R.d Sharma 2022 Mcqs Solutions for Class 9 Maths Chapter 2 Exponents Of Real Numbers are provided here with simple step-by-step explanations. These solutions for Exponents Of Real Numbers are extremely popular among class 9 students for Maths Exponents Of Real Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 Mcqs Book of class 9 Maths Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 Mcqs Solutions. All R.d Sharma 2022 Mcqs Solutions for class 9 Maths are prepared by experts and are 100% accurate.
Page No 26:
Question 1:
The value of is
(a) 5
(b) 125
(c) 1/5
(d) -125
Answer:
We have to find the value of. So,
The value of is 125
Hence the correct choice is
Page No 26:
Question 2:
The value of x − yx-y when x = 2 and y = −2 is
(a) 18
(b) −18
(c) 14
(d) −14
Answer:
Given
Here
By substituting in we get
The value of is – 14
Hence the correct choice is .
Page No 26:
Question 3:
The product of the square root of x with the cube root of x is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Answer:
We have to find the product (say L) of the square root of x with the cube root of x is. So,
The product of the square root of x with the cube root of x is
Hence the correct alternative is
Page No 26:
Question 4:
The seventh root of x divided by the eighth root of x is
(a) x
(b)
(c)
(d)
Answer:
We have to find he seventh root of x divided by the eighth root of x, so let it be L. So,
The seventh root of x divided by the eighth root of x is
Hence the correct choice is .
Page No 26:
Question 5:
The square root of 64 divided by the cube root of 64 is
(a) 64
(b) 2
(c)
(d) 642/3
Answer:
We have to find the value of .
So,
The value of is
Hence the correct choice is .
Page No 26:
Question 6:
The value of , is
(a) 400
(b) 324
(c) 289
(d) 196
Answer:
Disclaimer: In question in place of 29 it should be 19.
We have to find the value of
Hence the correct answer is option (a).
Page No 26:
Question 7:
When simplified is equal to
(a) xy
(b) x+y
(c)
(d)
Answer:
We have to simplify
So,
The value of is
Hence the correct choice is .
Page No 26:
Question 8:
If = 64 , what is the value of ?
(a) 1
(b) 3
(c) 9
(d) 27
Answer:
We have to find the value of provided
So,
Equating the exponents we get
By substitute in we get
The real value of is
Hence the correct choice is .
Page No 26:
Question 9:
If (23)2 = 4x, then 3x =
(a) 3
(b) 6
(c) 9
(d) 27
Answer:
We have to find the value ofprovided
So,
By equating the exponents we get
By substituting in we get
The value of is
Hence the correct choice is
Page No 26:
Question 10:
If x-2 = 64, then x1/3+x0 =
(a) 2
(b) 3
(c) 3/2
(d) 2/3
Answer:
We have to find the value ofif
Consider,
Multiply on both sides of powers we get
By taking reciprocal on both sides we get,
Substituting in we get
By taking least common multiply we get
Hence the correct choice is .
Page No 26:
Question 11:
When simplified is
(a) 9
(b) −9
(c)
(d)
Answer:
We have to find the value of
So,
Hence the correct choice is .
Page No 26:
Question 12:
Which one of the following is not equal to
(a)
(b)
(c)
(d)
Answer:
We have to find the value of
So,
Also,
Hence the correct alternative is .
Page No 27:
Question 13:
Which one of the following is not equal to ?
(a)
(b)
(c)
(d)
Answer:
We have to find the value of
So,
Since, is equal to ,,.
Hence the correct choice is
Page No 27:
Question 14:
If a, b, c are positive real numbers, then is equal to
(a) 1
(b) abc
(c)
(d)
Answer:
We have to find the value of when a, b, c are positive real numbers.
So,
Taking square root as common we get
Hence the correct alternative is .
Page No 27:
Question 15:
, then x =
(a) 2
(b) 3
(c) 4
(d) 1
Answer:
We have to find value of provided
So,
Equating exponents of power we get
Hence the correct alternative is
Page No 27:
Question 16:
The value of is
(a)
(b) 2
(c)
(d) 4
Answer:
Find the value of
Hence the correct choice is .
Page No 27:
Question 17:
If a, b, c are positive real numbers, then is equal to
(a) 5a2bc2
(b) 25ab2c
(c) 5a3bc3
(d) 125a2bc2
Answer:
Find value of.
Hence the correct choice is .
