Memory Based Questions for JEE Main April 3 Shift 1
Maths Questions
Q 1. Let $A$ be $3 \times 3$ matrix such that $\operatorname{det}(A)=5$. If $\operatorname{det}(3 \operatorname{adj}(2 A \operatorname{adj}(2 A)))=2^{\alpha} \cdot 3^\beta \cdot 5^\gamma$, then $(\alpha+\beta+\gamma)$ is equal to
1. 25
2. 26
3. 27
4. 28
Q 2. The sum of all rational numbers in $(2+\sqrt{3})^8$ is
1. 18117
2. 18817
3. 17280
4. 1800
Q 3. If the sum $\sum_{r=1}^9\left(\frac{r+3}{r}\right) \cdot{ }^9 C_r=\alpha \cdot\left(\frac{3}{2}\right)^9-\beta$, then the value of $(\alpha+\beta)^2$ is equal to
1. 9
2. 81
3. 27
4. 36
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) An ideal gas with an adiabatic exponent 1.5 , initially at $27^{\circ} \mathrm{C}$ is compressed adiabatically from 800 cc to 200 cc . The final temperature of the gas is
Q 2) In YDSE, light of intensity of $4I$ and $9I$ passes through two slits respectively. The difference of maximum and minimum intensity of the interference pattern is