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  • Set · 2 questions
    Consider equation-I: z3+2z2+2z+1=0z^3+2z^2+2z+1=0z3+2z2+2z+1=0 and equation-II: z1985+z100+1=0z^{1985}+z^{100}+1=0z1985+z100+1=0.
    • Q11701
      Lever: Cube roots of unity (1 + ω + ω² = 0, ω³ = 1)Concept: Applying ω: powers, expressions, related roots

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      [Q34 · Sep · 2023]
    • Q11702
      Lever: Cube roots of unity (1 + ω + ω² = 0, ω³ = 1)Concept: Applying ω: powers, expressions, related roots

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      [Q35 · Sep · 2023]
  • Set · 2 questions
    A quadratic equation is given by (a+b)x2−(a+b+c)x+k=0(a+b)x^2-(a+b+c)x+k=0(a+b)x2−(a+b+c)x+k=0, where a,b,ca,b,ca,b,c are real.
    • Q11703
      NDA Maths strategyConcept: Parametric Quadratics — Factor, Don't Force

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      [Q36 · Sep · 2023]
    • Q11704
      NDA Maths strategyConcept: Parametric Quadratics — Factor, Don't Force

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      [Q37 · Sep · 2023]
  • Set · 3 questions
    Let (1+x)n=1+T1x+T2x2+⋯+Tnxn(1+x)^n = 1 + T_1 x + T_2 x^2 + \cdots + T_n x^n(1+x)n=1+T1​x+T2​x2+⋯+Tn​xn.
    • Q11705
      Lever: Pascal / binomial-coefficient identitiesConcept: Weighted Sums via Differentiation

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      [Q38 · Sep · 2023]
    • Q11706
      Lever: Pascal / binomial-coefficient identitiesConcept: Weighted Sums via Differentiation

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      [Q39 · Sep · 2023]
    • Q11707
      Lever: Pascal / binomial-coefficient identitiesConcept: Weighted Sums via Differentiation

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      [Q40 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=x2−1f(x)=x^2-1f(x)=x2−1 and g∘f(x)=x−x+1g\circ f(x)=x-\sqrt{x+1}g∘f(x)=x−x+1​.
    • Q11708
      NDA Maths strategyConcept: Composition of functions

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      [Q41 · Sep · 2023]
    • Q11709
      NDA Maths strategyConcept: Composition of functions

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      [Q42 · Sep · 2023]
  • Set · 2 questions
    Let fff be defined on R∖{0}\mathbb{R}\setminus\{0\}R∖{0} and 2f(x)+f ⁣(1x)=x+32f(x)+f\!\left(\frac{1}{x}\right)=x+32f(x)+f(x1​)=x+3.
    • Q11710
      NDA Maths strategyConcept: Solving by substitution (x → 1/x, x → 1−x)

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      [Q43 · Sep · 2023]
    • Q11711
      NDA Maths strategyConcept: Standard derivatives to memorise

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      [Q44 · Sep · 2023]
  • Set · 2 questions
    A function is defined by f(x)=(x+1)2/3(2x+4)6/3(6x+9)f(x)=(x+1)^{2/3}(2x+4)^{6/3}(6x+9)f(x)=(x+1)2/3(2x+4)6/3(6x+9).
    • Q11712
      NDA Maths strategyConcept: Critical points and the derivative tests

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      [Q45 · Sep · 2023]
    • Q11713
      NDA Maths strategyConcept: Critical points and the derivative tests

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      [Q46 · Sep · 2023]
  • Set · 2 questions
    Given that 4x2+y2=94x^2+y^2=94x2+y2=9.
    • Q11714
      NDA Maths strategyConcept: AM-GM: the calculus-free shortcut

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      [Q47 · Sep · 2023]
    • Q11715
      Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)Concept: AM-GM: the calculus-free shortcut

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      [Q48 · Sep · 2023]
  • Set · 2 questions
    A function is defined by f(x)=π+sin⁡2xf(x)=\pi+\sin^2 xf(x)=π+sin2x.
    • Q11716
      NDA Maths strategyConcept: Finding the range

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      [Q49 · Sep · 2023]
    • Q11717
      NDA Maths strategyConcept: Finding the range

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      [Q50 · Sep · 2023]
  • Set · 2 questions
    A parabola passes through (1,2)(1,2)(1,2) and satisfies dydx=2yx, x>0,y>0\frac{dy}{dx}=\frac{2y}{x},\ x>0,y>0dxdy​=x2y​, x>0,y>0.
    • Q11718
      NDA Maths strategyConcept: The Latus Rectum

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      [Q51 · Sep · 2023]
    • Q11719
      NDA Maths strategyConcept: The Latus Rectum

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      [Q52 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=ax−1+bx−12f(x)=\dfrac{a^{x-1}+b^{x-1}}{2}f(x)=2ax−1+bx−1​ and g(x)=x−1g(x)=x-1g(x)=x−1.
    • Q11720
      NDA Maths strategyConcept: The 1^∞ form

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      [Q53 · Sep · 2023]
    • Q11721
      NDA Maths strategyConcept: The 1^∞ form

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      [Q54 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=2−x+2+xf(x)=\sqrt{2-x}+\sqrt{2+x}f(x)=2−x​+2+x​.
    • Q11722
      NDA Maths strategyConcept: Finding the domain (roots, denominators, logs)

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      [Q55 · Sep · 2023]
    • Q11723
      NDA Maths strategyConcept: Finding the domain (roots, denominators, logs)

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      [Q56 · Sep · 2023]
  • Set · 2 questions
    Let f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and g(x)=[x]−1g(x)=[x]-1g(x)=[x]−1. Let h(x)=f(g(x))g(f(x))h(x)=\frac{f(g(x))}{g(f(x))}h(x)=g(f(x))f(g(x))​.
    • Q11724
      Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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      [Q57 · Sep · 2023]
    • Q11725
      Lever: Modulus / absolute value behaviourConcept: Limits of the greatest-integer function

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      [Q58 · Sep · 2023]
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