AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

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AP State Syllabus 10th Class Maths Bits 1st Lesson Real Numbers with Answers

Question 1.
Find the rational number in between \(\frac { 1 }{ 2 }\) and √1
Answer:
\(\frac { 3 }{ 4 }\)

Question 2.
Write the name set of rational and ir-rational numbers.
Answer:
Real numbers.

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 3.
Write the logarithmic form of 35 = 243.
Answer:
log3243 = 5

Question 4.
Write the symbol of “implies”.
Answer:

Question 5.
Write the prime factorisation of 729.
Answer:
36

Question 6.
If ‘x’ and ‘y’ are two prime numbers, then find their HCF.
Answer:
1
Explanation:
HCF of any two prime numbers is always 1.

Question 7.
Find the value of log10 0.01.
Answer:
-2
Explanation:
log100.01 = log10 \(\frac{1}{10^{2}}\)
= log1010-2 = – 2

Question 8.
Find the number of odd numbers in between ‘0’ and 100.
Answer:
50

Question 9.
Write the exponential form of log48 = x.
Answer:
4x = 8.
Explanation:
Exponential form of log48 = x is 4x = 8

Question 10.
How much the value of \(\frac{36}{2^{3} \times 5^{3}}\) in decimal form ?
Answer:
0.036.

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 11.
LCM of two numbers is 108 and their HCF is 9 and one of them is 54, then find the second one.
Answer:
18
Explanation:
LCM x HCF = one number x second number
108 x 9 = 54 x second one , 108 x 9
⇒ Second one = \(\frac{108 \times 9}{54}\) = 18.

Question 12.
\(\frac { 3 }{ 8 }\) is example for decimal.
Answer:
Terminating decimal.

Question 13.
If \(\mathbf{a} \sqrt{\mathbf{c}}=\sqrt{\mathbf{a c}}\) , then find the value of ‘a’, (a, c are positive integers),
Answer:
a = 1

Question 14.
Find the value of 9 – \(0 . \overline{9}\).
Answer:
8
Explanation:
9 – \(\frac{9}{9}\) = 9 – 1 = 8.

Question 15.
Write rational number that equals to \(2 . \overline{6}\)
Answer:
\(\frac { 8 }{ 3 }\)

Question 16.
Write the value of log25 5.
Answer:
\(\frac { 1 }{ 2 }\)
Explanation:
log255 = log551 = \(\frac{1}{2}\)log55 = \(\frac{1}{2}\)

Question 17.
The fundamental theorem of arithmetic is applicable to, which least number ?
Answer:
2

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 18.
Find the last digit of 650.
Answer:
6

Question 19.
Which of the following is a terminat¬ing decimal ?
A) \(\frac { 10 }{ 81 }\)
B) \(\frac { 41 }{ 75 }\)
C) \(\frac { 8 }{ 125 }\)
D) \(\frac { 3 }{ 14 }\)
Answer:
C)

Question 20.
Find the value of log2 32.
Answer:
5

Question 21.
Which of the following is not irrational ?
A) √2
B) √3
C) √4
D) √5
Answer:
(C)

Question 22.
Find the value of log10 0.001.
Answer:
-3

Question 23.
Find the number of prime factors of 36.
Answer:
2 and 3
Explanation:
36 = 22 x 32
∴ Two prime numbers i.e., 2 and 3.

Question 24.
Write the exponential form of
Iog10 = -3.
Answer:
10-3 = 0.001

Question 25.
Define an irrational number.
Answer:
Which cannot be written in the form
of p/q where p, q ∈ Z, q ≠ 0.

Question 26.
Find the LCM of 24 and 36.
Answer:
72

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 27.
Find the logarithmic form of ab = c.
Answer:
logac = b.

Question 28.
If 3 log (x + 3) = log 27, then find the value of x.
Answer:
0
Explanation:
3 log (x + 3) = log 27
⇒ log (x + 3)3 = log 33
⇒ x + 3 = 3 ⇒ x = 0
log3729 = x ⇒ 3x = 729 = 36 ⇒ x = 6

Question 29.
If P1 and P2 are two odd prime num-bers, such that P1 > P2, then the value of \(\mathbf{P}_{1}^{2}-\mathbf{P}_{\mathbf{2}}^{2}\) results number
Answer:
An even number.

