Which of the following is a vertex of the positive region bounded by the inequalities:
\(4 x+y \geq 80 ; \quad 2 x+y \geq 60 ; \quad x, y \geq 0\)

The function \(f:[-1,1] \rightarrow \mathbb{R}\) (set of real numbers) given by \(f(x)=\frac{x}{x+3}\) 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:

Let X denotes the number of doublets obtained in 3 throws of a pair of dice.
match List - I with List - II

List - I	List - II
(A) P(X = 0)	(I) \(\frac{1}{216}\)
(B) P(X = 1)	(II) \(\frac{15}{216}\)
(C) P(X = 2)	(III) \(\frac{75}{216}\)
(D) P(X = 3)	(IV) \(\frac{125}{216}\)

Choose the correct answert from the option given below:

A metal wire under constant potential difference, when heated, shows that the drift velocity of the electron :

If the constraints in a linear programming problem are changed then,
(A) The problem is to be revaluated.
(B) Solution not defined.
(C) The objective function has to be modified.
(D) The objective function need not be modified.
(E) The change in constraints does not affect the solution.

Consider the differential equation \(x d y=(x+y) d x\). Which of the following are true?
(A) It is a homogenous differential equation
(B) It is a differential equation of order 2
(C) The general solution of the differential equation contains 2 arbitrary constants
(D) Integrating factor of differential equation is \(\frac{1}{x}\)
(E) Degree of the differential equation is not defined
Choose the correct answer from the options given below:

Which of the following is caused due to substitution of glutamic acid to valine on 6th position of B-globin chain of Haemoglobin molecule ?

Solution of differential equation \(\frac{d y}{d x}=\cos (x+y+3)\) is:

The number of all possible matrices of order \(3 \times 4\) with each entry 1, 2 or 3 are:

A 95% confidence interval for a population mean was reported to be 152 to 160. If the standard deviation \(\sigma=15\), then the sample size is (given \(Z_{0.025}=1.96\) ) :

The Mediterranean orchid Ophrys employs 'sexual deceit mechanism to get pollination done by

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
Cris reducing but Mn is oxidising in nature although both have \(d ^{ 1 }\) configuration. It is due to the reason that Cr configuration changes from