Page No 27:
Question 18:
If a, m, n are positive ingegers, then is equal to
(a) amn
(b) a
(c) am/n
(d) 1
Answer:
Find the value of .
So,
Hence the correct choice is
Page No 27:
Question 19:
If x = 2 and y = 4, then
(a) 4
(b) 8
(c) 12
(d) 2
Answer:
We have to find the value of if,
Substitute,into get,
Hence the correct choice is .
Page No 27:
Question 20:
The value of m for which is
(a)
(b)
(c) −3
(d) 2
Answer:
We have to find the value of for
By using rational exponents
Equating power of exponents we get
Hence the correct choice is .
Page No 27:
Question 21:
The value of (0.00243)3/5 + (0.0256)3/4 is
(a) 0.083
(b) 0.073
(c) 0.081
(d) 0.091
Answer:
Hence, the correct answer is option (d).
Page No 27:
Question 22:
(256)0.16 × (256)0.09
(a) 4
(b) 16
(c) 64
(d) 256.25
Answer:
We have to find the value of. So,
By using law of rational exponents
we get
The value of is 4
Hence the correct choice is .
Page No 27:
Question 23:
If 102y= 25, then 10-y equals
(a)
(b)
(c)
(d)
Answer:
We have to find the value of
Given that, therefore,
Hence the correct option is .
Page No 27:
Question 24:
If 9x+2 = 240 + 9x, then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1
Answer:
We have to find the value of
Given
By equating the exponents we get
Hence the correct alternative is .
Page No 28:
Question 25:
If x is a positive real number and x2 = 2, then x3 =
(a)
(b) 2
(c) 3
(d) 4
Answer:
We have to find provided. So,
By raising both sides to the power
By substituting in we get
The value of is
Hence the correct choice is .
Page No 28:
Question 26:
If and x > 0, then x =
(a)
(b)
(c) 4
(d) 64
Answer:
For, we have to find the value of x.
So,
By raising both sides to the power we get
The value of is
Hence the correct alternative is
Page No 28:
Question 27:
If , What is the value of g when t = 64?
(a)
(b)
(c)
(d)
Answer:
Given.We have to find the value of
So,
The value of is
Hence the correct choice is
Page No 28:
Question 28:
If then (2x)x equals
(a)
(b)
(c)
(d) 125
Answer:
We have to find the value of if
So,
Taking as common factor we get
By equating powers of exponents we get
By substituting in we get
Hence the correct choice is
Page No 28:
Question 29:
When simplified is
(a) 8
(b)
(c) 2
(d)
Answer:
Simplify
Hence the correct choice is .
Page No 28:
Question 30:
If then x =
(a) 2
(b) 3
(c) 5
(d) 4
Answer:
We have to find the value of provided
So,
By cross multiplication we get
By equating exponents we get
And
Hence the correct choice is
Page No 28:
Question 31:
The value of 64-1/3 (641/3-642/3), is
(a) 1
(b)
(c) −3
(d) −2
Answer:
Find the value of
So,
Hence the correct statement is.
Page No 28:
Question 32:
If , then =
(a) 25
(b)
(c) 625
(d)
Answer:
We have to find provided
So,
Substitute in to get
Hence the value of is
The correct choice is
Page No 28:
Question 33:
If (16)2x+3 =(64)x+3, then 42x-2 =
(a) 64
(b) 256
(c) 32
(d) 512
Answer:
We have to find the value ofprovided
So,
Equating the power of exponents we get
The value of is
Hence the correct alternative is
Page No 28:
Question 34:
If (16)2x+3 =(64)x+3, then 42x-2 =
(a) 64
(b) 256
(c) 32
(d) 512
Answer:
We have to find the value ofprovided
So,
Equating the power of exponents we get
The value of is
Hence the correct alternative is
Page No 28:
Question 35:
If a, b, c are positive integers such that then the maximum possible value of abc is
(a) 12
(b) 16
(c) 32
(d) 256
Answer:
Given that, a, b, c are positive integers such that .
Now,
Thus, the values of a, b, c can be 4, 2 and 2.
Therefore,
Hence, the correct answer is option (b).
Page No 28:
Question 36:
If a, b, c are positive integers such that , then the least possible value of abc is
(a) 24
(b) 36
(c) 162
(d) none of these
Answer:
Given that, a, b, c are positive integers such that .
Now,
Thus, the values of a, b, c can be 9, 2 and 2.
