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Choose the correct statement :- a)Every whole number is a natural number.
- b)Every integer is a rational number.
- c)Every integer is a whole number.
- d)Every rational number is an integer
Correct answer is option 'B'. Can you explain this answer?
Choose the correct statement :
a)
Every whole number is a natural number.
b)
Every integer is a rational number.
c)
Every integer is a whole number.
d)
Every rational number is an integer
|
Anirban Saha answered |
Explanation:
• Natural numbers: These are the counting numbers which start from 1 and go on infinitely. Example: 1, 2, 3, 4, 5, 6.....
• Whole numbers: These are the numbers that include 0 along with the natural numbers. Example: 0, 1, 2, 3, 4, 5, 6....
• Integers: These are the whole numbers along with their negative counterparts. Example: -3, -2, -1, 0, 1, 2, 3....
• Rational numbers: These are the numbers that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. Example: 1/2, -3/4, 0.25, 6/1, 4/2....
• Option A: Every whole number is a natural number. This statement is true as every whole number is a counting number and belongs to the set of natural numbers.
• Option B: Every integer is a rational number. This statement is true as every integer can be expressed in the form of p/q, where q=1. Hence, every integer is a rational number.
• Option C: Every integer is a whole number. This statement is true as every integer is either a natural number or a negative natural number, and hence belongs to the set of whole numbers.
• Option D: Every rational number is an integer. This statement is false as rational numbers include fractions and decimals which are not integers. For example, 1/2 and 0.5 are rational numbers but not integers.
Therefore, option B is the correct statement.
• Natural numbers: These are the counting numbers which start from 1 and go on infinitely. Example: 1, 2, 3, 4, 5, 6.....
• Whole numbers: These are the numbers that include 0 along with the natural numbers. Example: 0, 1, 2, 3, 4, 5, 6....
• Integers: These are the whole numbers along with their negative counterparts. Example: -3, -2, -1, 0, 1, 2, 3....
• Rational numbers: These are the numbers that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. Example: 1/2, -3/4, 0.25, 6/1, 4/2....
• Option A: Every whole number is a natural number. This statement is true as every whole number is a counting number and belongs to the set of natural numbers.
• Option B: Every integer is a rational number. This statement is true as every integer can be expressed in the form of p/q, where q=1. Hence, every integer is a rational number.
• Option C: Every integer is a whole number. This statement is true as every integer is either a natural number or a negative natural number, and hence belongs to the set of whole numbers.
• Option D: Every rational number is an integer. This statement is false as rational numbers include fractions and decimals which are not integers. For example, 1/2 and 0.5 are rational numbers but not integers.
Therefore, option B is the correct statement.
Which of the following number is rational?- a)π
- b)22/7
- c)√7 + 2
- d)0.141141114...
Correct answer is option 'B'. Can you explain this answer?
Which of the following number is rational?
a)
π
b)
22/7
c)
√7 + 2
d)
0.141141114...
|
Hridoy Nair answered |
-3.25
b) 0.6
c) √7
d) π
Answer: a) -3.25 and b) 0.6 are rational numbers.
b) 0.6
c) √7
d) π
Answer: a) -3.25 and b) 0.6 are rational numbers.
× √8 is equal to- a)2√6
- b)3√6
- c)4√6
- d)6√6
Correct answer is option 'C'. Can you explain this answer?
× √8 is equal toa)
2√6
b)
3√6
c)
4√6
d)
6√6
|
Amisha answered |
√12×√8
√2×√2×√3 × √2×√2×√2
2√3× 2√2
4√6
√2×√2×√3 × √2×√2×√2
2√3× 2√2
4√6
(√a + √b) (√a – √b) is- a)a + b
- b)2√a
- c)a – b
- d)2√b
Correct answer is option 'C'. Can you explain this answer?
(√a + √b) (√a – √b) is
a)
a + b
b)
2√a
c)
a – b
d)
2√b
|
K.arjun Arulmozhi answered |
Expanding the given expression:
√a * √a - √a * √b + √b * √a - √b * √b
Simplify the expression:
a - √ab + √ab - b
Combine like terms:
a - b
So, the correct answer is (a - b).
√a * √a - √a * √b + √b * √a - √b * √b
Simplify the expression:
a - √ab + √ab - b
Combine like terms:
a - b
So, the correct answer is (a - b).
Which of the following decimal is terminating?- a)3/11
- b)11/6
- c)1116
- d)15/7
Correct answer is option 'C'. Can you explain this answer?
Which of the following decimal is terminating?
a)
3/11
b)
11/6
c)
1116
d)
15/7
|
Vrinda Singh answered |
Terminating Decimals
A terminating decimal is a decimal number that ends after a finite number of digits. In other words, it has an endpoint and does not continue indefinitely.
Finding Terminating Decimals
To determine if a decimal is terminating, we need to convert the given fraction into decimal form.
To convert a fraction into decimal form, we need to divide the numerator by the denominator.
If the division results in a remainder of zero, the decimal is terminating.
If the division results in a non-zero remainder, the decimal is non-terminating.
Solution
a) 3/11
3 ÷ 11 = 0.272727...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
b) 11/6
11 ÷ 6 = 1.83333...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
c) 11/16
11 ÷ 16 = 0.6875
The division results in a remainder of zero, so the decimal is terminating.
d) 15/7
15 ÷ 7 = 2.142857...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
Therefore, the correct answer is option C, 11/16.
A terminating decimal is a decimal number that ends after a finite number of digits. In other words, it has an endpoint and does not continue indefinitely.
Finding Terminating Decimals
To determine if a decimal is terminating, we need to convert the given fraction into decimal form.
To convert a fraction into decimal form, we need to divide the numerator by the denominator.
If the division results in a remainder of zero, the decimal is terminating.
If the division results in a non-zero remainder, the decimal is non-terminating.
Solution
a) 3/11
3 ÷ 11 = 0.272727...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
b) 11/6
11 ÷ 6 = 1.83333...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
c) 11/16
11 ÷ 16 = 0.6875
The division results in a remainder of zero, so the decimal is terminating.
d) 15/7
15 ÷ 7 = 2.142857...
Since the division does not result in a remainder of zero, the decimal is non-terminating.
Therefore, the correct answer is option C, 11/16.
A rational number lying between √2 and √3 is- a)
- b)1.6
- c) √6
- d)1.9
Correct answer is option 'B'. Can you explain this answer?
A rational number lying between √2 and √3 is
a)
b)
1.6
c)
√6
d)
1.9
|
Arpita Behera answered |
The correct answer is option (b) 1.6
If x1/12 = 491/24 then find the value of x.- a)7
- b)2
- c)12
- d)49
Correct answer is option 'A'. Can you explain this answer?
If x1/12 = 491/24 then find the value of x.
a)
7
b)
2
c)
12
d)
49
|
Rajesh Desai answered |
To find the value of x, we need to isolate x in the given equation x1/12 = 491/24.
Step 1: Simplify the equation
To simplify the equation, we can multiply both sides by 12 to eliminate the fraction:
12 * x1/12 = 12 * 491/24
x = 491/2
Step 2: Divide the numerator by the denominator
To divide 491 by 2, we can use long division:
245
2 | 491
- 4
-----
9
- 8
-----
11
- 10
-----
1
So, 491 divided by 2 equals 245 with a remainder of 1. Therefore, x = 245 remainder 1.
Step 3: Check the answer
To verify our answer, we can substitute x = 245 into the original equation and see if it holds true:
245 * 1/12 = 491/24
Let's simplify the left side of the equation:
245 * 1/12 = 245/12
Now, let's simplify the right side of the equation:
491/24 = 245/12
As both sides of the equation are equal, we can conclude that x = 245 is indeed the correct value.
Step 4: Determine the correct option
The correct option is given as "A) 7". However, x = 245, not 7. Therefore, the given options are incorrect, and none of the options are correct for this particular question.
