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  • Set · 1 question
    The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP.
    • Q11951
      NDA Maths strategyConcept: The arithmetic mean and symmetric terms

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      [Q44 · Sep · 2024]
  • Set · 2 questions
    Let (8+37)20=U+V(8+3\sqrt{7})^{20}=U+V(8+37​)20=U+V and (8−37)20=W(8-3\sqrt{7})^{20}=W(8−37​)20=W, where UUU is an integer and 0<V<10<V<10<V<1.
    • Q11952
      NDA Maths strategyConcept: The Conjugate Trick — Irrational Parts Cancel

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      [Q45 · Sep · 2024]
    • Q11953
      NDA Maths strategyConcept: The Conjugate Trick — Irrational Parts Cancel

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      [Q46 · Sep · 2024]
  • Set · 2 questions
    The roots of the quadratic equation (a2b2−c2)x2+(b2c2−a2)x+(c2a2−b2)=0(a^2b^2-c^2)x^2+(b^2c^2-a^2)x+(c^2a^2-b^2)=0(a2b2−c2)x2+(b2c2−a2)x+(c2a2−b2)=0 are equal, a2≠b2≠c2a^2\neq b^2\neq c^2a2=b2=c2.
    • Q11954
      NDA Maths strategyConcept: Constructed Symmetric-Coefficient Equations

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      [Q47 · Sep · 2024]
    • Q11955
      NDA Maths strategyConcept: Constructed Symmetric-Coefficient Equations

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      [Q48 · Sep · 2024]
  • Set · 2 questions
    Let A=(3−342−340−11)A=\begin{pmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{pmatrix}A=​320​−3−3−1​441​​.
    • Q11956
      NDA Maths strategyConcept: The adjoint (adjugate)

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      [Q49 · Sep · 2024]
    • Q11957
      NDA Maths strategyConcept: The adjoint (adjugate)

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      [Q50 · Sep · 2024]
  • Q11958
    NDA Maths strategyConcept: Cross product — algebra and properties

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    [Q51 · Sep · 2024]
  • Q11959
    NDA Maths strategyConcept: Angle between two vectors via the dot-product formula

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    [Q52 · Sep · 2024]
  • Q11960
    NDA Maths strategyConcept: Solving for an angle from a perpendicularity / magnitude constraint

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    [Q53 · Sep · 2024]
  • Q11961
    NDA Maths strategyConcept: Collinearity of three points (and vector relations in regular figures)

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    [Q54 · Sep · 2024]
  • Q11962
    NDA Maths strategyConcept: Unit vectors, orthogonal triples, and decomposition

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    [Q55 · Sep · 2024]
  • Q11963
    NDA Maths strategyConcept: Parallelograms, squares and diagonals

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    [Q56 · Sep · 2024]
  • Q11964
    NDA Maths strategyConcept: The Sum of Focal Distances

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    [Q57 · Sep · 2024]
  • Q11965
    NDA Maths strategyConcept: Parallelograms, squares and diagonals

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    [Q58 · Sep · 2024]
  • Q11966
    NDA Maths strategyConcept: Diameter Form — Circle From Two Endpoints

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    [Q59 · Sep · 2024]
  • Q11967
    NDA Maths strategyConcept: Standard Forms & Their Elements

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    [Q60 · Sep · 2024]
  • Set · 2 questions
    A triangle ABCABCABC is inscribed in the circle x2+y2=100x^2+y^2=100x2+y2=100. BBB and CCC have coordinates (6,8)(6,8)(6,8) and (−8,6)(-8,6)(−8,6) respectively.
    • Q11968
      NDA Maths strategyConcept: Inscribed Angle and the Angle in a Semicircle

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      [Q61 · Sep · 2024]
    • Q11969
      NDA Maths strategyConcept: Inscribed Angle and the Angle in a Semicircle

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      [Q62 · Sep · 2024]
  • Set · 2 questions
    ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2,3)A(2,3)A(2,3), B(4,3)B(4,3)B(4,3), C(5,1)C(5,1)C(5,1) be the vertices.
    • Q11970
      NDA Maths strategyConcept: Parallelograms, squares and diagonals

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      [Q63 · Sep · 2024]
    • Q11971
      NDA Maths strategyConcept: Parallelograms, squares and diagonals

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      [Q64 · Sep · 2024]
  • Set · 2 questions
    Let 2x2+2y2+2z2+3x+3y+3z−6=02x^2+2y^2+2z^2+3x+3y+3z-6=02x2+2y2+2z2+3x+3y+3z−6=0 be a sphere.
    • Q11972
      NDA Maths strategyConcept: General equation, centre, and radius

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      [Q65 · Sep · 2024]
    • Q11973
      NDA Maths strategyConcept: General equation, centre, and radius

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      [Q66 · Sep · 2024]
  • Set · 2 questions
    Let SSS be the line of intersection of two planes x+y+z=1x+y+z=1x+y+z=1 and 2x+3y−4z=82x+3y-4z=82x+3y−4z=8 with direction ratios ⟨−7,6,1⟩\langle -7,6,1\rangle⟨−7,6,1⟩. If (l,m,n)(l,m,n)(l,m,n) are direction cosines of SSS, then what is the value of 43l2−m2−n243l^2-m^2-n^243l2−m2−n2?
    • Q11974
      NDA Maths strategyConcept: Perpendicular and parallel conditions

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      [Q67 · Sep · 2024]
    • Q11975
      NDA Maths strategyConcept: Reading direction ratios off a line

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      [Q68 · Sep · 2024]
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