Day 290: NDA Maths

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

Question 1 (case study, 2 parts)
Application of Derivatives. Asked once: NDA 2 2023
A function is defined by $f(x)=\begin{vmatrix} x+1 & 2 & 3 \\ 2 & x+4 & 6 \\ 3 & 6 & x+9 \end{vmatrix}$ .
45 $The function is decreasing on:$
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46 $The function attains local minimum value at:$
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Question 2
Binomial Theorem. Asked once: NDA 1 2019
22 $(1+ax)^n$
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Question 3
Circles. Asked once: NDA 1 2019
60 $x^2+y^2+4x-7y+12=0$
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Question 4
Complex Numbers. Asked once: NDA 1 2024
4 $x,y$
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Question 5 (case study, 2 parts)
Conics. Asked once: NDA 2 2021
Direction: Consider the following for the next two (02) items that follow. The two ends of the latus rectum of a parabola are (-2, 4) and (-2, -4).
59 $What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?$
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60 $Consider the following statements in respect of such parabolas: 1. One of the parabolas passes through the origin (0, 0). 2. The focus of one of the parabolas lies at (-2, 0). Which of the above statements is/are correct?$
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Question 1 (case study, 2 parts)