Day 107: NDA Maths

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

Question 1 (case study, 2 parts)
3D Geometry. Asked once: NDA 1 2023 (same type asked 4 times)
Consider the following for the next two (02) items that follow: Consider two lines whose direction ratios are $(2,-1,2)$ and $(k,3,5)$ . They are inclined at an angle $\dfrac{\pi}{4}$ .
63 $k$
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64 $What are the direction ratios of a line which is perpendicular to both the lines?$
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Question 2
3D Geometry. Asked once: NDA 2 2021 (same type asked 4 times)
63 $xy$
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Question 3
Binomial Distribution. Asked once: NDA 1 2023 (same type asked 4 times)
104 $A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly three heads?$
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Question 4
Sequence & Series. Asked once: NDA 2 2019 (same type asked 4 times)
34 $p$
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Question 5
Statistics. Asked once: NDA 2 2022 (same type asked 4 times)
114 $The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples was noted to be 0.7. Assume that all these couples survive to celebrate the silver jubilee of their marriage. The coefficient of correlation at that point of time will be$
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Question 1 (case study, 2 parts)