Day 182: NDA Maths

5 questions (9 parts). Try each one first, then open its answer.

Question 1 (case study, 5 parts)
Probability. Asked once: NDA 2 2023 (same type asked 4 times)
Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph.
116 $What is the probability that all three boys sit together?$
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117 $What is the probability that boys and girls sit alternatively?$
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118 $What is the probability that no two girls sit together?$
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119 $What is the probability that P and Q take the two end positions?$
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120 $What is the probability that Q and U sit together?$
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Question 2
Sets & Relations. Asked once: NDA 1 2017 (same type asked 4 times)
25 $S = \{x : x^2 + 1 = 0,\, x \text{ is real}\}$
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Question 3
Statistics. Asked once: NDA 1 2022 (same type asked 4 times)
105 $What is the coefficient of mean deviation of 21, 34, 23, 39, 26, 37, 40, 20, 33, 27 (taken from mean)?$
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Question 4
Statistics. Asked once: NDA 1 2020 (same type asked 4 times)
112 $The arithmetic mean of 100 observations is 40. Later, it was found that an observation '53' was wrongly read as '83'. What is the correct arithmetic mean?$
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Question 5
3D Geometry. Asked once: NDA 2 2018 (same type asked 4 times)
56 $(2, 3, 4)$
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Question 1 (case study, 5 parts)