Biology
1. Match the features of a plant cell with their corresponding examples
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2.
Shown below are some of the reactions that occur in the metabolic pathway leading to complete oxidation of glucose duri 3. In a given species of flowering plant, the colour of the seeds is exclusively determined by the colour of its seed coat. 4. During the CoVID-19 pandemic, SARS-CoV2 virus mutated multiple times giving rise to many variants. What is the genetic m 5. Lymph is an important body fluid. Choose the INCORRECT statement about the lymph.
6. Interneurons play an important role in the execution of spinal cord-mediated reflex action. Where are these interneurons 7. Osmoreceptors are sensitive to changes in ionic concentrations and volumes of body fluids. Which among the following bes 8. A single point mutation in gene ' $X$ ' results in breathing difficulty, hypertension as well as partial sterility. Whic 9. In a cross between individuals of the genotypes PpQQRrSS and ppqqRrSS, what will be the expected number of progenies wit 10. Organisms in which of the following phyla are triploblastic, acoelomate and have bilateral symmetry?
11. Consider the following biomes: Tropical Rainforest $(P)$; Tundra $(Q)$; Desert $(R)$ and Coastal zone $(S)$. The most pr 12. Nine percent of a population cannot taste a certain food item because of a recessive allele of the gene IAT. Assuming th 13. As opposed to DNA replication within the cell, discontinuous synthesis of DNA does NOT occur in a polymerase chain react 14. Which of the following figures CORRECTLY represents the chemiosmotic hypothesis of ATP synthesis occurring in a mitochon 15. Let ' $X$ ' be the perpendicular distance from the centromere of each chromosome to the equatorial plane of a human cell
Chemistry
1. The products of the reaction between aqueous solutions of $K_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ and $\frac{1}{2} 2. For the colourless complex $\left[M\left(H_2 O\right)_6\right]^{n+}$, where $M$ is a $3 d$ transition metal, the CORRECT 3. Choose the correct statement about the structure of $\mathrm{C}_{60}$ fullerene 4. $$ \text { The first to fifth ionization energies (IE) of two p-block elements } X \text { and } Y \text { are given bel 5. Which of the following expressions represents the hydrogen atom wave function $\psi(r)$ shown in the figure below? ( $r$ 6. $$ \text { Which of the following molecules are aromatic? } $$
7. Which of the following are aryl bromides?
8. Benzamide is treated with $\mathrm{Br}_2$ and $\mathrm{NaOH}(\mathrm{aq})$ to form the product $X$, which is then reacte 9. $$ \text {In the following reaction sequence, the major products } M, N \text {, and } O \text { respectively are } $$
10. The van der Waals equation for a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=R T$. What is the dimension of 11. $$ \text { The major product } P \text { of the following reaction is } $$
12. An aqueous solution contains 1.0 M of $\mathrm{X}^{2+}$ and 0.001 M of $\mathrm{Y}^2+$ ions at $25^{\circ} \mathrm{C} . 13. 2 g of naphthoic acid (molecular weight $=172 \mathrm{~g} \mathrm{~mol}^{-} 1$ ) dissolved in 20 mL of benzene shows a f 14. For the reaction involving ideal gases, $A(g)+2 B(g)=2 C(g)+3 D(g)$, which of the following plots is qualitatively corre 15. Identify the correct order of the molecules with respect to the magnitude of their dipole moment:
Mathematics
1. A randomly chosen card from a deck of 52 cards is given to be a black card (Spade or Club). What is the probability that 2.
