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All questions of Number System for Class 9 Exam

Which of the following  (100 - 990) x 100?
  • a)
    10000
  • b)
    100
  • c)
    9900
  • d)
    99000
Correct answer is option 'C'. Can you explain this answer?

Preksha Kapoor answered
Calculation:

(100 - 990) x 100
= (-890) x 100
= -89000
= -9900 x (-1)
= 9900

Explanation:

To solve the given expression, we need to follow the order of operations, which is also known as BODMAS or PEMDAS. In this case, we have only multiplication and subtraction, so we can perform them from left to right.

(100 - 990) x 100
= (-890) x 100 [Subtract 990 from 100, which gives -890]
= -89000 [Multiply -890 by 100]
= -9900 x (-1) [Express -89000 as a product of -9900 and -1]
= 9900 [Since a negative number multiplied by a negative number gives a positive number, the answer is positive]

Therefore, the correct answer is option 'C' (9900).

Which among these is the approximate value of π?
  • a)
    14/3
  • b)
    22/7
  • c)
    7/22
  • d)
    3/14
Correct answer is option 'D'. Can you explain this answer?

Aniket Yadav answered
The number π  is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant.

Which of the following is an rational number?
  • a)
    0.323223222322223…….
  • b)
    √180
  • c)
    √31
  • d)
    √196
Correct answer is option 'D'. Can you explain this answer?

Zachary Foster answered
- A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers.
- √196 is a rational number because it simplifies to 14/1, which is a fraction where both the numerator and denominator are integers.
- Options B and C are irrational numbers because they cannot be expressed as fractions.
- Option A is a repeating decimal, which can be rational if it eventually settles into a repeating pattern, but without further information, it is not clear if this is the case.

Between 3 and 4 there are
  • a)
    10,000 rational numbers
  • b)
    1000 rational numbers
  • c)
    Infinitely many rational numbers
  • d)
    500 rational numbers
Correct answer is option 'C'. Can you explain this answer?

Anita Menon answered
There is no single number between 3 and 4, there is an infinite amount of numbers. If you are asking for INTEGERS, there are none. If not, you can have unlimited numbers between 3 and 4. For example, a number could be 3.0000000000000000005 or 3.9999999999999997.

How many rational numbers can you find between 5 and 6?​
  • a)
    infinite
  • b)
    6
  • c)
    1
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

Jyoti Kapoor answered
There are infinitely many rational numbers between any two real numbers. For example ( 5 + 6 ) / 2 = 11 / 2 , the average of 5 and 6, is between them.

Which of the following is a rational number?
  • a)
    2√3
  • b)
    0
  • c)
    π
  • d)
    1+√3
Correct answer is option 'B'. Can you explain this answer?

Abhay Yadav answered
Rational Number

A rational number is a number that can be expressed in the form of p/q where p and q are integers and q is not equal to zero.

Given Options

a) 23 - This is an integer and can be written as 23/1. It is a rational number.
b) 0 - This can be written as 0/1. It is a rational number.
c) √2 - This is an irrational number as it cannot be expressed in the form of p/q where p and q are integers.
d) 1 3 - This is a mixed fraction and can be written as 4/3. It is a rational number.

Conclusion

Hence, the only rational number among the given options is 0.

=
  • a)
    -1/5
  • b)
    1/25
  • c)
    -1/25
  • d)
    1/5
Correct answer is option 'B'. Can you explain this answer?

Sanjana answered
(1/125)⅓ × (1/25)½ = [(1/5)³]⅓ × [(1/5)²]½ = (1/5)³×⅓ × (1/5 )²×½ = 1/5 × 1/5 = 1/25 ......ans

in the form of fraction is
  • a)
    2/13
  • b)
    3/11
  • c)
    3/13
  • d)
    2/11
Correct answer is option 'C'. Can you explain this answer?

Krishna Shukla answered
X=0.230769 (1) 1000000=230769.230769 
(2) subtracting 
(1) from (2) 230769 =9999999x then, x =230769/9999999 =3/13

A rational number between   and  is
  • a)
  • b)
  • c)
    2.1
  • d)
    3.1
Correct answer is option 'C'. Can you explain this answer?

Jyoti Kapoor answered
Rational numbers are those which can be expressed in the p/q form where q isn't equal to 0 and p,q are integers

There exists infinite rational numbers between any two numbers

Few rational numbers between √3=1.7320... and √5=2.236.. are
2, 1.8, 1.81, 1.9, 2.1, 2.22 

 Find (64)-3/2
  • a)
    -1/512
  • b)
    1/512
  • c)
    64
  • d)
    1/64
Correct answer is option 'B'. Can you explain this answer?

Mohit Chavan answered
To solve the given expression, we need to follow the order of operations or BODMAS (Brackets, Order or Exponents, Division or Multiplication, Addition or Subtraction) rule. Here, we have only division and exponent operations. So, we will perform the exponent operation first and then the division operation.

Given expression: (64)-3/2

Step 1: Exponent operation
(64)-3/2 = 1/(64)3/2
= 1/(64)(2/3) [since, a^m/n = (n√a)^m]
= 1/√(64)^2
= 1/√4096
= 1/64

Therefore, the correct option is (b) 1/512.

Every rational number is
  • a)
    a real number
  • b)
    a natural number
  • c)
    a whole number
  • d)
    an integer
Correct answer is option 'A'. Can you explain this answer?

