NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2

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NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2 is covered in this article with a detailed explanation. Chapter 1 Real Numbers Exercise 1.2 deals with the fundamental theorem of arithmetic. The 7 questions of the exercise cover the concept of factorization of composite numbers.

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CBSE X Related Questions

  • 1.
    If the zeroes of the polynomial $ax^2 + bx + \dfrac{2a}{b}$ are reciprocal of each other, then the value of $b$ is

      • $\dfrac{1}{2}$
      • 2
      • -2
      • $-\dfrac{1}{2}$

    • 2.
      Find the zeroes of the polynomial \(2x^2 + 7x + 5\) and verify the relationship between its zeroes and coefficients.


        • 3.

          Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
          Choose the correct option from the following:
          (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
          (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
          (C) Assertion (A) is true, but Reason (R) is false.
          (D) Assertion (A) is false, but Reason (R) is true.

          Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.
          Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

            • Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
            • Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
            • Assertion (A) is true, but Reason (R) is false.
            • Assertion (A) is false, but Reason (R) is true.

          • 4.
            Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).


              • 5.
                Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
                (i) $pqr + 1$ is a composite number
                (ii) $pqr + 1$ is a prime number


                  • 6.

                    Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

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