PYQ Vault

Day 262: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Statistics. Asked once: NDA 1 2024

    104
    Let x+2y+1=0x+2y+1=0 and 2x+3y+4=02x+3y+4=0 be two lines of regression computed from some bivariate data. If θ\theta is the acute angle between them, then what is the value of 488tan⁡3θ488\tan 3\theta?

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  2. Question 2

    Trigonometric Equations. Asked once: NDA 2 2024

    27
    What is the general solution of cos⁡100x−sin⁡100x=1\cos^{100}x-\sin^{100}x=1? (where nn is an integer)

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  3. Question 3

    Trigonometric Identities. Asked once: NDA 1 2026

    29
    If cos⁡θ=13\cos\theta=\dfrac{1}{3}, then what is the value of sin⁡ ⁣(θ2)sin⁡ ⁣(3θ2)\sin\!\left(\dfrac{\theta}{2}\right)\sin\!\left(\dfrac{3\theta}{2}\right)?

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  4. Question 4 (case study, 2 parts)

    Vectors. Asked once: NDA 1 2026

    For the next two (02) items that follow: Let a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} be unit vectors. Further, a⃗\vec{a} is perpendicular to b⃗\vec{b}; c⃗\vec{c} makes angle π3\frac{\pi}{3} with both a⃗\vec{a} and b⃗\vec{b}; and c⃗=pa⃗+qb⃗+r(a⃗×b⃗)\vec{c}=p\vec{a}+q\vec{b}+r(\vec{a}\times\vec{b}).
    69
    What is the value of (p+q)(p+q)?

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    70
    What is the value of r2r^2?

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  5. Question 5 (case study, 2 parts)

    3D Geometry. Asked once: NDA 1 2022

    Consider the following for the next two (02) items that follow: Let the plane 2xk+2y3+z3=2\frac{2x}{k}+\frac{2y}{3}+\frac{z}{3}=2 pass through the point (2,3,−6)(2,3,-6).
    94
    What are the direction ratios of a normal to the plane?

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    95
    If pp, qq and rr are the intercepts made by the plane on the coordinate axes respectively, then what is (p+q+r)(p+q+r) equal to?

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