A container contains 100 liters of milk.
From this container, 10 liters of milk is taken out and replaced by water.
This process is repeated two more times.
The amount of milk left in the container now is :

Consider the following data of expenses (in lakhs) of an organization year wise:

Year	2001	2002	2003	2004	2005
Expenses (Rs. lakh)	160	185	220	300	510

Then expected expenses trend for the year 2006 using method of least squares is:

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities. If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20 \%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:

The relation \(R\) in the set \(A=\{1,2,3\}\) given by \(R=\{(1,2),(2,1)\}\) is :

Match List-l with List-ll

List-l (Statement)	List-ll (Its value)
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}=e^{d y / d x}\) is	(I) 2
(B) Order of the differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\) is	(II) not defined
(C) Degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2-5 x^2=0\)	(III) 3
(D) If \(p\) is the order and \(q\) is the degree of the differential equation \(\frac{d y}{d x}+3 y=e^x\), then \(p+q\) is	(IV) 1

Choose the correct answer from the options given below :

For any square matrix \(A ;\left(A-A^{\prime}\right)\) is :

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

"Match the reaction order with their examples in List-II.

List-I	List-II
(A) First order reaction	(I) \(\text{C}_{12}\text{H}_{22}\text{O}_{11} + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{C}_6\text{H}_{12}\text{O}_6 + \text{C}_6\text{H}_{12}\text{O}_6\)
(B) Zero order reaction	(II) \(\text{N}_2\text{O}_5 \rightarrow 2\text{NO}_2 + \frac{1}{2}\text{O}_2\)
(C) Pseudo first order reaction	(III) \(\text{CH}_3\text{COOC}_2\text{H}_5 + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{C}_2\text{H}_5\text{OH}\)
(D) Second order reaction	(IV) \(2\text{NH}_3\text{(g)} \xrightarrow{\text{1130 K}\text{ Pt}} \text{N}_2\text{(g)} + 3\text{H}_2\text{(g)}\)

Choose the correct answer from the options given below:"

Match List I with List - II.

List-I (Transformer)	List-II
(A) Flux leakage	(I) Laminated core
(B) Energy loss due to resistance of winding	(II) By winding the primary and secondary one over the other
(C) Eddy current loss	(III) Using thick wires
(D) Hysteresis	(IV) By using soft iron core

Choose the correct answer from the options given below :

The rate constant for a reaction is \(3.5 \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}-^{-1}\). The order of the reaction is:

In a p-n junction, the magnitude of the drift current is lower than the magnitude of the diffusion current when the junction is

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus-

The standard reduction potential for \(Zn^{2+}/Zn\) is \(-0.76\) V and that for \(Fe^{2+}/Fe\) is \(-0.41\) V. The galvanic cell can be correctly represented by :