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Day 106: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Statistics. Asked once: NDA 1 2024 (same type asked 4 times)

    Marks obtained by 10 students: 24,47,18,32,19,15,21,35,50,41. Largest five observations: 32,35,41,47,50.
    119
    What is the mean deviation of the largest five observations?

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    120
    What is the variance of the largest five observations?

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  2. Question 2

    Statistics. Asked once: NDA 1 2021 (same type asked 4 times)

    116
    The average of a set of 15 observations is recorded, but later it is found that for one observation, the digit in the tens place was wrongly recorded as 8 instead of 3. After correcting the observation, the average is

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  3. Question 3

    3D Geometry. Asked once: NDA 1 2020 (same type asked 4 times)

    61
    What is the length of the diameter of the sphere whose centre is at (1,−2,3)(1,-2,3) and which touches the plane 6x−3y+2z−4=06x-3y+2z-4=0?

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  4. Question 4

    Lines. Asked once: NDA 2 2018 (same type asked 4 times)

    54
    Consider the following statements: 1. The distance between the lines y=mx+c1y=mx+c_1 and y=mx+c2y=mx+c_2 is ∣c1−c2∣1+m2\frac{|c_1-c_2|}{\sqrt{1+m^2}}. 2. The distance between the lines ax+by+c1=0ax+by+c_1=0 and ax+by+c2=0ax+by+c_2=0 is ∣c1−c2∣a2+b2\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}. 3. The distance between the lines x=c1x=c_1 and x=c2x=c_2 is ∣c1−c2∣|c_1-c_2|. Which of the above statements are correct?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2022 (same type asked 4 times)

    3
    Under which of the following conditions does the determinant ∣abcbcacab∣\begin{vmatrix}a & b & c\\b & c & a\\c & a & b\end{vmatrix} vanish? 1. a+b+c=0a+b+c=0 2. a3+b3+c3=3abca^3+b^3+c^3=3abc 3. a2+b2+c2−ab−bc−ca=0a^2+b^2+c^2-ab-bc-ca=0 Select the correct answer using the code given below:

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