Every rational number is a real number... Becoz combination of rational and irrational no.s together make Real number..........

Identify the irrational number among these.
  • a)
    √13
  • b)
    9
  • c)
    36
  • d)
    25
Correct answer is option 'A'. Can you explain this answer?

A)3 (This is a rational number as it can be expressed as 3/1 or 6/2 or any other integer divided by 1)

जुंडी का अर्थ है
  • a)
    मक्का
  • b)
    गेहूँ की बाली
  • c)
    धान की बाली
  • d)
    ज्वार की बाली
Correct answer is option 'D'. Can you explain this answer?

जुंडी का अर्थ है ज्वार की बाली।
जुंडी का तात्पर्य उन खाद्यान्नों से हे जो मोठे अनाजों के तौर पर प्रयुक्त होते हैं जैसे की बाजरा , ज्वार , रागी , मोठे अन्न.

The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by:
  • a)
    9
  • b)
    2
  • c)
    5
  • d)
    8
Correct answer is option 'A'. Can you explain this answer?

Ravi Verma answered
The answer is b.
The sum of the digit of the number is x if we subtract it frm any number the number is two.
let consider the number is 22 and sum is 4 hence  it isdivided by 2.

The value obtained on simplifying (√5 + √6)2
  • a)
    12 + 5√30
  • b)
    13 + 2√33
  • c)
    11 - 2√30
  • d)
    11 + 2√30
Correct answer is option 'D'. Can you explain this answer?

Pooja Shah answered
(a + b)2 = a2  +  b2  + 2ab
= (√5 + √6)2 
= (√5)2 + (√6)2 + 2(√5)(√6)
= 5 + 6 +2√30
= 11 + 2√30

Of the given numbers
(i) √23
(ii) √256
(iii) 0.3796
(iv) 7.478478…
(v) 1.101001000100001…
  • a)
    (i) and (v) are irrational
  • b)
    (iv) and (v) is irrational
  • c)
    only (v) is irrational
  • d)
    none are irrational
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 9 answered
i) √23
√23 = √23/1 = p/q, but p is not an integer.
Hence √23 is an irrational number.
ii) √225
√225 = 15/1 = p/q, where p and q are integers and q ≠ 0.
Hence √225 is a rational number.
iii) 0.3796
0.3796 is a rational number because it is a terminating decimal number.
iv) 7.478478...
7.478478... is a rational number as it is a non-terminating recurring decimal i.e, the block of numbers 478 is repeating.
v) 1.101001000100001 . . . .
It is an irrational number because it is a non-terminating and non-recurring decimal.

An irrational number between 2/5 and 3/7 is :
  • a)
    1/7
  • b)
    0.4381923…
  • c)
    7/10
  • d)
    √6/35
Correct answer is option 'D'. Can you explain this answer?

Nehmat Kaur answered
Co-Prime Numbers

Co-prime numbers are the numbers which have no common factors other than 1. In other words, two numbers are said to be co-prime if their HCF (highest common factor) is 1.

Explanation

- Option 'A', 2 and 3 are co-prime numbers because they have no common factors other than 1. Therefore, the correct answer is option 'A'.
- Option 'B', 2 and 4 are not co-prime numbers because they have a common factor of 2.
- Option 'C', 2 and 6 are not co-prime numbers because they have a common factor of 2.
- Option 'D', 2 and 110 are not co-prime numbers because they have a common factor of 2.

Therefore, the only pair of co-prime numbers among the given options is 2 and 3, which is option 'A'.

Given that  ∠A = 50° ∠C = 35° ∠E = ?
  • a)
    95°
  • b)
    105°
  • c)
    45°
  • d)
    65°
Correct answer is option 'A'. Can you explain this answer?

Anshika Rajput answered
Since the two triangles are similar so
angle B= angle E
so in triangle ABC if you find the value of angle B then u Will find the answer as 95.
because sum of these three angles of the triangle is 180.and
angle B= 180-(angle A+ angle C)
so angle B=180-(50+35)
angle B=95.

From the choices given below mark the co-prime numbers
  • a)
    2, 3
  • b)
    2, 4
  • c)
    2, 6
  • d)
    2, 110
Correct answer is option 'A'. Can you explain this answer?

Zachary Foster answered
To determine if two numbers are co-prime, we check if their greatest common divisor (GCD) is 1.

 

  • 2 and 3: HCF is 1. They are co-prime.

  • 2 and 4: HCF is 2. They are not co-prime.

  • 2 and 6: HCF is 2. They are not co-prime.

  • 2 and 110: HCF is 2. They are not co-prime.


  •  

 
Therefore, the correct answer is A: 2, 3.

Simplify: 
  • a)
    131/3
  • b)
    13-2/15
  • c)
    138/15
  • d)
    132/15
Correct answer is option 'B'. Can you explain this answer?

Showman answered
13^1/5 ÷ 13^1/3 = 13^(1/5 -1/3). = 13^(-2/15) This is because of the law of exponent where when base is same and powers are different and the two no.s are divided the powers get subtracted (a^m/a^n = a^(m-n)

Which of the following lies between 0 and -1?
  • a)
    0
  • b)
    -3
  • c)
    -0.9
  • d)
    4/3
Correct answer is option 'C'. Can you explain this answer?

Let's Tute answered
Any negative number that is greater than -1 but less than 0 falls within the specified range. So the correct answer is C. 

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