Mathematics - बीजगणित

Mathematics
Mathematics - बीजगणित

यदि 27^(x − 2/3) = 81, तो 2^(3x + 1) का मान है :

Options:

  1. 64
  2. 128
  3. 256
  4. 512

Right Answer: 128

दिया है 27^(x − 2/3) = 81। दोनों पक्षों को 3 के आधार पर लिखते हैं — 27 = 3³ तथा 81 = 3⁴। इससे (3³)^(x − 2/3) = 3⁴, अर्थात् 3^(3x − 2) = 3⁴। आधार समान होने पर घातांक बराबर होंगे, अतः 3x − 2 = 4, जिससे 3x = 6 और x = 2। अब पूछा गया मान ज्ञात करते हैं — 2^(3x + 1) = 2^(3 × 2 + 1) = 2⁷ = 128। घातांक के नियम (aᵐ)ⁿ = a^(mn) का प्रयोग ऐसे प्रश्नों में सबसे महत्वपूर्ण है। अतः सही उत्तर 128 है।

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This question is part of Mathematics - बीजगणित, which has 18 practice questions with answers.

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Frequently Asked Questions

The questions are drawn from the mathematics sections of teacher-eligibility tests such as CTET, HTET, REET, UPTET and MPTET, and from recruitment examinations including SSC (CGL, CHSL, MTS, CPO, GD and others), DSSSB, BPSC, KVS, NVS and various state-level exams. Because the arithmetic base of these papers overlaps heavily, one round of focused practice serves several exams at once.

Yes. Every quiz in this section can be attempted free of cost, with no registration required to view the answers and explanations.

Teaching-eligibility papers stay close to the school syllabus. Expect number system, fractions, decimals, LCM and HCF, percentage, ratio, profit and loss, simple interest, time and work, geometry, mensuration and data handling — plus a pedagogy portion covering the nature of mathematics, teaching methods, error analysis, remedial teaching and evaluation. The pedagogy questions are scoring and are frequently ignored by candidates. Confirm the exact list against the official syllabus of your exam.

The subject is the same; the demand is not. Teaching exams test whether you understand the concept well enough to explain it to a child, so the numbers stay simple and the pedagogy component carries real weight. SSC and DSSSB test speed under a hard time limit, so shortcut methods, approximation and mental calculation matter far more. Prepare the concept once, then practise it twice — slowly for the TET, and against the clock for SSC.

The questions are modelled on the pattern, difficulty and phrasing of previous-year papers released by the exam bodies listed in our sources section. Where a concept has been repeatedly asked, we retain the standard framing so that the practice matches what you will see in the hall.

Yes. Each question shows the correct option immediately after submission, along with a step-by-step solution. Where a faster method exists, it is given alongside the standard one.

The count varies by exam, by paper and by year — a TET paper, an SSC tier and a DSSSB post each weight mathematics differently, and the pattern is revised from time to time. Check the official notification for your exam and year rather than relying on any third-party figure, including ours.

Most teaching-eligibility and SSC-type examinations do not permit calculators in the exam hall. Practise without one from the first day, or your practice score will not survive contact with the real paper.

Short, frequent sessions beat long, rare ones. A focused set of 15–20 questions from one sub-topic each day, revisited after a week, produces better retention than a single long mixed test. Track accuracy, not just the raw score — a candidate who attempts 20 and gets 18 right is in a stronger position than one who attempts 40 and gets 25.

In most cases, yes. State teacher-eligibility tests and subordinate-services papers largely draw on the same NCERT-based arithmetic foundation. Use these quizzes for the core practice, then cover any state-specific portion from the official syllabus of that exam.
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References & Official Sources

Questions and answers are compiled from previous-year papers and official notifications published by the following examination authorities. Always verify the latest syllabus and pattern on the official website.

  1. Mathematics Quiz: Free MCQs for CTET, HTET, SSC & TET Exams — CTET — Central Board of Secondary Education (CBSE), Central Teacher Eligibility Test