Question 30.
Find the value of \(\log _{10} 2+\log _{10} 5\)
Answer:
1

Question 31.
If log3 729 = x, then find the value of x.
Answer:
6
Explanation:
log3 729 = x ⇒ 3x = 729 = 36 ⇒ x = 6

Question 32.
Write the number of digits in the fractional part of the decimal form of \(\frac{7}{40}\).
Answer:
3
Explanation:
\(\frac{7}{40}=\frac{7}{2^{3} \times 5^{1}}\)
In Denominator 2n x 5m is equal to 3.

Question 33.
Write the prime factorization of 144.
Answer:
24 x 32

Question 34.
Find the number of prime factors of 72.
Answer:
2

Question 35.
log3 x2 = 2, then find the value of x.
Answer:
3
Explanation:
log3x2 = 2 ⇒ 32 = x2 ⇒ x = 3

Question 36.
Find the value of \(9 \sqrt{2} \times \sqrt{2}\)
Answer:
18

Question 37.
Find the value of log0.1 0.01.
Answer:
2
Explanation:
log 0.1 0.01 = log10-1 10-2
= \(\frac{-2}{-1}\) log10 10 = 2

Question 38.
0.3030030003 ………………. is an ………………. number.
Answer:
Irrational.

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 39.
\(\frac{27}{82}\) is a …………. decimal.
Answer:
Non-terminating

Question 40.
If log 2 = 0.30103, then find log 32.
Answer:
1.50515
Explanation:
log 32 = log 25 = 5 log 2
= 5 x 0.30103 .
= 1.50515

Question 41.
Expand log 15.
Answer:
log5 + log3

Question 42.
Find the value of log10 10.
Answer:
1

Question 43.
Calculate the value of log8 128.
Answer:
\(\frac{7}{3}\)

Question 44.
Find the value of \(5 \sqrt{5}+6 \sqrt{5}-2 \sqrt{5}[/latex[
Answer:
9√5

Question 45.
743.2111111 … is a number.
Answer:
Rational

Question 46.
Find the value of log5 125.
Answer:
3

Question 47.
Expand log10 [latex]\frac{125}{16}\)
Answer:
3 log 5 – 4 log 2
Explanation:
log10 \(\frac{125}{16}\) = log10 125 – log1016
= log1053 – log1024
= 3 log 5 – 4 log 2

Question 48.
Find the L.C.M of the numbers 27 x 34 x 7 and 23 x 34 x 11.
Answer:
27 x 34 x 7 x 11

Question 49.
If loga ax2 – 5x + 8 = 2, then find x.
Answer:
2 or 3.
Explanation:
\(\log _{a} a^{x^{2}-5 x+8}=\log _{a} a^{2}\)
{2 was write down as 2-loga a}
x2 – 5x + 8 = 2
x2 – 5x + 6 = 0
by solving equation x = 2 or 3

Question 50.
Find the value of loga \(\frac{1}{a}\).
Answer:
– 1

Question 51.
Find the value of log1 1.
Answer:
Not defined.

Question 52.
If log10 0.00001 = x, then find x.
Answer:
-5

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 53.
Find the value of logb a • loga b.
Answer:
1.

Question 54.
16 x 64 = 4k, then find the value of k.
Answer:
5
Explanation:
16 x 64 = 4k
⇒ 42 x 43 = 4k
⇒ 45 = 4k
⇒ k = 5

I’m

Question 55.
Write exponential form of log464 = 3.
Answer:
43 = 64

Question 56.
Calculate the value of \(\log _{9} \sqrt{3 \sqrt{3 \sqrt{3}}}\)
Answer:
\(\frac{7}{16}\)

Question 57.
If ‘m’ and ‘n’ are co-primes, then find H.C.F of m2 and n2.
Answer:
1

Question 58.
\(\sqrt{5}+\sqrt{7}\) is number.
Answer:
An irrational.

Question 59.
Find the H.C.F. of the numbers
37 x 53 x 24 and 32 x 74 x 28.
Answer:
24 x 32

Question 60.
\(\frac{13}{125}\) is a ……………… decimaL
Answer:
Terminating

Question 61.
Write the decimal expansion of 0.225 in its rational form.
Answer:
\(\frac{9}{40}\)

Question 62.
How many prime factors are there in the prime factorization of 240.
Answer:
3

Question 63.
14.381 may certain the denominator when expressed in p/q form.
Answer:
23 x 53

Question 64.
By which numbers 7 x 11 x 17 +34 is divisible, write them.
Answer:
17 and 79
Explanation:
Given number = 7 x 11 x 17 + 34
= 17 (7 x 11 + 2)
= 17 x 79
Given number has 17 and 79 are factors.

