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CBSE Class 10 Real Numbers and Polynomials — practice questions — page 2

Explore 100 free Real Numbers and Polynomials questions in CBSE 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 31–60 of 100.

Euclid's division lemma states that for positive integers a and b, there exist unique q and r such that:Read the answer and worked solution →For any two positive integers, HCF × LCM equals:Read the answer and worked solution →The number √2 is:Read the answer and worked solution →A rational number p/q (in lowest terms) has a terminating decimal expansion if the prime factors of q are:Read the answer and worked solution →The HCF of 6 and 20 is:Read the answer and worked solution →The LCM of 6 and 20 is:Read the answer and worked solution →The product of the HCF and LCM of 6 and 20 is:Read the answer and worked solution →The decimal expansion of 1/3 is:Read the answer and worked solution →The decimal expansion of 7/8 is:Read the answer and worked solution →The number of prime numbers is:Read the answer and worked solution →The prime factorisation of 156 is:Read the answer and worked solution →The sum √3 + √5 is:Read the answer and worked solution →The Fundamental Theorem of Arithmetic states that every composite number can be expressed as:Read the answer and worked solution →What is the degree of the polynomial 5x³ − 2x² + 7?Read the answer and worked solution →Which of the following is NOT a polynomial?Read the answer and worked solution →What is p(−1) for p(x) = x³ − 3x + 2?Read the answer and worked solution →For what value of x is x = 2 a zero of x² − 4?Read the answer and worked solution →Identify the degree of the polynomial (2x − 3)(x + 1)(x² + 1).Read the answer and worked solution →Find the zero of p(x) = 3x − 12.Read the answer and worked solution →How many real zeroes does p(x) = x² + 4 have?Read the answer and worked solution →Find the zeroes of x² − 5x + 6.Read the answer and worked solution →How many real zeroes does p(x) = (x − 1)² have?Read the answer and worked solution →Find the zeroes of 4x² − 4x − 3.Read the answer and worked solution →For what value of k does p(x) = x² + kx + 9 have equal zeroes?Read the answer and worked solution →If α and β are zeroes of x² − 5x + 6, find α + β and αβ.Read the answer and worked solution →For 3x² + 7x − 2, find the sum and product of zeroes.Read the answer and worked solution →Construct a quadratic polynomial whose zeroes are 3 and 5.Read the answer and worked solution →One zero of x² − 7x + k is 3. Find k and the other zero.Read the answer and worked solution →If α and β are zeroes of x² + 5x + 4, find α + β + αβ.Read the answer and worked solution →Construct a quadratic whose zeroes are 2 and −7.Read the answer and worked solution →

Worked practice questions

Euclid's division lemma states that for positive integers a and b, there exist unique q and r such that:

  1. a = bq, with no remainder
  2. a = bq + r, where 0 ≤ r < b
  3. a = bq + r, where r > b
  4. a = b + qr
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Correct answer: B. a = bq + r, where 0 ≤ r < b

Euclid's division lemma: a = bq + r with 0 ≤ r < b, and q, r unique.

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For any two positive integers, HCF × LCM equals:

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

For two positive integers, HCF × LCM = product of the numbers.

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The number √2 is:

  1. a natural number
  2. an integer
  3. irrational
  4. rational
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Correct answer: C. irrational

√2 cannot be written as p/q, so it is irrational.

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