Let $\omega$ be a complex root of the quadratic polynomial $x^2+x+1$. The value of
$$ \left(\omega+\frac{1}{\omega}\ri 3. Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,
$$ \left.\left.\frac{d f}{d 4. Let $S$ be the set of all unit vectors in the $X Y$-plane. Then the set $S$ has
5. A lab reports that the global average temperature in the year 2020 was $14.9^{\circ} \mathrm{C}$ and predicts that the g 6. Let $X$ be the set of all $2 \times 2$ matrices with real entries and $R \subset X \times X$ be the relation $R=$ $\{(A, 7. For a natural number $n$, let $C_n$ be the curve in the $X Y$-plane given by $y=x^n$, where $0 \leq$ $x \leq 1$. Let $A_ 8. Let $f$ be a continuous function on $[0,1]$ and $F$ be its antiderivative. If $F(0)=1$ and $\int_0^1 f(x) d x=1$, then $ 9. Let $a$ be a nonzero real number and $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $f^{\prim 10. Let $A$ be the matrix $\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 1 & 1 & 1 \\ \sin \theta & 0 & \cos \th 11. Consider the vectors $\vec{a}=\hat{\imath}+x \hat{\jmath}+2 \hat{k}, \vec{b}=\hat{\imath}+2 \hat{\jmath}+x \hat{k}, \vec 12. Consider the tangent lines to the circle $x^2+y^2=1$ at points $P=(1,0)$ and $Q=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt 13. The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is
14. The value of the integral
$$ \int_1^{100} \frac{[x]}{x} d x $$
where $[x]$ is the greatest integer less than or equal to 15. For arbitrary constants $\alpha, \beta$, the differential equation representing the family of curves $y=$ $(\alpha x+\be
Physics
1. A particle experiences an acceleration $\vec{a}=\alpha \vec{v}$, where $\vec{v}$ is the velocity of the particle and $\a 2. A point mass $m$ attached to a massless string is undergoing circular motion in a vertical plane. The length of the stri 3. An object is released from rest from the inner edge of a hemispherical bowl, and it falls under gravity. The coefficient 4. As shown in the figure a block is resting on a frictionless floor and is attached to the free end of a spring. The right 5. A liquid of density $\rho$ in a container weighs $W$. A cubic block of side $L$ and density $\rho_b<\rho$ is pushed b 6. A monoatomic ideal gas at pressure $P$ and volume $V$ is first adiabatically compressed to volume $V / 8$ and then is al 7. A uniform taut string with two point charges $q$ and $-q$ attached to its ends passes over two massless pullies kept $L$ 8. Two uniformly charged concentric thin spherical shells of radii $r_1$ and $r_2$ have charges $+Q$ and $-Q$, respectively 9. Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has 10. Consider that in a fission of a single Plutonium ( $\mathrm{Pu}^{239}$ ) atom 207 MeV energy is released. Assuming all a 11. In the given circuit, the box $B$ either contains a capacitor, or an inductor or a resistor. The current $I$ versus time 12. In the given circuit each of the resistors is of $1 \mathrm{k} \Omega$ resistance and each of the capacitors has $4 \mu 13. A thin lens made of material of refractive index $n_l$ forms the image at the position $I$ of a point object held at $O$ 14. A conducting sphere of radius $a$ initially contains a uniform volume charge density $\rho$. What is the electric flux $ 15. The figures in the options show the photocurrent $J$ of a photoelectric material versus the frequency $f$ of an incident
1
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is
A
Increasing on the interval $(0,2)$
B
Decreasing on the interval $(-3,0)$
C
Increasing on the interval $(2,3)$
D
Decreasing on the interval $(3, \infty)$
2
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
The value of the integral
$$ \int_1^{100} \frac{[x]}{x} d x $$
where $[x]$ is the greatest integer less than or equal to $x$ for any real number $x$, is
A
$\log \left(\frac{100^{98}}{98!}\right)$
B
$\log \left(\frac{100^{99}}{98!}\right)$
C
$\log \left(\frac{100^{98}}{99!}\right)$
D
$\log \left(\frac{100^{99}}{99!}\right)$
3
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
For arbitrary constants $\alpha, \beta$, the differential equation representing the family of curves $y=$ $(\alpha x+\beta) e^x$ is
A
$y^{\prime \prime}-2 y^{\prime}+y=0$
B
$y^{\prime \prime}-y^{\prime}+y=0$
C
$y^{\prime \prime}-2 y^{\prime}-y=0$
D
$y^{\prime \prime}-y^{\prime}-y=0$
4
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1
A particle experiences an acceleration $\vec{a}=\alpha \vec{v}$, where $\vec{v}$ is the velocity of the particle and $\alpha$ is a constant. If the distances traveled by the particle in the time intervals $t_2-t_1$ and $t_3-t_1$ are $S_{12}$ and $S_{13}$, respectively, which of the following relations is true?
A
$ \frac{S_{13}}{S_{12}}=\frac{\log \left[\alpha\left(t_3-t_1\right)\right]}{\log \left[\alpha\left(t_2-t_1\right)\right]}$
B
$\frac{S_{13}}{S_{12}}=\frac{\exp \left[\alpha\left(t_3-t_1\right)\right]}{\exp \left[\alpha\left(t_2-t_1\right)\right]}$
C
$\frac{S_{13}}{S_{12}}=\frac{\exp \left[\alpha\left(t_3-t_1\right)\right]-1}{\exp \left[\alpha\left(t_2-t_1\right)\right]-1}$
D
$\frac{S_{13}}{S_{12}}=\frac{\log \left[\alpha\left(t_3-t_1\right)\right]-1}{\log \left[\alpha\left(t_2-t_1\right)\right]-1}$
Paper analysis
Total Questions
Biology
15
Chemistry
15
Mathematics
15
Physics
15
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