Question 65.
Write log\(\frac{x^{2} y^{3} z^{4}}{w^{5}}\) in the expanded form.
Answer:
2 log x + 3 log y + 4 log z – 5 log w
Explanation:
log x2y3z4 – log w5 = log x2 + log y3 + log z4 – log w5
= 2log x + 3log y + 4log z – 51og w

Question 66.
Write the logarithmic form of 122 = 144.
Answer:
log12 144 = 2

Question 67.
Expand log 81 x 25.
Answer:
4log 3 + 2 log 5

Question 68.
What is the L.C.M. of greatest two digit number and the greatest three digit number.
Answer:
9 x 11 x 111

Question 69.
Write logarithmic form of 192 = 361.
Answer:
log19361 = 2

Question 70.
3 X 5 x 7 x 11 + 35 is number.
Answer:
Composite

Question 71.
Write the decimal expansion of \(\frac{101}{99}\).
Answer:
\(1 . \overline{02}\)

Question 72.
If P1, p2, p3, …………… pn are co-primes, then
their LCM is
Answer:
P1p2 …………… pn

Question 73.
In the above problem find HCF.
Answer:
1

Question 74.
n2 – 1 is divisible by 8, if ‘n’ is number.
Answer:
An odd number.

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 75.
If x and y are any two co-primes, then find their L.C.M.
Answer:
x.y

Question 76.
Write \(\frac{70}{71}\) is which type of decimal ?
Answer:
Non-terminating, repeating.

Question 77.
0.12 112 1112 11112………………is…………… type of number.
Answer:
Irrational

Question 78.
Write \(\frac{123}{125}\) is which type of decimal ?
Answer:
Terminating.

Question 79.
Write the product of L.C.M. and H.C.F. of the least prime and least composite number.
Answer:
8

Question 80.
\(\sqrt{2}-2\) is…………………number.
An irrational.

Question 81.
Find the number of prime factors of 1024.
Answer:
Only one number, i.e., ‘2’. (i.e., 210)

Question 82.
Write the LCM of 208 and 209.
Answer:
208 x 209 (Product of even and odd number is its product)

Question 83.
Write the expansion of \(\frac{87}{625}\) terminates after how many places ?
Answer:
4 places.

Question 84.
The decimal expansion of \(\frac{87}{625}\) terminates after how many places ?
Answer:
4 places.

Question 85.
What is the H.C.F. of ‘n’ and ‘n + 1’, where ‘n’ is a natural number ?
Answer:
1

Question 86.
What is the prime factorisation of 20677.
Answer:
23 x 29 x 31

Question 87.
Find the HCF of 1001 and 1002.
Answer:
1

Question 88.
p, q are co-primes and q = 2n . 5m, where m > n, then write the decimal expansion of p/q terminates after how many places ?
Answer:
‘m’ places.

Question 89.
Write the decimal fprm of \(\frac{80}{81}\) and write repeats after how many places ?
Answer:
81 = 34, so not possible.

Question 90.
If a rational number p/q has a termi¬nating decimal, then write the prime factorisation of ‘q’ is of the form.
Answer:
q = 2m . 5n

Question 91.
Write the decimal expansion of \(\frac{7}{16}\) without actual division.
Answer:
0.4375

Question 92.
In the expansion of \(\frac{123}{125}\) terminates after how many places ?
Answer:
3 places.

Question 93.
What is the L.C.M of least prime and the least composite number ?
Answer:
Least composite

Question 94.
Write the decimal expansion of \(\frac{27}{14}\)
Answer:
\(1.9 \overline{285714}\)

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 95.
Which type of number was \(5.6789 \overline{1}\) ?
Answer:
Rational number

Question 96.
After how many places the decimal expansion of \(\frac{23}{125}\) terminates ?
Answer:
3 places.

Question 97.
Write the type of decimal expansion of \(\frac{9}{17}\)
Answer:
Non-terminating & repeating.

