Day 140: NDA Maths

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

Question 1
Lines. Asked once: NDA 1 2024 (same type asked 2 times)
60 $P$
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Question 2
Matrices & Determinants. Asked once: NDA 1 2017 (same type asked 2 times)
36 $A = \begin{pmatrix}\cos\theta & \sin\theta \\ -\sin\theta & \cos\theta\end{pmatrix}$
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Question 3 (case study, 3 parts)
Matrices & Determinants. Asked once: NDA 2 2022 (same type asked 2 times)
Consider the following for the next three (03) items that follow: Let $\Delta$ be the determinant of a matrix A, where $A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix}$ and $C_{11}, C_{12}, C_{13}$ be the cofactors of $a_{11}, a_{12}, a_{13}$ respectively.
28 $a_{11}C_{11} + a_{12}C_{12} + a_{13}C_{13}$
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29 $a_{21}C_{11} + a_{22}C_{12} + a_{23}C_{13}$
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30 $\begin{vmatrix} a_{21} & a_{31} & a_{11} \\ a_{23} & a_{33} & a_{13} \\ a_{22} & a_{32} & a_{12} \end{vmatrix}$
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Question 4
Permutation & Combination. Asked once: NDA 2 2019 (same type asked 2 times)
10 $What is the number of diagonals of an octagon ?$
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Question 5
Permutation & Combination. Asked once: NDA 2 2024 (same type asked 2 times)
15 $The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?$
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Question 1

Question 2

Question 3 (case study, 3 parts)

Question 4

Question 5