JEE Mains April 2 Shift 1 Memory Based Questions
Q 1. Find the maximum value of $n$ such that $50!$ is divisible by $3^n$.
Q 2. Let $P_n=\alpha^n+\beta^n, P_{10}=123, P_9=76, P_8=47$ and $P_1=1$, the quadratic equation whose roots are $\frac{1}{\alpha}$ and $\frac{1}{\beta}$.
1. $ x^2+x-1=0$
2. $x^2-2 x+1=0$
3. $x^2+x-2=0$
4. $x^2-x-2=0$
Q 3. Number of solutions in $[-2 \pi, 2 \pi]$ for equation $2 \sqrt{2} \cos ^2 \theta+(2-\sqrt{6}) \cos \theta-\sqrt{3}=0$.
Q 4. The total number of 10 digits sequences formed by only $\{0,1,2\}$ where 1 should be used at least 5 times and 2 should be used exactly three times, is
Q 5. Let $a_1, a_2, a_3, \ldots$. is an A.P. and $\sum_{k=1}^{12} a_{2 k-1}=-\frac{72}{5} a_1$ and $\sum_{k=1}^n a_{k=0}$. Then the value of $n$ is
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. 2487
4. 2587
Q 7. If a twice differentiable function $f$ satisfies $f^{\prime}(x)=f(x)$ such that $f(0)=\frac{1}{2}=f^{\prime}(0)$. Then find $f^{\prime \prime}\left(\frac{\pi}{3}\right)$
Q.6 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.7 What is the units of viscosity, intensity of wave and pressure gradient
Q.8 Which does not follow general trends among Halogens
(1) I. E
(2) Electro Affinity
(3) Ionic Radius
(4) Covalent Radius
Q.9 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.10 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.11 Relation between magnetic sucesptibility and magnetic permeability
Q.12 The ratio of magnetic field to center of circular coil to magnetic field at distance $x$ from the centre of circular coil
$
\left(\frac{x}{R}=3 / 4\right)
$
Q.13 The greatest value of $n, n \in N$. If $3^n$ divides 50 !
a) 20
b) 21
c) 22
d) 23
Q.14 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 $q$
Q.15 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.16 Which Amino acids is optically inactive
(1) Alanine
(2) Glycine
(3) Valine
(4) Aspartic Acid
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 $q$
You can download detailed questions and analysis from here:
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