Question 98.
Write the period of the decimal expansion of \(\frac{19}{21}\)
Answer:
904761

Question 99.
After how many digits will the deci-mal expansion of \(\frac{11}{32}\) terminates ?
Write it.
Answer:
5 places.

Question 100.
If \(\sqrt{2}\) = 1.414, then find \(3 \sqrt{2}\).
Answer:
4.242

Question 101.
Find the value of \(\frac{3}{8}\)
Answer:
0.375

Question 102.
Find the value of log 64 – log 4.
Answer:
16

Question 103.
Find the value of 128 ÷ 32.
Answer:
4

Question 104.
Find the value of 104.
Answer:
10000

Question 105.
Find the value of \(\sqrt{\mathbf{5}}\) .
Answer:
2.236

Question 106.
Find the value of log27 9.
Answer:
\(\frac{2}{3}\)

Question 107.
Find the value of | – 203 |.
Answer:
203

Question 108.
Complete the rule a(b + c).
Answer:
ab + ac

Question 109.
Find the value of log3 \(\frac{1}{9}\).
Answer:
-2

Question 110.
How much the LCM of 12, 15 and 21.
Answer:
420

Question 111.
Find the value of loga 1, a > 0.
Answer:
0

Question 112.
a + (-a) = 0 = (- a) + a is called ……………… property.
Answer:
Inverse

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 113.
Find the value of \(\sqrt{\mathbf{a}} \times \sqrt{\mathbf{b}}\)
Answer:
\(\sqrt{a b}\)

Question 114.
Find the value of 55.
Answer:
3125

Question 115.
Find the value of \(\frac{13}{4}\) .
Answer:
3.25

Question 116.
Find the value of \(\sqrt{12544}\)
Answer:
112

Question 117.
Find the value of log61.
Answer:
0

Question 118.
Find the value of log1010000.
Answer:
4

Question 119.
How much the HCF of 12 and 18.
Answer:
6

Question 120.
Which number has no multiplicative inverse ?
Answer:
0

Question 121.
How much the LCM of 306 and 657.
Answer:
22338

Question 122.
Find the value of logx \(\frac{\mathbf{a}}{\mathbf{b}}\).
Answer:
logxa – logxb

Question 123.
Find the value of log32 \(\frac{1}{4}\)

Question 124.
Find the value of \(\sqrt{2025}\)
Answer:
\(\frac{-2}{5}\)

Question 125.
Find the value of \(2 \sqrt{3}+7 \sqrt{3}+\sqrt{3}\)
Answer:
\(10 \sqrt{3}\)

Question 126.
Find the value of 22 x 5 x 7.
Answer:
140

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 127.
Find the value of log10 100.
Answer:
2

Question 128.
6n cannot end with this number. What is that number ? (When ‘n’ is a posi¬tive number).
Answer:
0

Question 129.
If 2x = y and log2 y = 3 then find (x – y)2.
Answer:
25

Question 130.
Find the value of log3 \(\frac{1}{27}\).
Answer:
-3

Question 131.
Expanded form of log101000.
Answer:
3 log 2 + 3 log 5

Question 132.
Find the value of log2512.
Answer:
9

Question 133.
Write \(\frac{3}{2}\) (log x) – (log y) as single form.
Answer:
\(\log \sqrt{\frac{x^{3}}{y^{2}}}\)

Question 134.
Find HCF of 1 and 143.
Answer:
1

Question 135.
Which of the following is a correct one ?
A) N⊂Z⊂W
B) N⊂W⊂Z
C) R⊂N⊂W
D) All the above
Answer:
(B)

Question 136.
Find the value of log216.
Answer:
4

Question 137.
Find the value of \(\log _{7} \sqrt{49}\)
Answer:
1

Question 138.
Find the value of log21024.
Answer:
10

Question 139.
Find the value of log18324.
Answer:
2

Question 140.
Express logarithmic form of ax = b.
Answer:
logab = x .

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 141.
Find the value of \((\sqrt{7}+\sqrt{5}) \cdot(\sqrt{7}-\sqrt{5})\)
Answer:
2

Choose the correct answer satisfying the following statements.

