From a container full of milk, 10 liters (1) was drawn and replaced by water. This process is repeated one more time. The ratio of quantity of milk and water left in the container is \(4: 5\). Then the capacity of the container is :

The corner points of the feasible region determined by the system of linear constraints are \((0,0),(0,40),(20,40),(60,20),(60,0)\).
The objective function is \(z=4 x+3 y\).
Compare the quantity in Column - A and Column - B.

Column - A	Column - B
Maximum value of z	350

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is:

Match List 1 with List 2.

List 1 (Differential equation)	List 2 (Sum of order and degree)
(A) \(\frac{d^2 y}{d x^2}+\frac{d y}{d x}+3 y=\sin x\)	(I) 2
(B) \(\frac{d y}{d x}=\sin (x+y)\)	(II) 3
(C) \(\sqrt{1+\left(\frac{d y}{d x}\right)^2}=\frac{d^2 y}{d x^2}\)	(III) 4
(D) \(x^2\left(\frac{d^2 y}{d x^2}\right)^3+y\left(\frac{d y}{d x}\right)^4+y^3=0\)	(IV) 5

Choose the Correct answer from the options given below :

If the maximum value of the function \(f(x)=\frac{\log _e x}{x}, x>0\) occurs at \(x=a\), then \(a^2 f^{\prime \prime}(a)\) is equal to:

The corner points of the feasible region with the constraints \(x+y \leq 30, x+y \geq 15, y \leq 20, x \leq 15\), and \(x, y \geq 0\) are

If \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\) then
\(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|\) is equal to :

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4} \\ k, & x=\frac{\pi}{4}\end{array}\right.\)
is continuous at \(x=\frac{\pi}{4}\), then the value of \(k\) is:

Match List - I with List - II.

LIST I	LIST II
A. Ovulatory phase	I. Proliferative phase
B. Follicular phase	II. Both LH and FSH attain peak level
C. Luteal phase	III. Breakdown of endometrial lining of uterus and its blood vessels
D. Menstrual phase	IV. Secretory phase

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Carbohydrates such as cane sugar, glucose, starch etc. belong to a class of naturally occurring organic compounds. Structurally these are polyhydroxy aldehydes or ketones or the compounds which produce such units on hydrolysis. Carbohydrates which are sweet in taste are called sugars. Theses sugars can be reducing or non-reducing. Monosaccharides cannot be hydrolyzed to simpler units whereas Oligosaccharides yield two to ten monosaccharide units on hydrolysis. Polysaccharides yield large number of monosaccharide units on hydrolysis. This class of biomolecules is essential for living systems as they serve as storage molecules in plants and animals. In addition, they provide raw materials for important industries like furniture, textiles, paper, lacquers and breweries. Two aldopentose form important constituents of nucleic acids. Carbohydrates are also called saccharides (Greek: sakcharon which means sugar). Sugar which is used in household and in milk also comes under this class of biomolecules.
Among below given carbohydrates, which one is not a polysaccharides ?

A DNA fragment contains 18% Thymine (T). The combined content of Cytosine (C) and Guanine in it would be:

The step 'B' in the figure is called as:

Identify the carbohydrate which is not a polysaccharide