Day 273: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1 (case study, 2 parts)
Sets & Relations. Asked once: NDA 1 2019
Consider the following for the next 02 (two) items that follow: In a school, all the students play at least one of three indoor games – chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.
16 $What can be the minimum number of students in the school?$
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17 $What can be the maximum number of students in the school?$
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Question 2
Statistics. Asked once: NDA 1 2024
Distribution: $x_i=1,2,3,\ldots,n$ with $f_i=1,2^{-1},2^{-2},\ldots,2^{-(n-1)}$ .
117 $\displaystyle\sum_i x_i f_i$
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Question 3 (case study, 2 parts)
Trigonometric Equations. Asked once: NDA 1 2023
Consider the following for the next two (02) items that follow: Given that $\sin x+\cos x+\tan x+\cot x+\sec x+\cosec x=7$ .
47 $The given equation can be reduced to$
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48 $\sin2x=a-b\sqrt{c}$
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Question 4
Trigonometric Identities. Asked once: NDA 2 2025
48 $x+\dfrac{1}{x}=2\cos\theta$
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Question 5 (case study, 2 parts)
Vectors. Asked once: NDA 2 2025
For the following two (02) items: Let $A(1,-1,0)$ , $B(-2,1,8)$ and $C(-1,2,7)$ are three consecutive vertices of a parallelogram $ABCD$ .
55 $D$
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56 $BCD$
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Question 1 (case study, 2 parts)

Question 2

Question 3 (case study, 2 parts)

Question 4

Question 5 (case study, 2 parts)