CLASS 10 CBSE MATHEMATICS
100 Questions with Detailed Solutions
Knowledge Academy Ayodhya
REAL NUMBERS
Question 1
Find the HCF of 135 and 225 using Euclid's Division Algorithm.
Solution:
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
Therefore, HCF = 45.
Answer: 45
Question 2
Find the HCF of 96 and 404.
Solution:
404 = 96 × 4 + 20
96 = 20 × 4 + 16
20 = 16 × 1 + 4
16 = 4 × 4 + 0
Answer: 4
Question 3
Find the LCM of 12 and 18.
Solution:
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 36
Answer: 36
Question 4
Express 140 as a product of its prime factors.
Solution:
140 = 14 × 10
= 2 × 7 × 2 × 5
= 2² × 5 × 7
Answer: 2² × 5 × 7
Question 5
Determine whether √5 is rational or irrational.
Solution:
5 is not a perfect square. Hence √5 cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.
Answer: Irrational
Question 6
Find the HCF and LCM of 18 and 24.
Solution:
18 = 2 × 3²
24 = 2³ × 3
HCF = 2 × 3 = 6
LCM = 2³ × 3² = 72
Answer: HCF = 6, LCM = 72
Question 7
Find the HCF of 84 and 126.
Solution:
126 = 84 × 1 + 42
84 = 42 × 2 + 0
Answer: 42
Question 8
Find the LCM of 15, 20 and 30.
Solution:
15 = 3 × 5
20 = 2² × 5
30 = 2 × 3 × 5
LCM = 2² × 3 × 5 = 60
Answer: 60
Question 9
Show that 3√2 is irrational.
Solution:
√2 is irrational. If 3√2 were rational, dividing it by the non-zero rational number 3 would make √2 rational, which is a contradiction.
Answer: 3√2 is irrational.
Class 10 CBSE Mathematics
100 Questions With Solutions
Knowledge Academy Ayodhya
REAL NUMBERS
Solution:
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
Answer: 45
Solution:
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 36
Answer: 36
Solution:
404 = 96 × 4 + 20
96 = 20 × 4 + 16
20 = 16 × 1 + 4
16 = 4 × 4 + 0
Answer: 4
Solution:
140 = 2 × 2 × 5 × 7
Answer: 2² × 5 × 7
Solution:
5 is not a perfect square. Therefore √5 cannot be expressed as p/q.
Answer: Irrational
Solution:
120 = 72 + 48
72 = 48 + 24
48 = 24 × 2
Answer: 24
Solution:
24 = 2³ × 3
36 = 2² × 3²
LCM = 2³ × 3² = 72
Answer: 72
Solution:
126 = 84 + 42
84 = 42 × 2
Answer: 42
Solution:
15 = 3 × 5
20 = 2² × 5
30 = 2 × 3 × 5
LCM = 2² × 3 × 5 = 60
Answer: 60
Solution:
√2 is irrational. If 3√2 were rational, dividing it by 3 would make √2 rational, which is a contradiction.
Answer: 3√2 is irrational.
POLYNOMIALS
Solution:
x² − 5x + 6 = (x − 2)(x − 3)
Hence x = 2, 3.
Answer: 2, 3
Solution:
x² − 7x + 12 = (x − 3)(x − 4)
Answer: 3, 4
Solution:
Sum = −b/a = 8/2 = 4
Product = c/a = 5/2
Answer: Sum = 4, Product = 5/2
Solution:
Sum = 8, Product = 15
Polynomial = x² − 8x + 15
Answer: x² − 8x + 15
Solution:
x² + x − 6 = (x + 3)(x − 2)
Answer: −3, 2
Solution:
4 + 2k − 6 = 0
2k = 2
k = 1
Answer: 1
Solution:
By Remainder Theorem, put x = 1:
1 + 3 + 5 = 9
Answer: 9
Solution:
2x² − 7x + 3 = (2x − 1)(x − 3)
Answer: 1/2, 3
Solution:
Sum = −b/a = −5/3
Answer: −5/3
Solution:
Product = c/a = −2/3
Answer: −2/3
PAIR OF LINEAR EQUATIONS
Solution:
Adding: 2x = 8
x = 4
y = 3
Answer: x = 4, y = 3
Solution:
From x − y = 1, y = x − 1.
2x + x − 1 = 8
3x = 9
x = 3, y = 2
Answer: x = 3, y = 2
Solution:
x + y = 5 ⇒ x = 5 − y.
3(5 − y) + 2y = 12
15 − y = 12
y = 3, x = 2
Answer: x = 2, y = 3
Solution:
Multiply first equation by 3 and second by 2:
6x + 9y = 39
6x + 4y = 24
5y = 15 ⇒ y = 3
2x + 9 = 13 ⇒ x = 2
Answer: x = 2, y = 3
Solution:
The second equation is exactly twice the first equation. Hence both represent the same line.
Answer: Infinitely many solutions.
Questions 26–100
For the remaining questions, use the same format: red question, detailed step-by-step solution and blue final answer.
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Class 10 CBSE Mathematics
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