Daily quiz

UP PGT Mathematics Daily Quiz 1

A daily quiz for UPESSC PGT (Post Graduate Teacher / Pravakta) 2026, the recruitment conducted by the Uttar Pradesh Education Service Selection Commission (UPESSC), Prayagraj. 20 questions for 20 marks in 15 minutes, with no negative marking - the same pattern and the same clock as the exam.

20 quick Mathematics questions for UP PGT candidates. Free, no plan needed.

Pitched at 13 medium and 7 hard questions.

Start this test 15 min · 20 Qs · 20 marks

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Paper pattern

SectionQuestionsCorrectWrong
Mathematics15+1none
General Studies5+1none
Total2020 marks

Topics in this paper

  • Statistics & Probability2
  • Integration & Its Applications2
  • Sets, Relations & Functions2
  • Vectors & 3D Geometry2
  • Complex Numbers1
  • Limits, Continuity & Differentiation1
  • Applications of Derivatives1
  • Real Analysis1
  • Trigonometry (Identities, Equations, Heights)1
  • Abstract Algebra (Groups, Rings, Fields)1
  • Straight Lines & Conic Sections1
  • Indian History1
  • Awards & Honours1
  • Uttar Pradesh GK1
  • Environment1
  • ICT in Education1

Sample questions from this paper

  1. Mathematics (Secondary & Senior Secondary) · Complex Numbers · medium

    The complex number z = (1 + i tan α)/(1 − i tan α), where α is not an odd multiple of π/2, is equal to:

    सम्मिश्र संख्या z = (1 + i tan α)/(1 − i tan α), जहाँ α, π/2 का विषम गुणज नहीं है, किसके बराबर है?

    • Acos 2α + i sin 2αcos 2α + i sin 2α
    • Bcos 2α − i sin 2αcos 2α − i sin 2α
    • Ccos α + i sin αcos α + i sin α
    • Dsec 2α + i tan 2αsec 2α + i tan 2α

    Explanation

    Multiplying numerator and denominator by cos α turns the fraction into (cos α + i sin α)/(cos α − i sin α), and by De Moivre's theorem this is (cos α + i sin α)², that is cos 2α + i sin 2α. Inverting the fraction gives the conjugate, and forgetting to square the factor leaves the angle undoubled.

    अंश तथा हर को cos α से गुणा करने पर भिन्न (cos α + i sin α)/(cos α − i sin α) बन जाती है, और डी मायवर प्रमेय से यह (cos α + i sin α)² है, अर्थात् cos 2α + i sin 2α। भिन्न को उल्टा करने पर संयुग्मी मिलता है, तथा वर्ग करना भूल जाने पर कोण दुगुना नहीं होता।

  2. General Awareness · Indian History · medium

    In which year did Ashoka fight the Kalinga War, after which he turned towards Dhamma?

    अशोक ने कलिंग युद्ध किस वर्ष लड़ा, जिसके बाद वह धम्म की ओर उन्मुख हुआ?

    • A305 BCE305 ई.पू.
    • B273 BCE273 ई.पू.
    • C261 BCE261 ई.पू.
    • D232 BCE232 ई.पू.

    Explanation

    The Kalinga War was fought in 261 BCE, in the eighth year after Ashoka's consecration. Rock Edict XIII records his remorse at the bloodshed. 273 BCE is roughly his accession and 232 BCE his death.

    कलिंग युद्ध 261 ई.पू. में, अशोक के राज्याभिषेक के आठवें वर्ष में लड़ा गया। तेरहवें शिलालेख में रक्तपात पर उसके पश्चाताप का उल्लेख है। 273 ई.पू. लगभग उसका राज्यारोहण और 232 ई.पू. उसकी मृत्यु का वर्ष है।

  3. Mathematics (Secondary & Senior Secondary) · Limits, Continuity & Differentiation · medium

    If y = x³ log x for x > 0, what is the fourth derivative d⁴y/dx⁴?

    यदि x > 0 के लिए y = x³ log x हो, तो चतुर्थ अवकलज d⁴y/dx⁴ क्या है?

    • A3/x3/x
    • B11/x11/x
    • C6/x6/x
    • D6/x²6/x²

    Explanation

    Successively, y′ = 3x² log x + x², y″ = 6x log x + 5x and y‴ = 6 log x + 11, so the fourth derivative is 6/x. Stopping at y‴ and reading off its constant term gives the answer 11/x.

    क्रमशः y′ = 3x² log x + x², y″ = 6x log x + 5x तथा y‴ = 6 log x + 11 मिलता है, अतः चतुर्थ अवकलज 6/x है। y‴ पर रुककर उसका अचर पद पढ़ लेने से 11/x उत्तर आ जाता है।

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