Biology
$$ \text { Match the entries in Column I with their functions described in Column II. } $$
Column I | Column II | ||
P. | Squamous epithelium | (i) | The nucleus is at the basal side of the cell; also helps in movement of particles and mucous. |
Q. | Cuboidal epithelium | (ii) | The nucleus is at the basal side of the cell; also helps in secretion and absorption. |
R. | Columnar epithelium | (iii) | The nucleus is at the center of the cell; also helps in secretion and absorption. |
S. | Ciliated epithelium | (iv) | It serves as a diffusion barrier. |
Match the biomolecules given in Column I with their corresponding chemical nature given in Column II.
Column I | Column II | ||
P. | Insulin | (i) | Secondary metabolite |
Q. | Inulin | (ii) | Homopolymer |
R. | Lectin | (iii) | Quaternary ammonium derivative |
S. | Lecithin | (iv) | Hetropolymer |
$$ \text { Match the terms in column I with their physiological roles given in Column II. } $$
Column I | Column II | ||
P. | Sertoli cells | (i) | Secretion of chorionic gonadotropin |
Q. | Follicle stimulating hormone | (ii) | Carries urine away from bladder |
R. | Placenta | (iii) | Carries urine away from kidney |
S. | Urethra | (iv) | Provides nutrition to developing spermatozoa |
(v) | Triggers ovulation |
$$ \text { The diagram represents an enzyme, its substrate and potential inhibitors }(P, Q, R, S, T) \text {. } $$

A 1000 base-pair DNA fragment was cloned between Hind III and EcoRI sites of the plasmid vector (plAT) of size 3500 base-pair. The cloned fragment had a Not I site as shown in the figure. In order to confirm the presence of the insert, the recombinant plasmid was digested completely with (a) Not I and EcoR I, and (b) Not I and Hind III.
In lane 1 the products of the digestion by Not I and EcoRI was loaded. In lane 2 the products of the digestion by Not I and Hind III was loaded. Which one of the following correctly represents the agarose gel electrophoresis profile of the digested recombinant plasmid for (a) and (b), respectively?

Chemistry
$$ \text { How many radial nodes does } \mathrm{Ca}^{+} \text {have in its } 4 \text { s orbital? } $$

$$ \text { Which amongst the following are chiral compounds? } $$

$$ \text { Which one amongst the following bases is NOT present in RNA? } $$

$$ \text { Which amongst the following are aromatic? } $$

Mathematics
Let $M$ be a $3 \times 3$ matrix with real entries such that
$$ \left\{\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]: M\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]\right\}=\left\{\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]: x_1+x_2=0=x_2+x_3\right\} $$
What is the value of the determinant of M ?
$$ \text { What is the total number of distinct divisors of } 2^9 \times 3^{19} \text { ? } $$
Consider the objective function $Z=x-y$ subject to the constraints
$$ \begin{aligned} & x+2 y \leq 10 \\ & x+y \geq 2 \\ & x \geq 0, y \geq 0 \end{aligned} $$
What is the minimum value of $Z$ subject to the above constraints?
Physics
The velocity $v(t)$ of a particle moving in one dimension is given by:
$$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T / 3 \\ \alpha T / 3, & T / 3 \leq t \leq 2 T / 3 \\ \alpha(T-t), & 2 T / 3 \leq t \leq T\end{cases} $$
where $\alpha(\neq 0)$ is a constant. What is the displacement of the particle from time $t=0$ to $T$ ?
Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given by $T=$ $2 \pi^{3 / 2} \alpha \sqrt{m} / q$. Given that $\epsilon_0$ is the
permittivity of free space, which of the following options is the dimensionally correct expression for $\alpha$ in SI units?

$$ \text { What is the effective resistance between } A \text { and } B \text { in the circuit shown below? } $$

