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Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers

Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers is an online chapter test in the Bihar Board Class 10 (Matric) pattern, covering Real Numbers. Attempt it on SeatBeat with a timer like the real exam, then see a detailed solution for every question and your score and weak-topic analysis.

20
Questions
20
Minutes
20
Marks
None
Negative marking
Attempt this test free

Topics in this test

TopicQuestions
Real Numbers20

Difficulty: 6 easy · 10 medium · 4 hard

Sample questions with answers

The first 5 questions of this free test.

  1. Q1. Using Euclid's division lemma with $b = 3$, every positive integer $a$ can be written as:

    • A. $3q$, $3q+1$, or $3q+2$, for some integer $q$
    • B. $3q$ or $3q+1$ only, for some integer $q$
    • C. $3q+1$ or $3q+2$ only, for some integer $q$
    • D. $2q$, $2q+1$, or $2q+2$, for some integer $q$
    Solution

    Euclid's division lemma applied with b = 3 shows every positive integer is of the form 3q, 3q+1 or 3q+2.

  2. Q2. Using Euclid's division lemma with $b = 6$, any positive odd integer can be shown to be of the form:

    • A. $6q+1$, $6q+3$ or $6q+5$, where $q$ is a whole number
    • B. $6q$ only, where $q$ is a whole number
    • C. $6q+1$ only, where $q$ is a whole number
    • D. $4q+1$, where $q$ is a whole number
    Solution

    Dividing any positive integer by 6 gives remainders 0 to 5; odd integers correspond only to the remainders 1, 3 and 5.

  3. Q3. Using Euclid's division algorithm, the HCF of $196$ and $38220$ is:

    • A. $196$
    • B. $4$
    • C. $38220$
    • D. $2$
    Solution

    Dividing 38220 by 196 leaves remainder 0 directly, so 196 itself is the HCF.

  4. Q4. To prove that $3 + 2\sqrt5$ is irrational, we argue that:

    • A. If $3+2\sqrt5$ were rational, then $\sqrt5$ would also have to be rational, contradicting the fact that $\sqrt5$ is irrational
    • B. $3+2\sqrt5$ equals a terminating decimal, so it must be rational
    • C. Irrational numbers can also be written in the form $\frac{p}{q}$
    • D. Since $\sqrt5$ is rational, $3+2\sqrt5$ must also be rational
    Solution

    If $3+2\sqrt5$ were rational, then $\sqrt5$ could be written as a rational number too, which contradicts the known fact that $\sqrt5$ is irrational.

  5. Q5. Which of the following numbers has a non-terminating, repeating decimal expansion?

    • A. $\frac{7}{24}$
    • B. $\frac{9}{40}$
    • C. $\frac{21}{50}$
    • D. $\frac{11}{125}$
    Solution

    24 = $2^3 \times 3$ contains the prime 3 besides 2, so $\frac{7}{24}$ gives a non-terminating repeating decimal, unlike the other options whose denominators have only 2 and 5 as prime factors.

Frequently asked questions

How many questions are in the Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers?

20 questions for 20 marks, to be answered in 20 minutes.

Is there negative marking in the Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers?

No — wrong answers are not penalised in this test.

Which topics does the Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers cover?

Real Numbers (20 questions).

Is the Bihar Board Class 10 (Matric) Mathematics · Ch 1: Real Numbers free?

Yes — this test is free. Create a free SeatBeat account and attempt it online; you get the solutions and your score analysis after submitting.

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