Match List I with List II

LIST I (Microorganism)	LIST II (Product Obtained)
A. Trichoderma polysporum	I. Ethanol
B. Monascus purpureus	II. Citric Acid
C. Saccharomyces cerevisiae	III. Cyclosporin A
D. Aspergillus niger	IV. Statins

Choose the correct answer from the options given below:

Verhulst pearl logistic population growth is represented by the equation:

In flowering plants, double fertilization results in the formation of:

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
Alfred Russel Wallace, a naturalist, arrived at conclusions similar to Darwin while working in:

If a pink flowered Snapdragon plant is crossed with a white flowered Snapdragon plant, what will be the phenotypic ratio of their progeny?

Identify the contraceptive measure which can not be practiced by human females:

Read the passage carefully. Attempt the questions.
In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of these regulatory mechanisms. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location. The malignant tumors, on the other hand are a mass of proliferating cells. These cells actively divide and starve the normal cells by competing for vital nutrients. Cells sloughed from such tumors reach distant sites through blood, and wherever they get lodged in the body, they start a new tumor there. This property is called metastasis. Transformation of normal cells into cancerous cells may be induced by physical, chemical or biological agents called carcinogens.
Benign tumors are normally remain confined to:

With reference to sampling, which of the following are correct?
(A) Simple random sampling is probability sampling
(B) Snow-ball sampling is non-probability sampling
(C) Stratified sampling is probability sampling
(D) Cluster sampling is non-probability sampling
Choose the correct answer from the options given below:

If \(P(A)=\frac{6}{11}, P(B)=\frac{5}{11}\) and \(P(A \cup B)=\frac{7}{11}\), then
A. \(P(A \cap B)=\frac{4}{11}\)
B. \(P(A \mid B)=\frac{ 4 }{ 5 }\)
C. \(P(B \mid A)=\frac{2}{5}\)
D. \(A\) and \(B\) are independent events
E. \(P(\) neither \(A\) nor \(B)=\frac{4}{11}\)
Choose the correct answer from the options given below:

Hepatitis B vaccine is produced from:

Match List - I with List - II. Match the integrating factors :

List - I (Differential Equation)	List - II (Integrating factor)
(A) \(\frac{d y}{d x}+3 y=e^{-2 x}\)	(I) \(\frac{1}{x}\)
(B) \(x \frac{d y}{d x}+y=3 x^2\)	(II) \(e^{-x}\)
(C) \(x \frac{d y}{d x}-y=3 x^2\)	(III) \(x\)
(D) \(\frac{d y}{d x}-y=x\)	(IV) \(e^{3 x}\)

Choose the correct answer from the options given below :

The value of \(|\vec{a}-\vec{b}|\), if two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|=1,|\vec{b}|=4\), and \(\vec{a} \cdot \vec{b}=5\) is :

Magnetic moment values for \(\left[ Fe \left( H _2 O \right)_6\right]^{3+}\) and \(\left[ Fe ( CN )_6\right]^{3-}\) are: