Corner points of the feasible region for a linear programming problem are \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\). Let \(F=4 x+6 y\) be the objective function. Then the minimum value of \(F\) occurs at :

The value of \(C\) which satisfies Rolle's Theorem for \(f(x)=\sin ^4 x+\cos ^4 x\) in \(\left[0, \frac{\pi}{2}\right]\). Then \(C\) is :

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

A person wishes to purchase a house for ₹ \(39,65,000\) with a down payment of ₹ \(5,00,000\) and balance in equal monthly installments (EMI) for 25 years.
If bank charges \(6 \%\) per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300}=4.465\) ]

Area bounded by the curves \(y^2=9 x\) and \(y=3 x\) is:

The length of perpendicular from the point (1,0,1) to the plane x - y + z = 4 is:

If order of matrices \(A, B\) and \(C\) are \(4 \times 3,5 \times 4\) and \(3 \times 7\) respectively, then order of \(C^{\prime} \times\left(A^{\prime} \times B^{\prime}\right)\) is :

The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)^3+4 y=0\) are :

Which one of the followings is not a feature of insecticidal protein crystals formed by Bacillus thuringiensis: -

Match List I with List II

LIST I	LIST II
A. \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{3 x^2}\)	I. 2
B. \(\lim _{x \rightarrow 4} \frac{x^2-16}{x-4}\)	II. 8
C. \(\lim _{x \rightarrow 0} \frac{\sin a x+4 x}{a x+\sin 4 x}\)	III. 1
D. \(\lim _{z \rightarrow 1} \frac{z^{1 / 3}-1}{z^{1 / 6}-1}\)	IV. \(\frac{2}{3}\)

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
The rupture of RBCs is associated with release of a toxic substance__________, which is responsible for the chill and high fever recurring every three to four days.

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
What are the sources of Vitamin B12?

If \(y=x \sin y\), then \(\frac{d y}{d x}\) is: