Download CBSE Sample Paper 2024-25 for class 12th to 8th

Sign in

Selfstudy

Selfstudy

Exponents And Powers Test - 7

Result

Exponents And Powers Test - 7

Score
-
out of -
Rank
-
out of -

TIME Taken - -

Self Studies

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Find the value of .

A

B

C

D

Solution

=

=

= 2 × =
Question 2
1 / -0

Simplify: (x^-2 + y^-2)^-2

A

B

C

D

Solution

(x^-2 + y^-2)^-2
=

=

=
Question 3
1 / -0

The value of y + 2y(y^2y) at y = 2 is

A
66

B
62

C
60

D
58

Solution

Put y = 2 in the given expression.
y + 2y(y^2y)
=
= 2 + 4(16) = 2 + 64 = 66
Therefore, option 1 is the correct answer.
Question 4
1 / -0

Which of the following options is the simplified form of the given expression?

A
-1

B
3

C
2

D
1

Solution

=
As we know the formula:

=
=
= 1
Question 5
1 / -0

If , find the value of x.

A
2

B
4

C
8

D
16

Solution

Exponents are same, so bases will be equal.
So, x = 8
Question 6
1 / -0

_{Find the value of the expression} .

A

B

C

D

Solution

We have,

=

As we know that 3⁶ = 729, 3⁵ = 243, 10⁶ = 1000000 and 10⁵ = 100000;

=

= =
Question 7
1 / -0

_If _{, find the value of} .

A

B

C

D

Solution

Squaring both sides,
Question 8
1 / -0

If × 3^x - 3^{(x - 2)} = 243, find the value of x.

A
7

B
4

C
5

D
3

Solution

× 3^x - 3^{(x - 2)} = 243
10 × 3^{(x - 2)}- 3^{(x - 2)} = 243
(10 - 1)(3^{(x - 2)}) = 243
3 ^{(x - 2)}= 27 = 3³
Bases are same.
x - 2 = 3
x = 5
Question 9
1 / -0

Which of the following values are equal?

A) 1^-1
B) 5⁰
C) 0¹
D) 1¹

A
A and B only

B
A, B and D only

C
C and B only

D
All are equal.

Solution

As 5⁰= 1;
1¹ = 1;

A, B and D are equal.
Question 10
1 / -0

Find the value of (4^-1 - 7^-1)^-1 - (4^-1 - 3^-1)^-1.

A

B

C

D

Solution

We have (4^-1 - 7^-1)^-1 - (4^-1 - 3^-1)^-1
=
=
=
=
=
=
Question 11
1 / -0

After expressing 7 × 10^-4 - 4000 × 10^-3 in standard form, we will get

A
3.993 × 10^-4

B
-3.9993 × 10⁰

C
7 × 10^-4

D
4 × 10^-4

Solution

=
=
= = -3.9993 × 10⁰
Question 12
1 / -0

If 2^{(x - y)} = 64 and 2^{(x + y)} = 256, find the value of x.

A
5

B
6

C
7

D
3

Solution

We have 2^{(x - y)} = 64 or 2^{(x - y)} = 2⁶
So, x - y = 6 ... (i)
Also, 2^{(x + y)} = 256 or 2^{(x + y)} = 2⁸
So, x + y = 8 ... (ii)
Adding equations (i) and (ii),
x + x = 14
Or x = 7
Question 13
1 / -0

The number of prime factors in 6¹⁰ × 7¹⁷ × 55²⁷is

A
102

B
103

C
6

D
5

Solution

For finding the number of prime factors, we need to check the number of prime factors of bases.

=
Here, in the question, there are three bases; 6, 7 and 55.
Now, 2 and 3 are the prime factors of 6.
7 is a prime factor of 7 only.
5 and 11 are the prime factors of 55.
There are total five prime factors, i.e. 2, 3, 5, 7 and 11 in the given exponent.
Question 14
1 / -0

If , find the value of x.

A
2

B
-1

C
-2

D
1

Solution

Bases are same, so powers will be equal.
-5 + 3 = x
Or x = -2
Question 15
1 / -0

The population of England is 5.11 × 10⁷ and that of Northern Ireland is 1.82 × 10⁶. What is the difference between the populations, in standard form?

A
4.192 × 10⁶

B
4.928 × 10⁷

C
5.923 × 10⁷

D
6.723 × 10⁷

Solution

Population of England = 5,11,00,000
Population of Northern Ireland = 18,20,000
Difference = 5,11,00,000 - 18,20,000 = 4.928 × 10⁷
Question 16
1 / -0

The distance between Mercury and Mars is approximately 2,05,00,00,000 miles. How can this distance be represented in standard index form?