In summary, the value of x is 245, not 7 as stated in the options.
Step 1: Simplify the equation
To simplify the equation, we can multiply both sides by 12 to eliminate the fraction:
12 * x1/12 = 12 * 491/24
x = 491/2
Step 2: Divide the numerator by the denominator
To divide 491 by 2, we can use long division:
245
2 | 491
- 4
-----
9
- 8
-----
11
- 10
-----
1
So, 491 divided by 2 equals 245 with a remainder of 1. Therefore, x = 245 remainder 1.
Step 3: Check the answer
To verify our answer, we can substitute x = 245 into the original equation and see if it holds true:
245 * 1/12 = 491/24
Let's simplify the left side of the equation:
245 * 1/12 = 245/12
Now, let's simplify the right side of the equation:
491/24 = 245/12
As both sides of the equation are equal, we can conclude that x = 245 is indeed the correct value.
Step 4: Determine the correct option
The correct option is given as "A) 7". However, x = 245, not 7. Therefore, the given options are incorrect, and none of the options are correct for this particular question.
In summary, the value of x is 245, not 7 as stated in the options.
If x-2 = 64, then x0 + x1/3- a)2/3
- b)3/2
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
If x-2 = 64, then x0 + x1/3
a)
2/3
b)
3/2
c)
2
d)
3
|
Avinash Patel answered |
∵ x–2 = 64
⇒ x-1 = 8
⇒ x = 1/8
⇒ x-1 = 8
⇒ x = 1/8
in the simplest form will be equal to :- a)49/20
- b)27/110
- c)22/10
- d)243/9900
Correct answer is option 'B'. Can you explain this answer?
in the simplest form will be equal to :a)
49/20
b)
27/110
c)
22/10
d)
243/9900
|
|
Aditi Sharma answered |
Given n = 
then x = 0.24545
10x = 2.4545 ...(i)
and 100x = 24.54545
and 1000x = 245.454545 ...(iii)
Subtracting eq (i) and eq (iii), we get
990x = 243
⇒ x = 243/990 = 27/110
then x = 0.2454510x = 2.4545 ...(i)
and 100x = 24.54545
and 1000x = 245.454545 ...(iii)
Subtracting eq (i) and eq (iii), we get
990x = 243
⇒ x = 243/990 = 27/110
If √3 = 1.732 and √5 = 2.236 then the value of 
is- a)11.904
- b)10.904
- c)3.968
- d)8.968
Correct answer is option 'A'. Can you explain this answer?
If √3 = 1.732 and √5 = 2.236 then the value of is
isa)
11.904
b)
10.904
c)
3.968
d)
8.968
|
|
Aditya Shah answered |
We have
= 3(2.236+1.732)
= 3(3.968)
= 11.904
= 3(2.236+1.732)
= 3(3.968)
= 11.904
Which of the following number is irrational?- a)7/8
- b)
- c)93/300
- d)190/30
Correct answer is option 'B'. Can you explain this answer?
Which of the following number is irrational?
a)
7/8
b)
c)
93/300
d)
190/30
|
Rohit Sharma answered |
Since,
- = 0.875 (Terminating decimal)
(Irrational)
93/300 = 31/100 = 0.31 (Terminating decimal)
190/30 =
(Repeating decimal)
∵ Repeating and terminating decimals are rational numbers.
- = 0.875 (Terminating decimal)
(Irrational)93/300 = 31/100 = 0.31 (Terminating decimal)
190/30 =
(Repeating decimal)∵ Repeating and terminating decimals are rational numbers.
then the respective values of α and b are- a)13, –7
- b)13, 7
- c)–13, 7
- d)–13, –7
Correct answer is option 'A'. Can you explain this answer?
then the respective values of α and b area)
13, –7
b)
13, 7
c)
–13, 7
d)
–13, –7
|
|
Avinash Patel answered |
= 10 + 3 – 7√3 = α + b
= 13 – 7√3 = α + b√3
⇒ α = 13, b = –7
If 
is equal to- a)2
- b)1/2
- c)4
- d)
Correct answer is option 'B'. Can you explain this answer?
