Calculate Three yearly moving averages for the following data

Year	2016	2017	2018	2019	2020	2021
Production (thousand tonnes)	200	220	231	254	202	243

The order and degree of differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\frac{d^2 y}{d x^2}\) respectively, are

Which of the following is correct about the Sinking Fund?

For independent events \( A_{1} , A_{2}, A_{3} , \ldots, A_{n}\) , if \(P(A_{i}\) \(= \frac{1}{i + 1}, \; i = 1, 2, 3 \ldots, n\), then the probability that none of the events occur is :

A car is moving along the curve \(y=x^3+12\). The point(s) on the curve at which the rate of change of its y-coordiante at a certain time is 3 times the rate of change of its x-coordinate is/are

For any 2 × 2 matrix, if \(A(\operatorname{adj} A)=\left[\begin{array}{cc}100 & 0 \\ 0 & 100\end{array}\right]\), then |A| is equal to:

Let \(\vec{a}=\hat{i}+\hat{j}, \vec{b}=\hat{i}-\hat{j}\) and \(\vec{c}=\hat{i}+\hat{j}+\hat{k}\). If \(\hat{m}\) is a unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\), then \(|\vec{c} \cdot \hat{m}|\) is equal to :

Read the passage carefully and answer the questions
Sodium dichromate \(Na _2 Cr _2 O _7\) and Potassium dichromate \(K _2 Cr _2 O _7\) are strong oxidizing agents; in acidic solution, its oxidising action can be represented as follows :
\(Cr _2 O _7^{2-}+14 H ^{+}+6 e^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O \left( E ^{\circ}=1.33 V\right)\)
The chromates and dichromates are interconvertible in aqueous solution depending upon pH of the solution.
The chromate ion is tetrahedral whereas the dichromate ion consists of two tetrahedra sharing one corner with \(Cr - O - Cr\) bond angle of \(126^{\circ}\)
Potassium permanganate is prepared by fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidising agent like \(KNO _3\).
This produces the dark green \(K _2 MnO _4\) which disproportionates in a neutral or acidic solution to give permanganate. It is a strong oxidizing agent. Hydrogen ion concentration of the solution plays 
an important part in the reduction of permanganate to manganate, manganese dioxide and manganese(II) salt.
Potassium permanganate forms dark purple (almost black) crystals which are isostructural with those of \(KClO _4\).
The salt is not very soluble in water \((6.4 g / 100 g\) of water at 293 K ), but when heated it decomposes at 513 K.
The number of moles of KMnO₄ required to react with one mole of sulphide ion in acidic solution is

If electron, deutron, \(\alpha\)-particle and proton have same kinetic energy, which one has the largest deBroglie wavelength.

Which type of interaction is shown by the marine fish and copepods:

Match List - I with List - II

List - I	List - II
(A) The degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)=x \sin \left(\frac{d y}{d x}\right)\)	(I) 4
(B) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0\)	(II) 1
(C) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\)	(III) Not defined
(D) The degree of differential equation \(1+\left(\frac{d y}{d x}\right)^4=7\left(\frac{d^2 y}{d x^2}\right)^3\)	(IV) 3

Choose the correct answer from the options given below:

In the decay chain given below the sequential order in which the radioactive radiations are emitted will be :
\(^{A}_{Z}X \to ^{A}_{Z+1}Y \to ^{A-4}_{Z-1}P^* \to ^{A-4}_{Z-1}P\)

What is the relation between phase difference \((\Delta \theta)\) and path difference \((\Delta x)\) ?