A
2.05 10⁹ miles

B
2.50 10⁸ miles

C
2.05 10⁸ miles

D
2.50 10⁷ miles

Solution

The distance from Mercury to Mars is 2,05,00,00,000 miles.
Standard index form: A 10ⁿ
As it is a big number, n will be positive.
Hence, the answer is 2.05 10⁹ miles.
Question 17
1 / -0

Rameshwari is a scientist. She is working on an experiment about atom. An atom is made up of protons, electrons, neutrons and nucleus. She finds out that the weight of a proton in the atom of an element is 0.00001275 on the carbon-12 scale. Express the weight of a proton in standard form.

A
1.275 × 10^-8

B
1.275 × 10^-4

C
1.275 × 10 ^-5

D
1.275 × 10^-6

Solution

Here, we have
0.00001275

=

=

=

= 1.275 × 10^{3 - 8}= 1.275 × 10^-5
Therefore, the weight of a proton is 1.275 × 10^-5on the carbon-12 scale.
Question 18
1 / -0

The height of World Trade Centre is 4.696 × 10⁵ mm. What will be its height when written in usual form?

A
46,96,000 mm

B
4,69,600 mm

C
4,696 mm

D
4,69,60,000 mm

Solution

The height has been given in standard form. When written in usual form, we get
4.696 × 10⁵ mm = 4.696 × 1,00,000 = 4,69,600 mm
Question 19
1 / -0

The mass of the Sun is approximately 2 × 10³⁰ kg and the mass of the Earth is 6 × 10²⁴ kg. What is the sum of both the masses?

A
1.785573 × 10²⁶ kg

B
2.000006 × 10³⁰ kg

C
4.0000006 × 10³⁰ kg

D
8 × 10⁵⁴ kg

Solution

Mass of Sun = 2 × 10³⁰ kg
Mass of Earth = 6 × 10²⁴ kg
Sum of masses = 2 × 10³⁰ + 6 × 10²⁴
= (2000000 + 6)10²⁴
= 2.000006 × 10³⁰kg
Question 20
1 / -0

If 6^x + 6^{x - 1} = 42, then 2^{x - 1} equals

A
0

B
1

C
2

D
3

Solution

6^x + 6^{x - 1} = 42
Or 6^{x - 1}(6 + 1) = 42
After taking 6^{x - 1}common and simplifying, we get
6^{x - 1}= 6
Or x = 2
Now, 2^{x - 1} = 2¹ = 2
Question 21
1 / -0

What is the value of ?

A

B

C

D

Solution
Question 22
1 / -0

Fill in the blanks:

(i) The value of 32^(0.16) × 32^(0.04) is P .

(ii) If 7⁵ × 28⁴ = 4⁴ × 7ⁿ, then n = Q .

(iii) The value of is R .

A
P = 2, Q = 9 and R = 1

B
P = 2, Q = 9 and R = 2

C
P = 2, Q = 3 and R = 2

D
P = 1, Q = 9 and R = 1

Solution

(i) 32^(0.16) × 32^(0.04) = (32)^0.2 = (32)^1/5 = (2⁵)^1/5 = 2

(ii) The best way to get the answer is to bring 4⁴ to the left side and divide.
So, the equation becomes:
7⁵ × (28/4)⁴= 7ⁿ7⁵ × (7)⁴ = 7ⁿOr 7^{5 + 4} = 7ⁿThus, n = 5 + 4 = 9

(iii)
Question 23
1 / -0

Match the expressions given in Column I with their correct answers in Column II.

A
P - D; Q - A; R - B; S - C

B
P - D; Q - B; R - A; S - C

C
P - D; Q - B; R - C; S - A

D
P - B; Q - A; R - D; S - C

Solution

P)

Q)= = = 730 + 3 = 733

R) = = = 81

S)
Question 24
1 / -0

If X = , Y = and Z = , find the values of the following expressions:

(i) x² + y² + z²
(ii) 5xyz

A
(i) (ii)

B
(i)(ii)

C
(i)(ii)

D
(i) (ii)

Solution

x = = =

y = = = 1

z === 4
i) = + 1 + 16 =

ii) 5xyz ==

User

Question Analysis

Correct -
Wrong -
Skipped -

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Self Studies

Get latest Exam Updates
& Study Material Alerts!

No, Thanks

Click on Allow to receive notifications

Allow Notification

Self Studies

Self Studies

To enable notifications follow this 2 steps:

First Click on Secure Icon
Second click on the toggle icon

Allow Notification

Get latest Exam Updates & FREE Study Material Alerts!

Self Studies

×

Open Now

"Enter your details to claim your prize if you win!"

Send OTP

Processing, please wait...

I agree to the Terms of Use & Privacy Policy