Question 142.
Statement (A) : 6n ends with the digit zero, where ‘n’ is natural number. Statement (B): Any number ends with digit zero, if its prime factor is of the form 2m x 5n, where m, n are natural numbers.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iii)
Explanation:
6n = (2 x 3)n = 2n x 3n
Its prime factors do not contain 5n i.e., of the form 2m x 5n, where m, n are natural numbers. Here (A) is incorrect but (B) is correct.
Hence, (iii) is the correct option.

Question 143.
Statement (A) : \(\sqrt{a}\) is an irrational number, where ‘a’ is a prime number.
Statement (B) : Square root of any prime number is an irrational number.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
As we know that square root of every prime number is an irrational number. So, both A and B are correct and B explains A. Hence (i) is the correct option.

Question 144.
Statement (A) : For any two positive integers a and b,
HCF (a, b) x LCM (a, b) – a x b.
Statement (B) : The HCF of two num-bers is 5 and their product is 150. Then their LCM is 40.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)
Explanation:
We have,
LCM (a, b) x HCF (a, b) = a xb LCM x 5 – 150 150
∴ LCM = \(\frac{150}{5}\) = 30
=> LCM = 30, i.e., (B) is incorrect and (A) is correct.
Hence, (ii) is the correct option.

Question 145.
Statement (A) : When a positive inte-ger ’a’ is divided by 3, the values of re-mainder can be 0, 1 (or) 2.
Statement (B) : According to Euclid’s Division Lemma a = bq + r, where 0 ≤ r < b and ‘r’ is an integer.
i) Both A and B are true.
ii) A is true, 3 is false
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
Given positive integers A and B, there exists unique integers q and r satisfy¬ing a = bq + r where 0 ≤ r < b.
This is known as Euclid’s Division Algorithm. So, both A and B are cor¬rect and B explains A.
Hence, (i) is the correct option.

Question 146.
Statement (A): A number N when di¬vided by 15 gives the remainder 2. Then the remainder is same when N is divided by 5.
Statement (B) : \(\sqrt{3}\) is an irrational number.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 147.
Statement (A): \(\frac{41}{1250}\) is a terminating decimal.
Statement (B) : The rational number p/q is a terminating decimal if q = 2m x 5n, where m, n are non-nega¬tive integers.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 148.
Statement (A) : \(\sqrt{3}\) is an irrational number.
Statement (B) : The square root of a prime number is an irrational.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
Clearly, both A and B are correct but B does not explain A.
Hence, (i) is correct option.

Question 149.
Statement (A) : \(\frac{27}{250}\) is a terminating decimal.
Statement (B) : The rational number p/q is a terminating decimal, if q = (2m x 5n) for some whole number m and n.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 150.
Statement (A): \(\frac{13}{3125}\) is a terminating decimal fraction.
Statement (B): If q = 2n . 5m where n, m are non-negative integers, then p/q is terminating decimal fraction.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
(B) is correct.
Since the factors of the denominator 3125 is of the form 2° x 55.
∴ \(\frac{13}{3125}\) is a terminatmg decimal.
∴ Since (A) follows from (B).
∴ Hence, (i) is the correct option.

Question 151.
Statement (A) : Denominator of 34.12345 is of the form 2m x 5n, where m, n are non-negative integers.
Statement (B) : 34.12345 is a termi-nating decimal fraction.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
(B) is clearly true.
Again 34.12345 = \(\frac{3412345}{100000}\)
= \(\frac{682469}{20000}=\frac{682469}{2^{5} \times 5^{4}}\)
Its denominator is of the form 2m x 5n
[m = 5, n = 4 are non-negative integers.]
∴ (A) is true.
Since (B) gives (A).
Hence, (i) is the correct option.

Question 152.
Statement (A): The H.C.F. of two num-bers is 16 and their product is 3072. Then their L.C.M. = 162.
Statement (B): If a, b are two positive integers, then H.C.F x L.C.M = a x b.
i) Both A and B are true.
ii) A is true, B is false.-
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iii)
Explanation:
Here (B) is true (standard result)
(A) is false.
∴ \(\frac{3072}{16}\) = 192 ≠ 162
Hence, (iii) is the correct option.

