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All questions of Exponents and Roots for Grade 9 Exam

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.

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.

The value of  25 is _________ .
  • a)
        3
  • b)
       10  
  • c)
        32
  • d)
          7
Correct answer is option 'C'. Can you explain this answer?

Value of 25

The value of 25 is:

- Option C) 32

Explanation:

- The question asks for the value of 25, which means we need to choose one of the given options that represents the actual value of 25.
- Option A) 3 is not the value of 25, as 25 is a two-digit number and 3 is a single-digit number.
- Option B) 10 is not the value of 25, as 10 is a number that comes after 9, and 25 is a number that comes after 24.
- Option D) 7 is not the value of 25, as 7 is a single-digit number and 25 is a two-digit number.
- Therefore, the correct option is C) 32, as 32 is the actual value of 25 when expressed in base 8 or octal system. In octal system, 25 is represented as 31, and when converted to decimal system, it becomes 3x8+1= 24+1= 25.

Conclusion:

- The value of 25 is 32 when expressed in octal system, which is represented by option C).

Multiplicative  inverse of 7-2 is _________ 
  • a)
    49                  
  • b)
    5                        
  • c)
    7                                
  • d)
    -14 
Correct answer is option 'A'. Can you explain this answer?

Anu Kumar answered
To find the multiplicative inverse of 7-2, we need to find a number that when multiplied by 7-2 gives us 1 as the product.

Let x be the multiplicative inverse of 7-2, then we have:

(7-2) * x = 1

Expanding the left-hand side, we get:

7x - 2x = 1

Simplifying, we get:

5x = 1

Dividing both sides by 5, we get:

x = 1/5

Therefore, the multiplicative inverse of 7-2 is 1/5, which is equivalent to 0.2 or 20%.

Option A, 49, is not the correct answer.

The  Base in the expression 1024 is __________.
  • a)
         1  
  • b)
      10                      
  • c)
       0                    
  • d)
      24
Correct answer is option 'D'. Can you explain this answer?

Prerna Nambiar answered
Base in the expression 1024 is 24.

Explanation:

In the number system, the base is the number of digits or values used to represent a number. For example, in the decimal number system, the base is 10, as there are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) used to represent any number.

In the given expression 1024, the number is written in the base 10 system. However, if we convert this number to the base 2 system (binary), we get:

1024 = 2^10

Therefore, the base in the expression 1024 is 2, as the number can be written as a power of 2 raised to the 10th power.

However, if we consider the number 1024 in the hexadecimal (base 16) system, we can write:

1024 = 4 x 16^2

Therefore, the base in the expression 1024 is 16, as the number can be written as a product of 4 and 16 raised to the 2nd power.

Similarly, if we consider the number 1024 in the octal (base 8) system, we can write:

1024 = 2^12

Therefore, the base in the expression 1024 is 8, as the number can be written as a power of 8 raised to the 12th power.

Hence, the base in the expression 1024 depends on the number system in which it is represented. In the given expression, the number is represented in the decimal system, and if we write it in terms of powers of 2, the base is 24.

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 

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 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.

Charge of an electron is  0.000,000,000,000,000,000,16 coulomb and in exponential form it can be written as
  • a)
    16 × 10-18 coulomb  
  • b)
      1.6 × 10-21 coulomb
  • c)
    1.6 × 10-19 coulomb              
  • d)
     16 × 10-21  coulomb
Correct answer is option 'C'. Can you explain this answer?

Amit Sharma answered
Any number written in the form m x 10n is a standard form if m is between 1 and 10, so we have 18 zeros before 16 and after decimal and one decimal place after 1 to make 16 less than 10. So we have 1.6 x 10-19.

7 × 10-5 m is the standard form of which of the following
  • a)
    0.0007 m              
  • b)
    0.000007 m          
  • c)
    0.0000007 m        
  • d)
    0.00007 m
Correct answer is option 'D'. Can you explain this answer?

Sahil Unni answered
The number 7 is a prime number, meaning it is only divisible by 1 and itself. It is the fourth smallest prime number and is often considered a lucky number in many cultures.

In standard form 21600000 is written as
  • a)
    2.16 × 107
  • b)
    216 × 107
  • c)
    2.16 × 105
  • d)
    216 × 100000 
Correct answer is option 'A'. Can you explain this answer?

C K Academy answered
count from rigth to left till you get last non-zero number 
like here 2 is the last non-zero number and for it we have to count 7 times
then write 2.16x 107

The value of (2/3)-2 is
  • a)
    4/9          
  • b)
    -2/9                    
  • c)
    9/4                            
  • d)
Correct answer is option 'C'. Can you explain this answer?

Shivani Khanna answered
Solution:
Given, (2/3)-2
We know that, (a/b)-c=(a- bc)/b
So, (2/3)-2 = (2-6)/3 = -4/3
Now, we need to simplify this answer to match with the given options.
Multiplying both the numerator and denominator by -1, we get,
-4/3= (-1)×(4/3)= -4/(-3)=4/3
Therefore, the value of (2/3)-2 is 4/3, which is represented by option C.

An irrational number between 5/7 and 7/9 is :
  • a)
    0.7512
  • b)
    0.75
  • c)
    0.750750075000…
  • d)
    √6
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 9 answered
There are infinitely many irrational numbers between 5/7 and 7/9.
(0.7507500075000.... is also an irrational number between 5/7 and 7/9;but it is not the only one;there are many others)

64 is the multiplicative  inverse of  
  • a)
    2-8
  • b)
    82
  • c)
    1/82
  • d)
    24
Correct answer is option 'C'. Can you explain this answer?

Navya Rane answered
Explanation:

Multiplicative inverse is a number which when multiplied by the given number gives the product as 1.

To find the multiplicative inverse of a number, we need to divide 1 by that number.

Let's check the options given:

a) 2^-8 = 1/2^8 = 1/256, which is not equal to 64, so it is not the correct answer.

b) 82 = 64, which is not the multiplicative inverse of 64, so it is not the correct answer.

c) 1/82 = 0.012195..., when we multiply 64 by 0.012195... we get 0.780487..., which is very close to 1, but not exactly 1 due to rounding. However, we can say that 1/82 is the multiplicative inverse of 64.

d) 24 = 1/64, which is not the correct answer.

Therefore, the correct answer is option c) 1/82.

Which of the following statements is false?
  • a)
    Rational numbers have a terminating or non terminating repeating decimal form.
  • b)
    Irrational numbers can be written in the form p/q where q is non zero and both p, q are integers
  • c)
    Rational numbers can be written in the form p/q where q is non zero and both p,q are integers
  • d)
    Every number on the number line is either rational or irrational, there’s no third alterntative
Correct answer is option 'B'. Can you explain this answer?

Nirali Shah answered
B) Irrational numbers can be written in the form p/q where q is non zero and both p, q are integers.

This statement is false. Irrational numbers cannot be written in the form p/q, where p and q are integers with q being nonzero. Irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations.

The standard form of 9030000000 is given by
  • a)
    9.03 × 109
  • b)
    90.3 × 107
  • c)
    903 × 106
  • d)
    9.03 × 10-9       
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 8 answered
Explanation:

  • To convert a number into standard form, we need to express it as a number between 1 and 10 multiplied by a power of 10.

  • For the number 9030000000, we can express it as 9.03 × 109.

  • Therefore, the standard form of 9030000000 is A: 9.03 × 109.

  •  

Find the value of the expression a2 for a = 10.
  • a)
    100
  • b)
    1
  • c)
    10
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sathvika answered
Multiply 10 twice i.e 10 × 10 because they asked 'a' to the power 2 . so multiply by twice, the solution is 100 .

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