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NCERT Solutions · Maths Ch 2
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17 questions · 2 exercises
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Ex 2.1
Ex 2.2
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 2.1 · 3 QUESTIONS
Exponents
Q1
Express the following in exponential form: (i) 6 × 6 × 6 × 6 (ii) y × y (iii) b × b × b × b (iv) 5 × 5 × 7 × 7 × 7 (v) 2 × 2 × a × a (vi) a × a × a × c × c × c × c × d
(2 marks)
Q2
Express each of the following as a product of powers of their prime factors in exponential form. (i) 648 (ii) 405 (iii) 540 (iv) 3600
(3 marks)
Q3
Write the numerical value of each of the following: (i) 2 × 10³ (ii) 7² × 2³ (iii) 3 × 4⁴ (iv) (–3)² × (–5)² (v) 3² × 10⁴ (vi) (–2)⁵ × (–10)⁶
(2 marks)
2
EXERCISE 2.2 · 14 QUESTIONS
End of chapter
Q1
Find out the units digit in the value of 2²²⁴ ÷ 4³². [Hint: 4 = 2²]
(1 mark)
Q2
There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?
(2 marks)
Q3
Write the given number as the product of two or more powers in three different ways. The powers can be any integers. (i) 64³ (ii) 192⁸ (iii) 32⁻⁵
(3 marks)
Q4
Examine each statement below and find out if it is ‘Always True’, ‘Only Sometimes True’, or ‘Never True’. Explain your reasoning. (i) Cube numbers are also square numbers. (ii) Fourth powers are also square numbers. (iii) The fifth power of a number is divisible by the cube of that number. (iv) The product of two cube numbers is a cube number. (v) q⁴⁶ is both a 4th power and a 6th power (q is a prime number).
(2 marks)
Q5
Simplify and write these in the exponential form. (i) 10⁻² × 10⁻⁵ (ii) 5⁷ ÷ 5⁴ (iii) 9⁻⁷ ÷ 9⁴ (iv) (13⁻²)⁻³ (v) m⁵n¹²(mn)⁹
(2 marks)
Q6
If 12² = 144 what is (i) (1.2)² (ii) (0.12)² (iii) (0.012)² (iv) 120²
(3 marks)
Q7
Circle the numbers that are the same — 2⁴ × 3⁶, 6⁴ × 3², 6¹⁰, 18² × 6², 6²⁴
(2 marks)
Q8
Identify the greater number in each of the following — (i) 4³ or 3⁴ (ii) 2⁸ or 8² (iii) 100² or 2¹⁰⁰
(2 marks)
Q9
A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. If they choose to use the digits 0–9, how many digits should the code consist of?
(2 marks)
Q10
64 is a square number (8²) and a cube number (4³). Are there other numbers that are both squares and cubes? Is there a way to describe such numbers in general?
(2 marks)
Q11
A digital locker has an alphanumeric passcode of length 5 (it can have both digits and letters). Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?
(2 marks)
Q12
The worldwide population of sheep (2024) is about 10⁹, and that of goats is also about the same. What is the total population of sheep and goats? (i) 20⁹ (ii) 10¹¹ (iii) 10¹⁰ (iv) 10¹⁸ (v) 2 × 10⁹ (vi) 10⁹ + 10⁹
(2 marks)
Q13
Calculate and write the answer in scientific notation: (i) If each person in the world had 30 pieces of clothing, find the total number of pieces of clothing. (ii) There are about 100 million bee colonies in the world. Find the number of honeybees if each colony has about 50,000 bees. (iii) The human body has about 38 trillion bacterial cells. Find the bacterial population residing in all humans in the world. (iv) Total time spent eating in a lifetime in seconds.
(2 marks)
Q14
What was the date 1 arab (1 billion) seconds ago?
(2 marks)