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 153.
Statement (A) : 2 is a rational num¬ber.
Statement (B): The square roots of all positive integers are irrationals.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)
Explanation:
Here (B) is not true.
∴ \(\sqrt{4} \neq 2\) which is not an irrational
number.
Clearly, (A) is true.
∴ (ii) is the correct option.
Question 154.
Statement (A) : If L.C.M. {p, q} = 30 and H.C.F. {p, q} = 5, then pq = 150.
Statement (B): L.C.M. of a, b x H.C.F. of a, b = a • b.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 155.
Statement (A) : n2 – n is divisible by 2 for every positive integer.
Statement (B): \(\sqrt{2}\) is a rational num¬ber.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)

Question 156.
Statement (A): n2 + n is divisible by 2 for every positive integer n.
Statement (B): If x and y are odd posi-tive integers, from x2 + y2 is divisible by 4.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Read the below passages and answer to the following questions.
If p is prime, then \(\sqrt{\mathbf{p}}\) is irrational and if a, b are two odd prime num-bers, then a2 – b2 is composite.

Question 157.
Is \(\sqrt{7}\) is a rational number ?
Answer:
No, it is an irrational number.

Question 158.
The results of 1192 – 1112 is a ………..
number.
Answer:
Composite

L.C.M. of several fractions
= \(\frac{\text { LCM of their numerators }}{\text { HCF of their denominators }}\)
H.C.F. of several fractions = \(\frac{\text { HCF of their numerators }}{\text { LCM of their denominators }}\)

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 159.
Find the LCM of the fractions \(\frac{5}{16}, \frac{15}{24}\) and \(\frac{25}{8}\)
Answer:
\(\frac{75}{8}\).
Explanation:
L.C.M. of \(\frac{5}{16}, \frac{15}{24}\) and \(\frac{25}{8}\)
= \(\frac{\text { L.C.M. of numerators }}{\text { H.C.F. of denominators }}\)
L.C.M’. of 5, 15 and 25 is 75.
H.C.F. of 16, 24 and 8 is 8.
The H.C.F. of the given fractions = \(\frac{75}{8}\)

Question 160.
Find the HCF of \(\frac{2}{5}, \frac{6}{25}\) and \(\frac{8}{35}\).
Answer:
\(\frac{2}{175}\)
Explanation:

Question 161.
Find the HCF of the fractions \(\frac{8}{21}, \frac{12}{35}\) and \(\frac{32}{7}\)
Answer:
\(\frac{4}{105}\)
[H+] ion concentration in a soap used by Sohan is 9.2 x 10-22.
Explanation:
H.C.F. of given fraction is
\(\frac{\text { H.C.F. of } 8,12,32}{\text { L.C.M. of } 21,35,7}\)
= \(\frac{4}{105}\)

Question 162.
Which mathematical concept is used to find pH of a soap ?
Answer:
Logarithms.

Question 163.
How much the pH of soap used by Sohan ?
Answer:
pH = 21.04.

Question 164.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (1)
Answer:
A – (iii), B – (iv)

Question 165.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (2)
Answer:
A – (i), B – (ii)

Question 166.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (3)
Answer:
A – (iii), B – (i)

Question 167.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (4)
Answer:
A – (ii), B – (v), C – (iii)

Question 168.
Write the correct matching options:
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (5)
A – (i), B – (iv)

Question 169.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (6)
Answer:
A – (ii), B – (iii)

Question 170.
Write the correct matching options :
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (7)
Answer:
A – (ii), B – (v)

Question 171.
Write the correct matching options:
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (8)
Answer:
A – (iii), B – (iv)

Question 172.
Write the correct matching options:
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (9)
Answer:
A — (i), B – (ii), C — (v)

Question 173.
What is the value of \(\log _{\frac{2}{3}}\left(\frac{27}{8}\right)\)
Answer:
-3

Question 174.
Write the decimal form of the rational number \(\frac{7}{2^{2} \times 5}\)
AP Model Paper
Answer:
0.35

AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers

Question 175.
What is the value of \(\log _{\sqrt[3]{5}} \sqrt{5}\) ?
Solution:
AP 10th Class Maths Bits Chapter 1 Real Numbers with Answers (10)

Question 176.
Which statement do you agree with ? P: The product of two irrational num-bers is always a rational number.
Q : The product of a rational and an irrational number is always an irra-tional number,
i) Only P ii) Only Q iii) Both P and Q
Answer:
(ii)

Question 177.
Express 3 log22 = x in exponential form.
Solution:
3 log22 = x
log223 = x ⇒ log28 = x ⇒ 2x = 8