A container contains 50 litres of milk. From this container 10 litres of milk was taken out and replaced by water. This process is repeated two more times. How much milk is now left in the container?

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 area of the region bounded by \(x=y^2\) and the line \(x=4\) in square units is :

If \(A\) and \(B\) are two events such that \(P(A \mid B)=P(B \mid A)\), and \(A \cap B \neq \emptyset\), then :

Determine the value of k for which the function \(f(x)=\left\{\begin{array}{ll}\frac{x^2-9}{x-3}, & x \neq 3 \\ k, & x=3\end{array}\right.\) is continuous at x = 3

The feasible region of an LPP Max Z = 3x + 2y subject to \(x \geq 0, y \geq 0, x -2 y \leq 3\) is:

Which of the following statements about the Sinking Fund are correct?
(A) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future capital expense.
(B) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future repayment of a long-term debt.
(C) It is set up for any purpose that it may serve.
(D) It is a fund that is accumulated for the purpose of paying off a financial obligation at some future designated date.
Choose the correct answer from the options given below :

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the followings is not the example of cellular barrier?

If \(y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}\), then

The following reaction of benzene with carbon monoxide and hydrogen chloride in the presence of aluminum trichloride to give benzaldehyde is known as

Arrange the following in the increasing order of their van't Hoff factors :
A. Very dilute \(MgCl_2\) solution
B. Very dilute \(AlCl_3\) solution
C. Very dilute \(NaCl\) solution
D. Very dilute \(Al_2O_3\) solution
E. Very dilute Urea solution\nChoose the correct answer from the options given below :

Which of the following statements are correct?
(A) A fund which is created to accumulate money over the years to discharge a future obligation is called a sinking fund.
(B) The amount or future value of perpetuity is well-defined.
(C) The sinking fund be used in any emergency.
(D) An equated monthly installment is a fixed payment made by a borrower to a lender at a specific date every : month to clear off the loan.
Choose the correct answer from the options given below :

A machine costing ₹1,00,000 has a useful life of 5 years. The estimated scrap value is ₹20,000.
Using straight line method, the annual depreciation is: