If the corner points of bounded feasible region for an LPP are (0, 2), (3,0), (6,0), (6, 8) and (0,5) then the minimum value of the objective function \(f = 4x + 6y\) occur at

The probability distribution of a random variable X is

X	0	1	2	3	4
P(X)	0.2	k	k	2k	k

Match List-I with List-II

List-I	List-II
(A) value of \(k\)	(I) \(\frac{16}{25}\)
(B) \(P(x \geq 2)\)	(II) \(\frac{9}{25}\)
(C) \(P(X=3)\)	(III) \(\frac{4}{25}\)
(D) \(P(X<2)\)	(IV) \(\frac{8}{25}\)

Choose the Correct answer from the options given below :

If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then value of \(\frac{d y}{d x}\) at \(t=\pi / 4\) is

Match List - I with List - II

List - I (terms)	List - II (Definitions)
(A) POPULATION	(I) Measurable characteristics of the population such as mean, variance, standard deviation etc. of population
(B) SAMPLE	(II) Measurable characteristics of the sample such as mean, variance, standard deviation etc. of a sample
(C) PARAMETER	(III) Finite set of statistical individuals drawn from a population for investigation
(D) STATISTIC	(IV) Collection of objects having the same characteristics

Choose the correct answer from the options given below:

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5 % per annum compounded semi-annually is:
[Given \((1.025)^{20}=1.6386\)]

A container is full of pure milk. From this container, one third of milk is taken out and then an equal amount of water is poured into the container to fill it. This operation is repeated four times. The final ratio of milk and water in the container is :

The probability of a shooter hitting a target is \(\frac{2}{3}\)
Minimum how many number of times must the shooter fire so that the probability of hitting the target at least once is more than 0.98.

Match the Matrix in List - I with its Adjoint's Determinant in List - II.
List - I (Matrix A) :

LIST 1	LIST 2
(A) \(\left[\begin{array}{ll}3 & 1 \\ 4 & 2\end{array}\right]\)	(I) 9
(B) \(\left[\begin{array}{cc}5 & -1 \\ 4 & 2\end{array}\right]\)	(II) 8
(C) \(\left[\begin{array}{cc}6 & -1 \\ 2 & 1\end{array}\right]\)	(III) 14
(D) \(\left[\begin{array}{ll}4 & 1 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups.
Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The compound having the highest boiling point is

Which of the following is a complementary sequence of 5' GAATTC ---- 3'?

In an a.c. circuit, a resistor, a capacitor and an inductor are connected in series, in which \( X_C = X_L = R \). The impedance of this circuit will be

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be :

A resistor develops 200 J of thermal energy in 5 s when a current of 2 A is passed through it. If the current is measured to 5 A, what will be the energy developed in 12 s ?