The product of order and degree of the differential equation \(\left(\frac{d^3 y}{d x^3}\right)^2+x^2 y\left(\frac{d^2 y}{d x^3}\right)^3=2 x^5\) is:

Match List-I with List-II

List-I (Lines)	List-II (Direction Ratios)
(A) \(\frac{x-1}{2}=\frac{2-y}{1}=z\)	(I) \((1,3,-1)\)
(B) \(\frac{2 x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}\)	(II) \((2,-2,0)\)
(C) \(\frac{x+1}{2}=\frac{3-y}{2}=z=2\)	(III) \((2,-1,1)\)
(D) \(\frac{2 x-3}{4}=\frac{1-2 y}{2}=\frac{z}{5}\)	(IV) (2, -1, 5)

Choose the correct answer from the options given below:

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

In a 500 m race, the ratio of speeds of two participants \(A\) and \(B\) is \(4: 5\).
If \(A\) has a start of 180 m , then the distance by which \(A\) wins is :

\(\int \frac{d x}{e^x+e^{-x}}\) is equal to

Match List - I with List - II. If \(A=\left|\begin{array}{ccc}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{array}\right|\)

List - I	List - II
(A) \(M_{23}\)	(I) -17
(B) \(A_{32}+a_{13}\)	(II) -1
(C) \(A\) (Determinant value)	(III) 0
(D) \(a_{13} A_{12}+a_{23} A_{22}+a_{33} A_{32}\)	(IV) 12

Choose the correct answer from the options given below :

The random variable X has the following probability distribution

X	0	1	2	3
P(X)	a	a	b	b

such that E\(\left(x^2\right)\) = 2E(x), then the value of b is:

The transfer of pollen grains from one plant to the stigma of a different plant is known as:

Fertilization in human female takes place in -

The pollination which involves the transfer of pollen grain from the anther
to the stigma of another flower of the same plant is known as-

When \(CuSO_4\) solution is electrolysed using platinum electrodes, which of the following is true ?

Read the Passage carefully and answer the the questions
Insulin consists of two short polypeptide chains : chain A and chain B, that are linked together by disulphide bridges. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis of diseases. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (α-1-antitrypsin) used to treat emphysema. Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment.
In 1997, an American company got patent rights on Basmati rice through the US Patent and Trademark Office. This allowed the company to sell a ‘new’ variety of bvasnmati, in the US and abroad. This ‘new’ variety of Basmati had actually been derived from Indian farmer's varieties.. Indiian Basmati was crossed with semi-dwarf varieties and claimed as an invention or a novelty. This is a case of :

In Vallisneria, the pollination is carried by: