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PHYSICS

Question 1

A transformer has an efficiency of

80 \%

and works at

10 \mathrm{~V}

and

4 \mathrm{~kW}

. If the secondary voltage is

240 \mathrm{~V}

, then the current in the secondary coil is :

Options:

A)

1.33 \mathrm{~A}

B)

13.33 \mathrm{~A}

C)

1.59 \mathrm{~A}

D)

15.1 \mathrm{~A}

MATHEMATICS

Question 2

For $\alpha, \beta, \gamma \neq 0$ , if $\sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pi$ and $(\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta$ , then $\gamma$ equals

Options:

A)

\sqrt{3}

B)

\frac{\sqrt{3}}{2}

C)

\frac{1}{\sqrt{2}}

D)

\frac{\sqrt{3}-1}{2 \sqrt{2}}

MATHEMATICS

Question 3

If

(\alpha, \beta)

is the orthocenter of the triangle

\mathrm{ABC}

with vertices

A(3,-7), B(-1,2)

and

C(4,5)

, then

9 \alpha-6 \beta+60

is equal to :

Options:

A)

30

B)

40

C)

25

D)

35

PHYSICS

Question 4

A vector in

x-y

plane makes an angle of

30^{\circ}

with

y

-axis. The magnitude of

\mathrm{y}

-component of vector is

2 \sqrt{3}

. The magnitude of

x

-component of the vector will be :

Options:

A)

\sqrt{3}

B)

2

C)

6

D)

\frac{1}{\sqrt{3}}

PHYSICS

Question 5

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p-1)$ seconds and $\mathrm{S}_2$ in first $p$ seconds. The displacement $\mathrm{S}_1+\mathrm{S}_2$ will be made in time :

Options:

A)

(2 p+1) s

B)

(2 p-1) s

C)

\left(2 p^2-2 p+1\right) s

D)

\sqrt{\left(2 p^2-2 p+1\right)} s

CHEMISTRY

Question 6

The correct reaction profile diagram for a positive catalyst reaction.

Options:

A)

JEE Main 2023 (Online) 8th April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 13 English Option 1

B)

JEE Main 2023 (Online) 8th April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 13 English Option 2

C)

JEE Main 2023 (Online) 8th April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 13 English Option 3

D)

CHEMISTRY

Numerical TypeQuestion 7

The sum of oxidation state of the metals in $\mathrm{Fe}(\mathrm{CO})_{5}, \mathrm{VO}^{2+}$ and $\mathrm{WO}_{3}$ is ___________.

PHYSICS

Question 8

Proton $(\mathrm{P})$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$ ):

Options:

A)

1 : 1

B)

1 : 43

C)

1 : 1849

D)

43 : 1

CHEMISTRY

Question 9

Strong reducing and oxidizing agents among the following, respectively, are :

Options:

A)

\mathrm{Ce}^{4+}

and

\mathrm{Eu}^{2+}

B)

\mathrm{Eu}^{2+}

and

\mathrm{Ce}^{4+}

C)

\mathrm{Ce}^{4+}

and

\mathrm{Tb}^{4+}

D)

\mathrm{Ce}^{3+}

and

\mathrm{Ce}^{4+}

MATHEMATICS

Question 10

The straight lines $\mathrm{l_{1}}$ and $\mathrm{l_{2}}$ pass through the origin and trisect the line segment of the line L : $9 x+5 y=45$ between the axes. If $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ are the slopes of the lines $\mathrm{l_{1}}$ and $\mathrm{l_{2}}$ , then the point of intersection of the line $\mathrm{y=\left(m_{1}+m_{2}\right)}x$ with L lies on :

Options:

A)

6 x-y=15

B)

6 x+y=10

C)

\mathrm{y}-x=5

D)

y-2 x=5

MATHEMATICS

Numerical TypeQuestion 11

If

\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+

constant, then

\beta-\alpha

is equal to ____________.

