Class-8 Ganita prakash ASSERTION & REASONING Maths ch-2 Power play with answer key

 Class-8 Ganita prakash ASSERTION & REASONING Maths ch-2 Power play

Assertion and Reasoning Questions with Answer Keys

Assertion and Reasoning Questions with Answer Keys

(A) Both true and R explains A
(B) Both true but R does not explain A
(C) A true but R false
(D) A false but R true

1. A: Doubling every day is an example of exponential growth.
   R: In exponential growth, the quantity increases by a fixed multiple each time.
   Answer: A

2. A: $2^{10} = 1024$ means 2 multiplied by itself 10 times equals 1024.
   R: The base tells how many times to multiply the exponent by itself.
   Answer: C

3. A: Scientific notation expresses numbers as $x \times 10^n$ with $1 \le x < 10$.
   R: This makes it easier to write and compare very large or small numbers.
   Answer: A

4. A: In the magical pond, the pond is one-quarter full on Day 28.
   R: Each day’s lotus count is double the previous day’s.
   Answer: A

5. A: Linear growth can overtake exponential growth if given enough time.
   R: In exponential growth, increase per step decreases over time.
   Answer: D

6. A: $a^m \times a^n = a^{m+n}$ for all integers m and n.
   R: Multiplying powers with the same base adds the exponents.
   Answer: A

7. A: $a^{-n} = 1/a^n$ for $a \neq 0$.
   R: Negative exponents represent reciprocals.
   Answer: A

8. A: The number 64 is both a perfect square and a perfect cube.
   R: $64 = 8^2$ and $64 = 4^3$.
   Answer: A

9. A: The cube of any even number is odd.
   R: Cube of even = even × even × even = even.
   Answer: D

10. A: The largest 3-digit power of 2 is $2^9$.
    R: $2^9 = 512$ and $2^{10} = 1024$.
    Answer: A

11. A: Multiplying by $10^3$ increases a number’s value by 100.
    R: $10^3 = 1000$, so it multiplies the number by 1000.
    Answer: D

12. A: $(a^m)^n = a^{mn}$ holds for all integers m, n.
    R: Raising a power to another power multiplies exponents.
    Answer: A

13. A: The number of 6-letter passwords from A–Z is $26^6$.
    R: Each letter has 26 choices, independent of others.
    Answer: A

14. A: Linear growth means adding the same amount each step.
    R: Linear growth is faster than exponential growth for small step sizes.
    Answer: B

15. A: In scientific notation, the exponent tells the number of decimal shifts.
    R: Shifting decimal right means negative exponent.
    Answer: C