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CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions

CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions is an online chapter test in the CBSE Class 10 pattern, covering Arithmetic Progressions. 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.

30
Questions
20
Minutes
30
Marks
None
Negative marking
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Topics in this test

TopicQuestions
Arithmetic Progressions30

Difficulty: 8 medium · 22 hard

Arithmetic Progressions MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

  1. Q1. What is the first negative term of the AP $20, 15, 10, 5, \ldots$?

    समान्तर श्रेणी $20, 15, 10, 5, \ldots$ का पहला ऋणात्मक पद क्या है?

    • A. $-5$
    • B. $5$
    • C. $0$
    • D. $-10$
    Solution

    From $20+(n-1)(-5)<0$ we get $n>5$, so the first negative term is the $6$th term, $a_6=20-25=-5$; the $5$th term is $0$, which is not negative.

    $20+(n-1)(-5)<0$ से $n>5$ प्राप्त होता है, इसलिए पहला ऋणात्मक पद $6$वां पद है, $a_6=20-25=-5$; $5$वां पद $0$ है, जो ऋणात्मक नहीं है।

  2. Q2. In an AP, if $a_m = \frac{1}{n}$ and $a_n = \frac{1}{m}$ (where $m \neq n$), what is the value of $a_{mn}$?

    एक समान्तर श्रेणी में, यदि $a_m = \frac{1}{n}$ और $a_n = \frac{1}{m}$ (जहाँ $m \neq n$), तो $a_{mn}$ का मान क्या है?

    • A. $0$
    • B. $mn$
    • C. $1$
    • D. $\frac{1}{mn}$
    Solution

    Solving the two equations gives $d=\frac{1}{mn}$ and $a=\frac{1}{mn}$, so $a_{mn}=a+(mn-1)d=\frac{1}{mn}+\frac{mn-1}{mn}=1$.

    दोनों समीकरणों को हल करने पर $d=\frac{1}{mn}$ और $a=\frac{1}{mn}$ प्राप्त होता है, इसलिए $a_{mn}=a+(mn-1)d=\frac{1}{mn}+\frac{mn-1}{mn}=1$.

  3. Q3. Which of the following statements about an Arithmetic Progression is correct?

    समान्तर श्रेणी के बारे में निम्नलिखित में से कौन-सा कथन सही है?

    • A. An AP must always have a finite number of terms. / एक समान्तर श्रेणी में हमेशा पदों की संख्या सीमित होनी चाहिए।
    • B. If the common difference of a progression is zero, it is not considered an AP. / यदि किसी श्रेणी का सार्व अंतर शून्य है, तो उसे समान्तर श्रेणी नहीं माना जाता।
    • C. The common difference of an AP can never be negative or a fraction. / समान्तर श्रेणी का सार्व अंतर कभी भी ऋणात्मक या भिन्न नहीं हो सकता।
    • D. If $a, b, c$ are three consecutive terms of an AP, then $2b = a + c$. / यदि $a, b, c$ किसी समान्तर श्रेणी के तीन क्रमागत पद हैं, तो $2b = a + c$.
    Solution

    If $a, b, c$ are three consecutive terms of an AP, the middle term is the average of the other two, so $2b=a+c$; an AP can have a negative or zero common difference and may have infinitely many terms.

    यदि $a, b, c$ किसी समान्तर श्रेणी के तीन क्रमागत पद हैं, तो मध्य पद अन्य दो का औसत होता है, इसलिए $2b=a+c$; एक समान्तर श्रेणी का सार्व अंतर ऋणात्मक या शून्य भी हो सकता है और इसमें अनंत पद भी हो सकते हैं।

Frequently asked questions

How many questions are in the CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions?

30 questions for 30 marks, to be answered in 20 minutes.

Is there negative marking in the CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions cover?

Arithmetic Progressions (30 questions).

Is the CBSE Class 10 Mathematics · Ch 5: Arithmetic Progressions free?

It is part of the CBSE Class 10 Test Series 2027 — Chapter-wise + Full Tests (44 tests, ₹199). You can first try Hindi · Ch 1: Surdas ke Pad for free.

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Arithmetic Progressions MCQ | CBSE Class 10 | SeatBeat