Day 122: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

Question 1
Permutation & Combination. Asked once: NDA 1 2024 (same type asked 3 times)
13 $How many four-digit natural numbers are there such that all of the digits are even?$
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Question 2
Permutation & Combination. Asked once: NDA 1 2022 (same type asked 3 times)
49 $In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?$
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Question 3
Probability. Asked once: NDA 1 2023 (same type asked 3 times)
120 $n$
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Question 4 (case study, 3 parts)
Sets & Relations. Asked once: NDA 2 2022 (same type asked 3 times)
Consider the following for the next three (03) items that follow: A university awarded medals in basketball, football and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
34 $How many received medals in exactly two of the three sports?$
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35 $How many received medals in at least two of three sports?$
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36 $How many received medals in exactly one of three sports?$
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Question 5
Trigonometric Identities. Asked once: NDA 1 2020 (same type asked 3 times)
23 $\tan\theta=\frac{\cos 17°-\sin 17°}{\cos 17°+\sin 17°}$
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Question 1