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Day 69: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Matrices & Determinants. This type asked 2 times: NDA 2 2022, NDA 1 2024. This one: NDA 1 2024

    29
    If A=(sin⁡2θ−cos⁡2θ0cos⁡2θsin⁡2θ0001)A=\begin{pmatrix}\sin2\theta & -\cos2\theta & 0\\\cos2\theta & \sin2\theta & 0\\0 & 0 & 1\end{pmatrix}, then which of the following statements is/are correct? (A) A−1=adj AA^{-1}=\text{adj }A (B) AA is skew-symmetric matrix. (C) A−1=ATA^{-1}=A^T Select the correct answer using the code given below:

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  2. Question 2

    Matrices & Determinants. This type asked 2 times: NDA 2 2021, NDA 1 2024. This one: NDA 1 2024

    20
    If ABCABC is a triangle, then what is the value of the determinant ∣cos⁡Csin⁡B0tan⁡A0sin⁡B0tan⁡(B+C)cos⁡C∣\begin{vmatrix}\cos C & \sin B & 0\\\tan A & 0 & \sin B\\0 & \tan(B+C) & \cos C\end{vmatrix}?

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  3. Question 3 (case study, 2 parts)

    Probability. This type asked 2 times: NDA 1 2021, NDA 1 2024. This one: NDA 1 2024

    Let AA and BB be two events such that P(A∪B)≥0.75P(A\cup B)\geq0.75 and 0.125≤P(A∩B)≤0.3750.125\leq P(A\cap B)\leq0.375.
    111
    What is the minimum value of P(A)+P(B)P(A)+P(B)?

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    112
    What is the maximum value of P(A)+P(B)P(A)+P(B)?

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  4. Question 4

    Statistics. This type asked 2 times: NDA 1 2023, NDA 1 2024. This one: NDA 1 2024

    103
    From data (−4,1),(−1,2),(2,7)(-4,1),(-1,2),(2,7) and (3,1)(3,1), the regression line of yy on xx is obtained as y=a+bxy=a+bx, then what is the value of 2a+15b2a+15b?

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  5. Question 5

    Trigonometric Identities. This type asked 2 times: NDA 1 2017, NDA 1 2024. This one: NDA 1 2024

    48
    If tan⁡α\tan\alpha and tan⁡β\tan\beta are the roots of the equation x2−6x+8=0x^2-6x+8=0, then what is the value of cos⁡(2α+2β)\cos(2\alpha+2\beta)?

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