Day 39: NDA Maths

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

Question 1
Vectors. This type asked 3 times: NDA 1 2017, NDA 1 2019, NDA 2 2022. This one: NDA 2 2022
69 $2x^2\hat{i}+3x\hat{j}+\hat{k}$
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Question 2 (case study, 3 parts)
3D Geometry. This type asked 3 times: NDA 2 2017, NDA 1 2018, NDA 1 2022. This one: NDA 1 2022
Consider the following for the next three (03) items that follow: The plane $6x+ky+3z-12=0$ where $k eq0$ meets the coordinate axes at $A$ , $B$ and $C$ respectively. The equation of the sphere passing through the origin and $A$ , $B$ , $C$ is $x^2+y^2+z^2-2x-3y-4z=0$ .
91 $k$
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92 $p$
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93 $What is the equation of the line through the origin and the centre of the sphere?$
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Question 3
Application of Derivatives. This type asked 3 times: NDA 1 2020, NDA 1 2021, NDA 1 2022. This one: NDA 1 2022
66 $f(x)=\frac{1}{\tan x+\cot x}$
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Question 4
Functions. This type asked 3 times: NDA 2 2018, NDA 1 2019, NDA 1 2022. This one: NDA 1 2022
59 $f(x)=\sqrt{1-(x-1)^2}$
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Question 5
Matrices & Determinants. This type asked 3 times: NDA 2 2017, NDA 2 2018, NDA 1 2022. This one: NDA 1 2022
2 $(a-b)(b-c)(c-a) = 2$
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Question 1