ……….
(viii) Multiplication of rational numbers is ……. over addition.
(ix) Division of a rational number by a non-zero rational number is a ………..
(x) The rational number which is additive inverse of itself is …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) \(\frac { -5 }{ 9 }\) is the additive inverse of \(\frac { 5 }{ 9 }\).
(ii) Every integer is a rational number.
(iii) Zero has its multiplicative inverse.
(iv) Every rational number is an integer.
(v) Division of two rational numbers is alwasy closed.
(vi) Non-terminating, non-recurring decimal numbers are rational numbers.
(vii) 0 is the multiplicative identity of rational numbers.
(viii) Non-terminating recurring decimal numbers are not rational numbers.
(ix) Subtraction of two rational numbers is not associative.
(x) Reciprocal of 1 is 1.
(xi) The multiplicative inverse is also called a reciprocal.
(xii) Between two different rational numbers, there are infinitely many number of rational numbers.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 18):
Question 3.
Additive inverse of \(\frac { -2 }{ -5 }\) is
(a) \(\frac { 2 }{ 5 }\)
(b) \(\frac { 5 }{ 2 }\)
(c) \(\frac { 2 }{ -5 }\)
(d) \(\frac { 5 }{ -2 }\)
Solution:

Question 4.
Multiplicative inverse of \(\frac { -3 }{ 7 }\) is
(a) \(\frac { 7 }{ 3 }\)
(b) \(\frac { -7 }{ 3 }\)
(c) \(\frac { 3 }{ 7 }\)
(d) None of these
Solution:

Question 5.
Sum of a rational number and its additive inverse is
(a) 1
(b) 0
(c) -1
(d) None of these
Solution:

Question 6.
Rational numbers are not closed under
(a) addition
(b) subtraction
(c) multiplication
(d) division
Solution:

Question 7.
0 ÷ \(\frac { 2 }{ 3 }\) is equal to
(a) \(\frac { 2 }{ 3 }\)
(b) \(\frac { 3 }{ 2 }\)
(c) 0
(d) not defined
Solution:

Question 8.
\(\frac { 2 }{ 3 }\) ÷ 0 is equal to
(a) \(\frac { 2 }{ 3 }\)
(b) \(\frac { 3 }{ 2 }\)
(c) 0
(d) not defined
Solution:

Question 9.
\(\frac { p }{ q } +\left( \frac { r }{ s } +\frac { t }{ u } \right) =\left( \frac { p }{ q } +\frac { r }{ s } \right) +\frac { t }{ u }\) is called
(a) commutative property
(b) associative property
(c) distributive property
(d) None of these
Solution:

Question 10.
Multiplication of a non-zero rational number and its reciprocal is
(a) 0
(b) 1
(c) -1
(d) None of these
Solution:

Question 11.
Product of rational number \(\frac { -2 }{ 5 }\) and its additive inverse is
(a) 0
(b) 1
(c) \(\frac { -4 }{ 25 }\)
(d) \(\frac { -5 }{ 2 }\)
Solution:

Question 12.
Sum of rational number \(\frac { 4 }{ 7 }\) and its reciprocal is
(a) \(\frac { 28 }{ 65 }\)
(b) \(\frac { 65 }{ 28 }\)
(c) \(\frac { -28 }{ 65 }\)
(d) \(\frac { -65 }{ 28 }\)
Solution:

Question 13.
Sum of two rational numbers is 0, if one ofthem is \(\frac { -4 }{ 5 }\), then other is
(a) \(\frac { 5 }{ 4 }\)
(b) \(\frac { 4}{ 5 }\)
(c) \(\frac { -5 }{ 4 }\)
(d) \(\frac { -4 }{ 5 }\)
Solution:

Question 14.
Product of two rational numbers is 1, if one of them is \(\frac { 10 }{ 3 }\), then other is
(a) \(\frac { 3 }{ 10 }\)
(b) \(\frac { -3}{ 10 }\)
(c) \(\frac { 10 }{ 3 }\)
(d) None of these
Solution:

Question 15.
Rational number represented by the point P on the number line is

(a) \(\frac { -5 }{ 7 }\)
(b) \(\frac { -3}{ 7 }\)
(c) \(\frac { -5 }{ 8 }\)
(d) \(\frac { -4 }{ 8 }\)
Solution:

Question 16.
What should be subtracted from \(\frac { -5 }{ 3 }\) to get \(\frac { -2 }{ 7 }\)?
(a) \(\frac { 29 }{ 21 }\)
(b) \(\frac { -21}{ 29 }\)
(c) \(\frac { -29 }{ 21 }\)
(d) \(\frac { 21 }{ 29 }\)
Solution:

Question 17.
Reciprocal of a negative number is
(a) positive
(b) negative
(c) can not say
(d) does not exist
Solution:

Question 18.
Which of the following statement is true?

Solution:

Value Based Questions

Question 1.
Ram donated \(\frac { 1 }{ 10 }\) of his salary to an orphanage, \(\frac { 1 }{ 3 }\) of his salary spent on food, \(\frac { 1 }{ 4 }\) of salary on rent and electricity and \(\frac { 1 }{ 20 }\) of his salary on telephone. This month he donated ₹ 5000 in Prime Minister relief fund for Uttarakhand victims. He was left with ₹ 3000 with him, find his monthly salary. Should we donate the money for needy people? What values are being promoted?
Solution:

Question 2.
In an Examination \(\frac { 1 }{ 3 }\) of the total students used unfair means and out of which \(\frac { 1 }{ 4 }\) caught red handed while cheating. If 5 students caught red handed then find the total number of students appeared in exam.
Why should we not use unfair means in an examination?
What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
Area ol a square is 4 sq. in more than \(\frac { 2 }{ 3 }\) of the area of a rectangle. If the area of square is 64 sq. m, then find the dimensions of the rectangle, given that breadth is \(\frac { 2 }{ 5 }\) of length.
Solution:

Question 2.
Rahul can do \(\frac { 2 }{ 7 }\) of a certain work in 6 days while Suresh can do \(\frac { 3 }{ 5 }\) of the same work in 9 days. They started work together but after 7 days Rahul left the work. Find in how many days Suresh can complete the remaining work?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths