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Andhra Pradesh SSC (Class 10) Real Numbers and Polynomials — practice questions — page 2

Explore 115 free Real Numbers and Polynomials questions in Andhra Pradesh SSC (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 115.

The square of any odd integer, when divided by 8, leaves remainderRead the answer and worked solution →The decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal places?Read the answer and worked solution →How many positive integers less than 1000 are divisible by neither 2 nor 5?Read the answer and worked solution →If $p$ is a prime and $p \mid a^2$, then which must be true?Read the answer and worked solution →The unit digit of $7^{2026}$ isRead the answer and worked solution →The smallest positive integer that is divisible by every integer from 1 to 10 isRead the answer and worked solution →If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(a,b)}{\text{HCF}(a,b)}$ equalsRead the answer and worked solution →Which of the following is an irrational number?Read the answer and worked solution →The remainder when $2^{100}$ is divided by 7 isRead the answer and worked solution →Two positive integers have HCF 9 and LCM 90. If one number is 18, the other isRead the answer and worked solution →The HCF of two consecutive positive integers isRead the answer and worked solution →If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equalsRead the answer and worked solution →The degree of a polynomial is:Read the answer and worked solution →A polynomial of degree 1 is called a:Read the answer and worked solution →A polynomial of degree 2 is called a:Read the answer and worked solution →The general form of a quadratic polynomial is:Read the answer and worked solution →For $p(x) = x^2 - 3x - 4$, the value of $p(2)$ is:Read the answer and worked solution →The zeroes of a polynomial $p(x)$ are the values of $x$ for which:Read the answer and worked solution →For a quadratic $ax^2 + bx + c$, the sum of its zeroes is:Read the answer and worked solution →For a quadratic $ax^2 + bx + c$, the product of its zeroes is:Read the answer and worked solution →A quadratic polynomial can have at most how many zeroes?Read the answer and worked solution →The zeroes of the polynomial $x^2 - 3x - 4$ are:Read the answer and worked solution →Which of the following is NOT a polynomial?Read the answer and worked solution →A cubic polynomial can have at most how many zeroes?Read the answer and worked solution →A polynomial of degree 3 is called a:Read the answer and worked solution →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 →

Worked practice questions

The square of any odd integer, when divided by 8, leaves remainder

  1. 3
  2. 5
  3. 0
  4. 1
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Correct answer: D. 1

An odd integer is $2k+1$; its square is $4k(k+1)+1$. Since $k(k+1)$ is even, $4k(k+1)$ is a multiple of 8, so the square is $\equiv 1 \pmod 8$.

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The decimal expansion of $\dfrac{257}{2^3 \cdot 5^4}$ terminates after how many decimal places?

  1. 3
  2. 4
  3. 5
  4. 7
Show answer and solution

Correct answer: B. 4

A fraction $\dfrac{p}{2^m 5^n}$ terminates after $\max(m,n)$ places. Here $m=3, n=4$, so it terminates after $\max(3,4) = 4$ places.

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How many positive integers less than 1000 are divisible by neither 2 nor 5?

  1. 300
  2. 500
  3. 450
  4. 400
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Correct answer: D. 400

**From 1 to 999:** divisible by 2 → 499, by 5 → 199, by 10 → 99. By inclusion-exclusion, divisible by 2 or 5 $= 499+199-99 = 599$. Neither $= 999 - 599 = 400$.

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