If is equal to
is equal toa)
2
b)
1/2
c)
4
d)
|
|
Avinash Patel answered |
2-m x 2-m =2-2
⇒ (2)-2m = (2)-2
⇒ m = 1
Substituting the value of m in,
⇒ (2)-2m = (2)-2
⇒ m = 1
Substituting the value of m in,
10x = 64, then the value of 
is
- a)8
- b)6.4
- c)640
- d)80
Correct answer is option 'D'. Can you explain this answer?
10x = 64, then the value of is
is a)
8
b)
6.4
c)
640
d)
80
|
|
Avinash Patel answered |
∵ 10x = 64 ⇒ (10x)1/2 = (64)1/2 = 8
∴ 10x/2 = 8 ⇒
= 8.10 = 80
∴ 10x/2 = 8 ⇒
= 8.10 = 80
, then m =
The decimal expansion of √2 is- a)non-terminating non-recurring
- b)1.4121
- c)finite decimal
- d)non-terminating recurring
Correct answer is option 'A'. Can you explain this answer?
The decimal expansion of √2 is
a)
non-terminating non-recurring
b)
1.4121
c)
finite decimal
d)
non-terminating recurring
|
|
Anika Bhatia answered |
Is a never-ending, non-repeating decimal.
If 
then x, y have values equal to
- a)3, 5
- b)5, 3
- c)3, 4
- d)3, 6
Correct answer is option 'B'. Can you explain this answer?
If then x, y have values equal to
then x, y have values equal toa)
3, 5
b)
5, 3
c)
3, 4
d)
3, 6
|
|
Aditi Sharma answered |
Rationalising the denominator we have
∴ x = 5, y = 3
∴ x = 5, y = 3
The value of 
is- a)5
- b)-5
- c)4
- d)-4
Correct answer is option 'A'. Can you explain this answer?
The value of is
isa)
5
b)
-5
c)
4
d)
-4
|
|
Avinash Patel answered |
Here
Similarly
Rearranging all the terms in the required pattern, we have
= 3 + 2 = 5
Similarly
Rearranging all the terms in the required pattern, we have
= 3 + 2 = 5
× 50 equals- a)1000
- b)200
- c)500
- d)1500
Correct answer is option 'C'. Can you explain this answer?
× 50 equalsa)
1000
b)
200
c)
500
d)
1500
|
|
Shilpa Choudhury answered |
Here
∴ Required value = 10 × 50 = 500
∴ Required value = 10 × 50 = 500
= y then y is equal to 
If x = 2 + √3, then x + 1/x is equal to:- a)2√3
- b)4
- c)14
- d)7
Correct answer is option 'B'. Can you explain this answer?
If x = 2 + √3, then x + 1/x is equal to:
a)
2√3
b)
4
c)
14
d)
7
|
|
Aditi Sharma answered |
Given x = 2 + √3 then
When 15√15 divided by 3√3 find the quotient.- a)5√3
- b)3√5
- c)3√3
- d)5√5
Correct answer is option 'D'. Can you explain this answer?
When 15√15 divided by 3√3 find the quotient.
a)
5√3
b)
3√5
c)
3√3
d)
5√5
|
|
Akanksha Choudhury answered |
It is not clear what is meant by "When 15." Could you please provide more context or clarify your question?
If m – n = 1, then 
= (1/3)x then x =
- a)2
- b)-2
- c)3
- d)-3
Correct answer is option 'C'. Can you explain this answer?
If m – n = 1, then = (1/3)x then x =
= (1/3)x then x =a)
2
b)
-2
c)
3
d)
-3
|
Meera Rana answered |
⇒ (3)3(n-m) = (3)-x
⇒ x = 3(m – n) = 3 [m - n = 1]
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