Which of the following functions from Z to Z are bijections ? (where Z is the set of integers)

Consider a L.P.P, Maximize \(Z=3 x+5 y\) subject to constraints \(2 x+6 y \leq 6, x-y \geq 0, x \geq 0, y \geq 0\). Then which of the following are true?
(A) The feasible region of L.P.P is bounded region
(B) The corner points of the feasible region are \((0,0),(2,2),(0,1)\)
(C) Maximum value of Z is 9
(D) Point \((1,3)\) lies in the feasible region
Choose the correct answer from the options given below :

Corner points of the feasible region for LPP are: \((4,0),(0,5),(7,0),(5,2)\) and \((0,3)\). Let \(Z=3 x+6 y\) be the objective function. Then, the value of (Max. \(Z-\) Min. \(Z\) ) i :

Linear inequalities corresponding to the shaded feasible region \(O A B C O\) in the given figure are

A random variable X has the following probability distribution

X	0	1	2	3	4	5
P(X)	0.1	k	0.2	2k	0.3	k

Then \(P(X<3)\) is

Mr. X wishes to purchase a flat for Rs. \(44,65,000\) with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years.
If the bank charges \(6 \%\) per annum compounded monthly, the EMI is :
[Given: \((1.005)^{300}=4.465\)]

The greatest possible value of \(a\) such that the function\(f(x)=x^2+a x+1\) is always decreasing in the interval \([1,2]\), is:

Match List I with List II.

LIST I	LIST II
A. Lactic acid bacteria	I. Saccharomyces cerevisiae
B. Ethanol	II. Propionibacterium sharmanii
C. Swiss Cheese	III. Lactobacillus
D. Penicillin	IV. Penicillium notatum

Choose the correct answer from the options given below:

Which solutions will have the highest boiling point?

Match List-I with List-II

List-I	List-II
(A) Adenine	(I) Purine
(B) Thymine	(II) Pyrimidine
(C) Uracil	(III) DNA
(D) Deoxyribose	(IV) RNA

Choose the correct answer from the options given below:

In the plot of \(\log \frac{[R]_{0}}{[R]}\) versus time for a first order reaction (where [R] represents the concentration of the reactant), the slope and intercept are respectively equal to

Development of fruits without fertilization is known as -

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Match Column I with Column II

Column I	Column II
(A) ZIFT	(I) Sperm injected into ovum
(B) ICSI	(II) Embryo in uterus
(C) IUI	(III) Embryo in fallopian tube
(D) IUT	(IV) Semen in uterus

Choose the correct answer from the options given below