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Karnataka SSLC (Class 10) Real Numbers and Polynomials — practice questions — page 4

Explore 112 free Real Numbers and Polynomials questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Real Numbers and Polynomials questions and exercises with answers

Showing questions 91–112 of 112.

For any two positive integers, HCF × LCM equalsRead the answer and worked solution →The HCF of 12 and 18 isRead the answer and worked solution →The LCM of 12 and 18 isRead the answer and worked solution →If the HCF of two numbers is 9 and their LCM is 90, and one number is 18, the other number isRead the answer and worked solution →Using Euclid's algorithm, the HCF of 96 and 404 isRead the answer and worked solution →The prime factorisation of 140 isRead the answer and worked solution →The product of the HCF and LCM of the numbers 8 and 20 isRead the answer and worked solution →The sum of a rational number and an irrational number is alwaysRead the answer and worked solution →The decimal expansion of an irrational number isRead the answer and worked solution →The largest number that divides both 60 and 96 exactly (their HCF) isRead the answer and worked solution →The degree of the polynomial $3x^2 + 2x + 1$ isRead the answer and worked solution →A real number $k$ is a zero of the polynomial $p(x)$ ifRead the answer and worked solution →The maximum number of zeroes that a quadratic polynomial can have isRead the answer and worked solution →The zero of the linear polynomial $p(x) = x - 3$ isRead the answer and worked solution →For the quadratic polynomial $ax^2+bx+c$, the sum of its zeroes isRead the answer and worked solution →For the quadratic polynomial $ax^2+bx+c$, the product of its zeroes isRead the answer and worked solution →The zeroes of the polynomial $x^2 - 5x + 6$ areRead the answer and worked solution →The sum of the zeroes of the polynomial $2x^2 - 8x + 6$ isRead the answer and worked solution →A quadratic polynomial whose zeroes are 2 and 3 isRead the answer and worked solution →The product of the zeroes of the polynomial $3x^2 - x - 6$ isRead the answer and worked solution →The number of zeroes of the polynomial whose graph meets the x-axis at exactly two points isRead the answer and worked solution →Compare these factor totalsRead the answer and worked solution →

Worked practice questions

For any two positive integers, HCF × LCM equals

  1. the sum of the two numbers
  2. the product of the two numbers
  3. the difference of the two numbers
  4. the larger of the two numbers
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Correct answer: B. the product of the two numbers

1. There is a fixed relation between HCF and LCM of two numbers. 2. **HCF × LCM = product of the two numbers.** 3. e.g. for 12 and 18: 6 × 36 = 216 = 12 × 18. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch8 'Real Numbers', §8.3_

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The HCF of 12 and 18 is

  1. 3
  2. 2
  3. 6
  4. 9
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Correct answer: C. 6

1. $12 = 2^2 \times 3$ and $18 = 2 \times 3^2$. 2. HCF = product of the lowest powers of common primes = $2^1 \times 3^1 = 6$. 3. So the HCF is 6. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch8 'Real Numbers', §8.3_

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The LCM of 12 and 18 is

  1. 72
  2. 6
  3. 216
  4. 36
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Correct answer: D. 36

1. $12 = 2^2 \times 3$, $18 = 2 \times 3^2$. 2. LCM = product of the highest powers of all primes = $2^2 \times 3^2 = 36$. 3. Check: HCF × LCM = 6 × 36 = 216 = 12 × 18 ✓. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch8 'Real Numbers', §8.3_

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