Some Memory Based Questions
Memory based questions of the April 2 Shift 2 paper is provided below
2nd April Shift 2 Maths
Q 1. Total number of terms in an A.P are even. Sum of odd terms is 24 and sum of even terms is 30. Last term exceeds the first term by $\frac{21}{2}$. Find the total number of terms.
Q 2. If the domain of the function $f(x)=\frac{1}{\sqrt{3 x+10-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$ then $(1+a)^2+b^2$ is equal to
1. 25
2. 16
3. 24
4. 26
Q 3. If $\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then number solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is
Q 4. Find the eccentricity of ellipse in which length of minor axis is equal to onefourth of the distance between foci
1. $\frac{4}{\sqrt{17}}$
2. $\frac{2}{\sqrt{17}}$
3. $\frac{7}{\sqrt{17}}$
4. $\frac{8}{\sqrt{17}}$
Chemistry
Q.1 Which of the following statement(s) is correct is/are for the adiabatic process?
A. Molar heat capacity is zero.
B. Molar heat capacity is infinite.
C. Work done on gas is equal to increase in internal energy
D. The increase in temperature results in decrease in internal energy
1 A and C only
2 B and C only
3 A and D only
Q.2 Which does not follow general trends among Halogens
(1) I. E
(2) Electro Affinity
(3) Ionic Radius
(4) Covalent Radius
Q.3 Relation between magnetic sucesptibility and magnetic permeability
Q.4 Which Amino acids is optically inactive
(1) Alanine
(2) Glycine
(3) Valine
(4) Aspartic Acid
Q.4 In the following graph between $\mathrm{t}_{1 / 2}$ and initial concentration [ $\mathrm{A}_0$ ]. If slope of the graph is $79.62 \mathrm{M}^{-1} \mathrm{~min}$. and initial concentration is 2.5 M . Find the concentration of A after 10 min .
Q.5 $100 \mathrm{~g} \mathrm{CaCO}_3$ when reacted with 0.19 mole of HCl then the moles of $\mathrm{CaCl}_2$ formed is $\mathrm{P} \times 10^{-3} \mathrm{~mol}$. Find P ?
Q.6 Vapour pressure of pure liquid A is 200 mm Hg . If 1 mol of A and 3 mol of B are mixed. Assuming solution to be ideal, find the vapour pressure of pure liquid ' B ', if total pressure of solution is 500 mm Hg
Q.7
$$
\begin{aligned}
& \mathrm{CaCO}_3+2 \mathrm{HCl} \rightleftharpoons \mathrm{CaCl}_2+\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 \\
& 1000 \mathrm{~g} 2 \mathrm{l}, 2 \mathrm{M}
\end{aligned}
$$
Find moles of $\mathrm{CaCl}_2$ Produced.
(1) 10
(2) 2
(3) 6
(4) 8
Q.8 Which of the following property does not have the regular trend in group $17^{\text {th }}$ of the period table?
(1)XAtomic size
(2) I.E.
(3) Electronegativity
(4)Electron Affinity
Q.9 Statement-I: Ga has larger metallic radius than Al .
Statement-II: $\mathrm{Ga}^{+3}$ has larger ionic radius than $\mathrm{Al}^{+3}$.
In the light of the above statements, choose the most appropriate answer from the options given below:
(1) Both Statement-I and Statement-II are false
(2) Statement-I is false but Statement-II is true
(3) Both Statement I and Statement-II are true
(4) Statement-I is true but Statement-II is false
Q.10 In $A X_A Y, X$ and $Y$ are the top two electronegative atoms and A has the highest ionization enthalpy in its period. Predict the hybridization of $A X_A Y$.
(1) $\mathrm{sp}^3$
(2) $\mathrm{sp}^3 \mathrm{~d}$
(3) $\mathrm{sp}^3 \mathrm{~d}^2$
(4) $s p^2$
Physics
Q.1 What is the units of viscosity, intensity of wave, and pressure gradient
Q.2 The figure shows an infinite plane having uniform charge density $\sigma$ and a small charged particle having charge $q$ and mass $m$ suspended by a light insulating thread. Find $\sigma$ if the charge is in equilibrium.
$1 \quad \frac{2 f_0 m g}{q}$
$2 \frac{\varepsilon_0 m g}{2 q}$
$3 \quad \frac{2 q}{\varepsilon_0 m g}$
$4 \frac{2 q \varepsilon_0}{m g}$
Q.3 Find the ratio of $\left(\gamma=\frac{C_p}{C_v}\right)$ for two gases having degree of freedoms $f=3$ and $f=5$.
Q.4 The ratio of the magnetic field to the center of the circular coil to the magnetic field at a distance $x$ from the center of a circular coil
$
\left(\frac{x}{R}=3 / 4\right)
$
Q.5 Two point charges $q$ and $9 q$ are placed at a distance of $l$ from each other. Then the electric field is zero at a
1 Distance $\frac{l}{4}$ from charge $9 q$
2 Distance $\frac{3 l}{4}$ from charge $q 3$ Distance $\frac{l}{3}$ from charge $9 q$
4 Distance $\frac{l}{4}$ from charge $q$
Q.6 Given the equation of a hyperbola $H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its directrix is $x=\sqrt{\frac{10}{81}}$ with a focus at $(\sqrt{10}, 0)$, then find the value of $9\left(e+l^2\right)$, where $I$ is length of latus rectum is
1 2697
2 2597
$3 \quad 2487$
$4 \quad 2587$
Q. Two point charges $q$ and $9 q$ are placed at distance of $l$ from each other. Then the electric field is zero at a
1 Distance $\frac{l}{4}$ from charge $9 q$
2 Distance $\frac{3 l}{4}$ from charge $q$3 Distance $\frac{l}{3}$ from charge $9 q$
4 Distance $\frac{l}{4}$ from charge $q$
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