List of practice Questions

Let \( E \) and \( F \) be two events such that \( P(E) = 0.1, P(F) = 0.3, P(E \cup F) = 0.4 \). Then \( P(F \,|\, E) \) is:
If \( A \) and \( B \) are two skew-symmetric matrices, then \( AB + BA \) is:
If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - 2\hat{j} + \hat{k} \), then \( \vec{a} \) and \( \vec{b} \) are:
If \( \alpha, \beta \), and \( \gamma \) are the angles which a line makes with the positive directions of \( x, y, z \) axes respectively, then which of the following is not true?
The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:
If the sides of a square are decreasing at the rate of \( 1.5 \, \mathrm{cm/s} \), the rate of decrease of its perimeter is:
\( \int_{-a}^a f(x) \, dx = 0 \), if:
\( x \log x \frac{dy}{dx} + y = 2 \log x \) is an example of a:
A function \( f(x) = |1 - x + |x|| \) is:
If \( A = [a_{ij}] \) is an identity matrix, then which of the following is true?
(ii) Describe the different steps in the sexual mode of reproduction in the life cycle of a malarial parasite.
Study the following list of bioactive substances and their action:
\[ \begin{array}{|c|c|} \hline \textbf{Bioactive Substance} & \textbf{Role} \\ \hline \text{Statin} & \text{Removal of oil stains} \\ \text{Cyclosporin A} & \text{Removal of clots from blood vessels} \\ \text{Streptokinase} & \text{Lowering of blood cholesterol} \\ \text{Lipase} & \text{Immunosuppressive agent} \\ \hline \end{array} \]
Select the option that gives the correct identification of ovum, morula, and blastocyst in a human female reproduction system as shown in the following diagram:
\begin{figure}[h!] \centering \includegraphics[width=0.5\linewidth]{Screenshot 20250115 135817.png} % Replace with the correct path to your image \caption{Human Female Reproductive System} \label{Human Female Reproductive System} \end{figure}
In a fertilized ovule of an angiosperm, the cells in which n, 2n, and 3n conditions respectively occur are:
Study the table given below:
\[ \begin{array}{|c|c|} \hline \textbf{Contraceptive/Contraceptive Method} & \textbf{Mode of Action} \\ \hline \text{A. The pill} & \text{I. Prevent sperm reaching cervix} \\ \text{B. Condom} & \text{II. Prevent implantation} \\ \text{C. Vasectomy} & \text{III. Inhibits ovulation} \\ \text{D. CopperT} & \text{IV. Semen contains no sperm} \\ \hline \end{array} \] Select the option where contraceptive/contraceptive method are correctly matched with their mode of action.
(b) Write the symptoms of malaria in humans and explain what causes these symptoms.
(ii) Compare the two types of flowers with reference to:
(1) Characteristic feature
(2) Modes of pollination
(iii) List any two ‘out breeding devices’ in flowering plants. Explain why do plants develop such devices.
(a). Study the schematic diagram given below and answer the questions:
\begin{figure}[h!] \centering \includegraphics[width=0.5\linewidth]{Screenshot 20250115 144456.png} % Replace with the correct path to your image \caption{Diagram} \label{Diagram} \end{figure} (i) Identify the polarity from ‘X’ to ‘Y’ in the mRNA segment shown. Mention how many more amino acids can be added to the polypeptide that is being translated and why.
(ii) Write the initiating codon for translation, its anticodon, and the amino acid it codes for.
(iii) Explain the charging of an adaptor molecule. Why this molecule needs to be charged?
(b) Answer the following questions on sicklecell anaemia:
(i) Why is sicklecell anaemia, a human blood disorder, so named?
(ii) Explain the genetic basis that results in the expression of this disorder.
(iii) Work out a cross to explain how normal parents may have a sicklecell anaemic child.
Describe the following:
(a) Describe the life cycle of HIV from the time of its entry into the human body till full blown AIDS sets in.