Exponents and Powers Quiz

If x = 82/3. 32-2/5, then find the value of x-5.

1. 5
2. 1
3. 2
4. 0

Answer: (b) 1

If 2x = 3y = 6z , then find the value of 1/x + 1/y + 1/z.

1. 1/z
2. 2/z
3. 3/z
4. 4/z

Answer: (b) 2/z

Find the value of the given expression:

1. 6
2. 1
3. 0
4. 5

Answer: (a) 6

In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following: Assertion: ((2/3)2)3 × (1/3)-2 × 3-1 × 1/6 is 32/729. Reason: ((a-m)n) = am × n, for any value of a.

1. Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).
3. Assertion (A) is true and Reason (R) is false.
4. Assertion (A) is false and Reason (R) is true.

Answer: (c) Assertion (A) is true and Reason (R) is false.

The length of a bacterium is 25 × 10-7 metre, while the length of a grain of sand is 15 × 10-6 metre. Find how many times the size of the bacterium fits into the size of the grain of sand.

1. 1
2. 5
3. 7
4. 6

Answer: (d) 6

Jennifer distributed a sum of money among her three sons, x3 to the first son, x4 to the second son and x to the third son. The total sum of the money given to them is $324, and the product of the amounts received by the three sons is $65,536. How much is the amount given to the second son?

1. $256
2. $456
3. $196
4. $562

Answer: (a) $256

Which of the following statement are not true? (a) xy > yx, if x = 2 and y = 4 (b) x = 1 for all values of x (c) x-y > y-x if x = -103 and y = -104 (d) xy > yx , if x = 4 and y = 2.

1. (c), (b), (d)
2. (a), (c), (d)
3. (a), (b), (c)
4. (a), (b), (d)

Answer: (d) (a), (b), (d)

Find the value of the given expression, if x = 2, a = 1, b = 2, c= 3.

1. x
2. 8
3. 1
4. 0

Answer: (c) 1

Read the passage and answer the following question: In a small town, the local government decided to encourage the use of solar panels to reduce carbon emissions. To achieve this, they partnered with a solar power company that specialises in solar panels. The formula for the efficiency of their solar cells is given by E = E0 × 2n, where E0 is the initial efficiency of the solar cells, and n is the number of years after the panels were installed. The initial efficiency, was 25 watts per square meter, and the amount owed after each month follows the equation A = P × (1.05)n , where A is the amount owed after n months, and P is the initial amount borrowed. calculate the efficiency of solar panels after 3 years.

1. 400 w/m2
2. 200 w/m2
3. 800 w/m2
4. 100 w/m2

Answer: (b) 200 w/m2

Read the passage and answer the following question: In a small town, the local government decided to encourage the use of solar panels to reduce carbon emissions. To achieve this, they partnered with a solar power company that specialises in solar panels. The formula for the efficiency of their solar cells is given by E = E0 × 2n, where E0 is the initial efficiency of the solar cells, and n is the number of years after the panels were installed. The initial efficiency, was 25 watts per square meter, and the amount owed after each month follows the equation A = P × (1.05)n , where A is the amount owed after n months, and P is the initial amount borrowed. Calculate how much Mrs. Patel will owe after 3 months if the initial cost of the panels was $5000.

1. $5788.13
2. $5000
3. $2875.12
4. $50000

Answer: (a) $5788.13