The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

Components of Time Series are :
(A) Secular Trend Component
(B) Seasonal Component
(C) Moving Average Component
(D) Cyclical Component
Choose the correct answer from the options given below :

The interval on which the function \(f(x)=x^4-\frac{x^3}{3}\) is strictly decreasing, is :

A card is picked up at random from 52 playing cards. Given that the picked card is a queen, then the probability of this card to be a card of spade is:

Solution of the differential equation \(y \log _e y d x-x d y=0\) is (Where \(c\) is an arbitrary constant)

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then

Let \(X\) denote the number of hours a student studies on a selected day. The probability distribution of \(X\) is given by (where \(k\) is some unknown constant)
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.5, & \text { if } x_i=0 \\k x_i, & \text { if } x_i=1 \\k\left(4-x_i\right), & \text { if } x_i=2 \text { or } 3 \\0, & \text { otherwise }\end{array}\right.\)
Then the value of \(k\) 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.
Baculoviruses are-

When the electron in a hydrogen atom jumps from the 2nd orbit to the 1st orbit, the wavelength of the radiation emitted is \(\lambda\).
When the electron jumps from the 3rd orbit to the 1st orbit, the wavelength of emitted radiation is:

There are 4 bulbs out of which 2 are defective. Each bulb is tested in random order till both the defective bulbs are identified. The probability that only two tests are required to identify the defective bulbs is:

Below given are some statements about electronic devices:
(A) Diodes can be used for rectifying an ac voltage.
(B) For semiconductors, band gap energy \( E_g > 3 \, eV \).
(C) By changing the external applied voltage, junction barriers can be changed.
(D) p-n junction is the 'key' to all semiconductor devices.
Choose the correct answer from the options given below:

\(\text{t}_{99.9\%}\) with respect to \(\text{t}_{90\%}\) for a first order reaction is :

STIs are reported to be very high among persons in which age group?