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

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 1–30 of 115.

Which of the following fractions will have a non-terminating recurring decimal expansion?Read the answer and worked solution →Which of the following rational numbers has a terminating decimal expansion?Read the answer and worked solution →Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?Read the answer and worked solution →Which statement is always true about the sum of a rational number and an irrational number?Read the answer and worked solution →If $p$ is a prime number and $p$ divides $a^2$, then which statement must be true?Read the answer and worked solution →Which of the following is a rational number?Read the answer and worked solution →For any two positive integers $a$ and $b$, which relation is always true?Read the answer and worked solution →If the prime factorisations of two numbers are $2^3\times 3^2\times 5$ and $2^2\times 3\times 5^2$, then their HCF isRead the answer and worked solution →Using Euclid's division algorithm, what is the HCF of 135 and 225?Read the answer and worked solution →Which of the following best describes the set of real numbers?Read the answer and worked solution →If $p$ is a prime number and $p$ divides $a^2$, then which conclusion must be true?Read the answer and worked solution →Given that $\operatorname{HCF}(306,657)=9$, what is $\operatorname{LCM}(306,657)$?Read the answer and worked solution →For any two positive integers $a$ and $b$, which identity is always true?Read the answer and worked solution →For the numbers 6, 72 and 120, which pair gives the HCF and LCM respectively?Read the answer and worked solution →The prime factorizations of 96 and 404 are $96=2^5\times 3$ and $404=2^2\times 101$. What is their LCM?Read the answer and worked solution →If $6=2\times 3$ and $20=2^2\times 5$, then their HCF and LCM respectively areRead the answer and worked solution →If $\alpha,\beta,\gamma$ are the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$, then $\alpha\beta\gamma$ is equal toRead the answer and worked solution →A quadratic polynomial has sum of zeroes $-3$ and product of zeroes $2$. Which of the following is one such polynomial?Read the answer and worked solution →The zeroes of the quadratic polynomial $x^2+7x+10$ areRead the answer and worked solution →If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $ax^2+bx+c$ with $a\neq 0$, then $\alpha+\beta$ equalsRead the answer and worked solution →Which statement is true for a polynomial of degree $n$?Read the answer and worked solution →For the polynomial $p(x)=x^2-3x-4$, what is the value of $p(-1)$?Read the answer and worked solution →The zero of the linear polynomial $ax+b$ with $a\neq 0$ isRead the answer and worked solution →Which of the following is not a polynomial in the variable $x$?Read the answer and worked solution →For any integer $n$, the expression $n^2 - 1$ is always divisible by 8 when $n$ isRead the answer and worked solution →The product of any three consecutive positive integers is always divisible byRead the answer and worked solution →The number of trailing zeros at the end of $50!$ isRead the answer and worked solution →If $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ isRead the answer and worked solution →The largest number that divides 245 and 1029, leaving remainders 5 and 5 respectively, isRead the answer and worked solution →For some integer $m$, every odd integer can be written in the formRead the answer and worked solution →

Worked practice questions

Which of the following fractions will have a non-terminating recurring decimal expansion?

  1. $\frac{3}{40}$
  2. $\frac{7}{125}$
  3. $\frac{11}{24}$
  4. $\frac{9}{20}$
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Correct answer: C. $\frac{11}{24}$

A rational number has a recurring decimal if, in lowest terms, the denominator contains a prime factor other than 2 or 5. Since $24=2^3\times 3$ contains 3, $\frac{11}{24}$ is non-terminating recurring. The others have denominators made only of 2s and 5s.

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Which of the following rational numbers has a terminating decimal expansion?

  1. $\frac{7}{12}$
  2. $\frac{13}{25}$
  3. $\frac{11}{18}$
  4. $\frac{5}{21}$
Show answer and solution

Correct answer: B. $\frac{13}{25}$

A rational number terminates when, in lowest terms, its denominator has only 2s and/or 5s as prime factors. Here $25=5^2$, so $\frac{13}{25}$ terminates. The other denominators contain 3 or 7, so they are recurring decimals.

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Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?

  1. Only $r+x$
  2. Only $rx$
  3. Both $r+x$ and $\frac{x}{r}$
  4. Neither $r+x$ nor $rx$
Show answer and solution

Correct answer: C. Both $r+x$ and $\frac{x}{r}$

The notes state that the sum of a rational and an irrational number is irrational. They also state that the product and quotient of a non-zero rational number and an irrational number are irrational. **Hence both $r+x$ and $x/r$ are irrational.**

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