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  • Set · 2 questions
    Let ϕ(a)=∫aa+100π∣sin⁡x∣ dx\phi(a)=\displaystyle\int_a^{a+100\pi}|\sin x|\,dxϕ(a)=∫aa+100π​∣sinx∣dx.
    • Q11876
      NDA Maths strategyConcept: The Leibniz rule — differentiating an integral

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      [Q89 · Apr · 2024]
    • Q11877
      NDA Maths strategyConcept: The Leibniz rule — differentiating an integral

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      [Q90 · Apr · 2024]
  • Q11878
    NDA Maths strategyConcept: Critical points and the derivative tests

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    [Q91 · Apr · 2024]
  • Q11879
    NDA Maths strategyConcept: Critical points and the derivative tests

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    [Q92 · Apr · 2024]
  • Set · 2 questions
    Let f(x)=∣x−1∣f(x)=|x-1|f(x)=∣x−1∣, g(x)=[x]g(x)=[x]g(x)=[x] and h(x)=f(x)⋅g(x)h(x)=f(x)\cdot g(x)h(x)=f(x)⋅g(x) where [⋅][\cdot][⋅] is the greatest integer function.
    • Q11880
      Lever: Modulus / absolute value behaviourConcept: Integrating greatest-integer (floor) functions

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      [Q93 · Apr · 2024]
    • Q11881
      Lever: Modulus / absolute value behaviourConcept: Integrating greatest-integer (floor) functions

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      [Q94 · Apr · 2024]
  • Set · 2 questions
    Let ∫dxx+1−x−1=α(x+1)3/2+β(x−1)3/2+c\displaystyle\int\dfrac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{3/2}+\beta(x-1)^{3/2}+c∫x+1​−x−1​dx​=α(x+1)3/2+β(x−1)3/2+c.
    • Q11882
      NDA Maths strategyConcept: Rationalising a Surd Denominator

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      [Q95 · Apr · 2024]
    • Q11883
      NDA Maths strategyConcept: Rationalising a Surd Denominator

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      [Q96 · Apr · 2024]
  • Set · 2 questions
    The circle x2+y2−2x=0x^2+y^2-2x=0x2+y2−2x=0 is partitioned by line y=xy=xy=x in two segments. Let A1,A2A_1,A_2A1​,A2​ be the areas of major and minor segments respectively.
    • Q11884
      NDA Maths strategyConcept: Area of a Circular Segment by a Chord

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      [Q97 · Apr · 2024]
    • Q11885
      NDA Maths strategyConcept: Area of a Circular Segment by a Chord

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      [Q98 · Apr · 2024]
  • Set · 2 questions
    Let 3f(x)+f ⁣(1x)=1x+13f(x)+f\!\left(\dfrac{1}{x}\right)=\dfrac{1}{x}+13f(x)+f(x1​)=x1​+1.
    • Q11886
      NDA Maths strategyConcept: Solving by substitution (x → 1/x, x → 1−x)

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      [Q99 · Apr · 2024]
    • Q11887
      NDA Maths strategyConcept: Direct evaluation — simplify, then integrate

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      [Q100 · Apr · 2024]
  • Q11888
    NDA Maths strategyConcept: Selection probability with combinations

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    [Q101 · Apr · 2024]
  • Q11889
    NDA Maths strategyConcept: Recovering n and p from the Moments

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    [Q102 · Apr · 2024]
  • Q11890
    NDA Maths strategyConcept: Lines of Regression

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    [Q103 · Apr · 2024]
  • Q11891
    NDA Maths strategyConcept: Angle Between the Two Regression Lines

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    [Q104 · Apr · 2024]
  • Q11892
    NDA Maths strategyConcept: Variance

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    [Q105 · Apr · 2024]
  • Q11893
    NDA Maths strategyConcept: Harmonic progression — flip to the reciprocal AP

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    [Q106 · Apr · 2024]
  • Q11894
    NDA Maths strategyConcept: Harmonic Mean (HM)

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    [Q107 · Apr · 2024]
  • Q11895
    NDA Maths strategyConcept: Probability with arrangements

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    [Q108 · Apr · 2024]
  • Q11896
    NDA Maths strategyConcept: Choosing numbers with a property

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    [Q109 · Apr · 2024]
  • Q11897
    NDA Maths strategyConcept: Choosing numbers with a property

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    [Q110 · Apr · 2024]
  • Set · 2 questions
    Let AAA and BBB be two events such that P(A∪B)≥0.75P(A\cup B)\geq0.75P(A∪B)≥0.75 and 0.125≤P(A∩B)≤0.3750.125\leq P(A\cap B)\leq0.3750.125≤P(A∩B)≤0.375.
    • Q11898
      NDA Maths strategyConcept: Minimum and maximum of combined probabilities

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      [Q111 · Apr · 2024]
    • Q11899
      NDA Maths strategyConcept: Minimum and maximum of combined probabilities

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      [Q112 · Apr · 2024]
  • Set · 1 question
    Events A,B,CA,B,CA,B,C: P(A)=0.6,P(B)=0.4,P(C)=0.5,P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2P(A)=0.6,P(B)=0.4,P(C)=0.5,P(A\cup B)=0.8,P(A\cap C)=0.3,P(A\cap B\cap C)=0.2P(A)=0.6,P(B)=0.4,P(C)=0.5,P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2 and P(A∪B∪C)≥0.85P(A\cup B\cup C)\geq0.85P(A∪B∪C)≥0.85.
    • Q11900
      NDA Maths strategyConcept: Minimum and maximum of combined probabilities

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      [Q113 · Apr · 2024]
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