Therefore,
Hence, the correct answer is option (b).
Page No 28:
Question 37:
If 2x = 3y = 6z, then
(a)
(b)
(c)
(d) 1
Answer:
Given that, 2x = 3y = 6z.
Let 2x = 3y = 6z = k.
Thus, .
Now,
Thus,
Hence, the correct answer is option (c).
Page No 29:
Question 38:
If xy = yz = zx and xz = y2, then which of the following is correct?
(a)
(b)
(c)
(d)
Answer:
Given: xy = yz = zx and xz = y2
Hence, the correct answer is option (a).
Page No 29:
Question 39:
If 6x – y = 36 and 3x + y = 729, then x2–y2 =
(a) 12
(b) 4
(c) 24
(d) 8
Answer:
Given: 6x – y = 36 and 3x + y = 729
Hence, the correct answer is option (a).
Page No 29:
Question 40:
Which is the greatest among 3198, 2764, 9100 and 8149?
(a) 9100
(b) 8149
(c) 2764
(d) 3198
Answer:
Converting all the numbers to base 3 for comparing.
3198 is already a number with base 3.
So,
⇒ 2764 < 8149 < 3198 < 9100
Thus, the greatest among 3198, 2764, 9100 and 8149 is 9100.
Hence, the correct answer is option (a).
Page No 29:
Question 41:
If then 12xy =
(a) 1
(b)
(c) 3
(d)
Answer:
Given:
Hence, the correct answer is option (a).
Page No 29:
Question 42:
If 0 < y < x, which statement must be true?
(a)
(b)
(c)
(d)
Answer:
Given
Option (a) :
Left hand side:
Right Hand side:
Left hand side is not equal to right hand side
The statement is wrong.
Option (b) :
Left hand side:
Right Hand side:
Left hand side is not equal to right hand side
The statement is wrong.
Option (c) :
Left hand side:
Right Hand side:
Left hand side is not equal to right hand side
The statement is wrong.
Option (d) :
Left hand side:
Right Hand side:
Left hand side is equal to right hand side
The statement is true.
Hence the correct choice is .
Page No 29:
Question 43:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion):
Statement-2 (Reason):
Answer:
Statement-2 (Reason):
Thus, Statement-2 is true.
Statement-1 (Assertion):
Thus, Statement-1is true.
Also, Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 29:
Question 44:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If ax = by = cz = abc, then xy + yz + zx = xyz.
Statement-2 (Reason): If an = k, then .
Answer:
Statement-2 (Reason): If an = k, then .
an = k
⇒
Thus, Statement-2 is true.
Statement-1 (Assertion): If ax = by = cz = abc, then xy + yz + zx = xyz.
As bases are same equate the powers.
Thus, Statement-1 is true.
Also, Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 29:
Question 45:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): .
Statement-2 (Reason): .
Answer:
Statement-2 (Reason): .
Then,
Now, let .....(2)
Multiplying (2) on both sides by , we get
.....(3)
Subtracting (3) from (2), we get
Substituting (4) in (1), we get
Thus, Statement-2 is true.
Statement-1 (Assertion): .
Using statement 2 for n = 4 and a = 7, we get
Thus, Statement-1 is true.
Also, Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 29:
Question 46:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion):
Statement-2 (Reason):
Answer:
Statement-2 (Reason):
Thus, Statement-2 is true.
Statement-1 (Assertion):
Now, according to Statement-2:
Thus, Statement-1 is false.
Hence, the correct answer is option (d).
Page No 29:
Question 47:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion):
Statement-2 (Reason):
Answer:
Statement-2 (Reason):
So, y = x does not satisfy the equation.
Thus, Statement-2 is false.
Statement-1 (Assertion):
Now as y is a square root and it is a real number.
∴ y must be positive, i.e., must be positive.
⇒ y = 3 .....(2)
From (1) and (2), we get
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is false.
Hence, the correct answer is option (c).
Page No 29:
Question 48:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) âStatement-1 is false, Statement-2 is true.
Statement-1 (Assertion): If m, n are positive integers, then for any positive real number a,
Statement-2 (Reason): If m, n, p are rational numbers and a is any positive real number, then
Answer:
Statement-2 (Reason): If m, n, p are rational numbers and a is any positive real number, then
Thus, Statement-2 is true.
Statement-1 (Assertion): If m, n are positive integers, then for any positive real number a,
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
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