PHYSICS

Question 12

The root mean square velocity of molecules of gas is

Options:

A)

Proportional to temperature (

T

)

B)

Inversely proportional to square root of temperature

\left( {\sqrt {{1 \over T}} } \right)

C)

Proportional to square of temperature (

T^2

)

D)

Proportional to square root of temperature (

\sqrt T

)

CHEMISTRY

Question 13

The primary and secondary valencies of cobalt respectively in $\mathrm{[Co(NH_3)_5Cl]Cl_2}$ are :

Options:

A)

2 and 8

B)

2 and 6

C)

3 and 5

D)

3 and 6

PHYSICS

Numerical TypeQuestion 14

The velocity of a small ball of mass $0.3 \mathrm{~g}$ and density $8 \mathrm{~g} / \mathrm{cc}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3 \mathrm{~g} / \mathrm{cc}$ , then the value of viscous force acting on the ball will be $x \times 10^{-4} \mathrm{~N}$ , The value of $x$ is _________. [use $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$

CHEMISTRY

Numerical TypeQuestion 15

$20 \mathrm{~mL}$ of $0.02\, \mathrm{M}$ hypo solution is used for the titration of $10 \mathrm{~mL}$ of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of $\mathrm{Cu}^{2+}$ is found to be ____________ $\times 10^{-2} \,\mathrm{M}$ . [nearest integer]

Given : $2 \,\mathrm{Cu}^{2+}+4 \,\mathrm{I}^{-} \rightarrow \mathrm{Cu}_{2} \mathrm{I}_{2}+\mathrm{I}_{2}$

$\mathrm{I}_{2}+2 \mathrm{~S}_{2} \mathrm{O}_{3}^{2-} \rightarrow 2 \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}$

CHEMISTRY

Numerical TypeQuestion 16

An organic compound with 51.6% sulfur is heated in a Carius tube. The amount of this compound which will form 0.752 g of barium sulphate is ___________ $\times$ 10^{$-$ 1} g.

(Given molar mass of barium sulphate 233 g mol^{$-$ 1}) (Nearest integer).

PHYSICS

Question 17

JEE Main 2022 (Online) 25th July Morning Shift Physics - Simple Harmonic Motion Question 40 English

In figure $(\mathrm{A})$ , mass ' $2 \mathrm{~m}^{\text {' }}$ is fixed on mass ' $\mathrm{m}$ ' which is attached to two springs of spring constant $\mathrm{k}$ . In figure (B), mass ' $\mathrm{m}$ ' is attached to two springs of spring constant ' $\mathrm{k}$ ' and ' $2 \mathrm{k}^{\prime}$ . If mass ' $\mathrm{m}$ ' in (A) and in (B) are displaced by distance ' $x^{\prime}$ horizontally and then released, then time period $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ corresponding to $(\mathrm{A})$ and (B) respectively follow the relation.

Options:

A)

\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{3}{\sqrt{2}}

B)

\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}

C)

\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}

D)

\frac{T_{1}}{T_{2}}=\frac{\sqrt{2}}{3}

MATHEMATICS

Question 18

Let a set A = A₁ $\cup$ A₂ $\cup$ ..... $\cup$ A_k, where A_i $\cap$ A_j = $\phi$ for i $\ne$ j, 1 $\le$ j, j $\le$ k. Define the relation R from A to A by R = {(x, y) : y $\in$ A_i if and only if x $\in$ A_i, 1 $\le$ i $\le$ k}. Then, R is :

Options:

A)

reflexive, symmetric but not transitive.

B)

reflexive, transitive but not symmetric.

C)

reflexive but not symmetric and transitive.

D)

an equivalence relation.

MATHEMATICS

Question 19

The area of the bounded region enclosed by the curve

$y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$ and the x-axis is :

Options:

A)

{9 \over 4}

B)

{45 \over 16}

C)

{27 \over 8}

D)

{63 \over 16}

CHEMISTRY

Numerical TypeQuestion 20

The standard free energy change ( $\Delta$ G $^\circ$ ) for 50% dissociation of N₂O₄ into NO₂ at 27 $^\circ$ C and 1 atm pressure is $-$ x J mol^{$-$ 1}. The value of x is ___________. (Nearest Integer)

[Given : R = 8.31 J K^{$-$ 1} mol^{$-$ 1}, log 1.33 = 0.1239 ln 10 = 2.3]

MATHEMATICS

Question 21

The number of distinct real roots of the equation

x⁷ $-$ 7x $-$ 2 = 0 is

Options:

A)

5

B)

7

C)

1

D)

3