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Feb 1, 2024

JEE Mains

Shift: 1

Total Questions Available: 90

Question 1

Which of the following reactions are disproportionation reactions?

(A) Cu+→Cu2++Cu\mathrm{Cu}^{+} \rightarrow \mathrm{Cu}^{2+}+\mathrm{Cu}

(B) 3MnO42−+4H+⟶2<br/><br/>MnO4−+MnO2+2H2O3 \mathrm{MnO}_4^{2-}+4 \mathrm{H}^{+} \longrightarrow 2 <br/><br/>\mathrm{MnO}_4^{-}+\mathrm{MnO}_2+2 \mathrm{H}_2 \mathrm{O}

(C) 2KMnO4⟶K2MnO4+MnO2+O22 \mathrm{KMnO}_4 \longrightarrow \mathrm{K}_2 \mathrm{MnO}_4+\mathrm{MnO}_2+\mathrm{O}_2

(D) 2MnO4−+3Mn2++2H2O⟶5MnO2+4H+2 \mathrm{MnO}_4^{-}+3 \mathrm{Mn}^{2+}+2 \mathrm{H}_2 \mathrm{O} \longrightarrow 5 \mathrm{MnO}_2+4 \mathrm{H}^{+}

Choose the correct answer from the options given below :

Options:

A)

(A), (B)

B)

(A), (D)

C)

(B), (C), (D)

D)

(A), (B), (C)

Question 2

In Kjeldahl's method for estimation of nitrogen, CuSO4\mathrm{CuSO}_4 acts as :

Options:

A)

catalytic agent

B)

hydrolysis agent

C)

reducing agent

D)

oxidising agent

Question 3

Given below are two statements :

Statement (I) : The NH2\mathrm{NH}_2 group in Aniline is ortho and para directing and a powerful activating group.

Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation).

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Both Statement I and Statement II are correct

B)

Both Statement I and Statement II are incorrect

C)

Statement I is correct but Statement II is incorrect

D)

Statement I is incorrect but Statement II is correct

Question 4

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): PH3\mathrm{PH}_3 has lower boiling point than NH3\mathrm{NH}_3.

Reason (R) : In liquid state NH3\mathrm{NH}_3 molecules are associated through vander Waal's forces, but PH3\mathrm{PH}_3 molecules are associated through hydrogen bonding.

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Both (A) and (R) are correct and (R) is the correct explanation of (A)

B)

(A) is not correct but (R) is correct

C)

(A) is correct but (R) is not correct

D)

Both (A)(\mathbf{A}) and (R)(\mathbf{R}) are correct but (R)(\mathbf{R}) is not the correct explanation of (A)(\mathbf{A})

Question 5

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with AgCN\mathrm{AgCN} form isocyanide as the main product.

Reason (R): KCN\mathrm{KCN} and AgCN\mathrm{AgCN} both are highly ionic compounds.

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

(A) is correct but (R)(\mathbf{R}) is not correct

B)

Both (A) and (R) are correct and (R) is the correct explanation of (A)

C)

(A) is not correct but (R) is correct

D)

Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Question 6

If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is :

Options:

A)

CATTAGCT

B)

TACGAAGT

C)

ATGCGACT

D)

GTACTTAC

Numerical TypeQuestion 7

The number of white coloured salts, among the following is

(a) SrSO4\mathrm{SrSO}_4

(b) Mg(NH4)PO4\mathrm{Mg}\left(\mathrm{NH}_4\right) \mathrm{PO}_4

(c) BaCrO4\mathrm{BaCrO}_4

(d) Mn(OH)2\mathrm{Mn}(\mathrm{OH})_2

(e) PbSO4\mathrm{PbSO}_4

(f) PbCrO4\mathrm{PbCrO}_4

(g) AgBr\mathrm{AgBr}

(h) PbI2\mathrm{PbI}_2

(i) CaC2O4\mathrm{CaC}_2 \mathrm{O}_4

(j) [Fe(OH)2(CH3COO)]\left[\mathrm{Fe}(\mathrm{OH})_2\left(\mathrm{CH}_3 \mathrm{COO}\right)\right]

Numerical TypeQuestion 8

The potential for the given half cell at 298 K298 \mathrm{~K} is (-) __________ ×10−2 V\times 10^{-2} \mathrm{~V}

2H(aq)++2e−⟶H2( g)[H+]=1M,PH2=2 atm \begin{aligned} & 2 \mathrm{H}_{(\mathrm{aq})}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_2(\mathrm{~g}) \\\\ & {\left[\mathrm{H}^{+}\right]=1 \mathrm{M}, \mathrm{P}_{\mathrm{H}_2}=2 \mathrm{~atm}} \end{aligned}

(Given : 2.303RT/F=0.06 V,log⁡2=0.32.303 \mathrm{RT} / \mathrm{F}=0.06 \mathrm{~V}, \log 2=0.3 )

Numerical TypeQuestion 9

Consider the following reaction :

3PbCl2+2(NH4)3PO4→Pb3(PO4)2+6NH4Cl 3 \mathrm{PbCl}_2+2\left(\mathrm{NH}_4\right)_3 \mathrm{PO}_4 \rightarrow \mathrm{Pb}_3\left(\mathrm{PO}_4\right)_2+6 \mathrm{NH}_4 \mathrm{Cl}

If 72 mmol72 ~\mathrm{mmol} of PbCl2\mathrm{PbCl}_2 is mixed with 50 mmol50 ~\mathrm{mmol} of (NH4)3PO4\left(\mathrm{NH}_4\right)_3 \mathrm{PO}_4, then the amount of Pb3(PO4)2\mathrm{Pb}_3\left(\mathrm{PO}_4\right)_2 formed is ________ mmol (nearest integer).

Numerical TypeQuestion 10

The number of molecules/ion/s having trigonal bipyramidal shape is _______.

PF5,BrF5,PCl5,[PtCl4]2−,BF3,Fe(CO)5\mathrm{PF}_5, \mathrm{BrF}_5, \mathrm{PCl}_5,\left[\mathrm{Pt} \mathrm{Cl}_4\right]^{2-}, \mathrm{BF}_3, \mathrm{Fe}(\mathrm{CO})_5

Question 11

Let S=∣z∈C:∣z−1∣=1\mathrm{S}=|\mathrm{z} \in \mathrm{C}:| z-1 \mid=1 and (2−1)(z+zˉ)−i(z−zˉ)=22∣(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2} \mid. Let z1,z2∈Sz_1, z_2 \in \mathrm{S} be such that ∣z1∣=max⁡z∈s∣z∣\left|z_1\right|=\max\limits_{z \in s}|z| and ∣z2∣=min⁡z∈S∣z∣\left|z_2\right|=\min\limits _{z \in S}|z|. Then ∣2z1−z2∣2\left|\sqrt{2} z_1-z_2\right|^2 equals :

Options:

A)

1

B)

4

C)

3

D)

2

Question 12

Let the median and the mean deviation about the median of 7 observation 170,125,230,190,210170,125,230,190,210, a, b be 170 and 2057\frac{205}{7} respectively. Then the mean deviation about the mean of these 7 observations is :

Options:

A)

31

B)

28

C)

30

D)

32

Question 13

Let a→=−5i^+j^−3k^,b→=i^+2j^−4k^\overrightarrow{\mathrm{a}}=-5 \hat{i}+\hat{j}-3 \hat{k}, \overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}-4 \hat{k} and

c→=(((a→×b→)×i^)×i^)×i^\overrightarrow{\mathrm{c}}=(((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \hat{i}) \times \hat{i}) \times \hat{i}. Then c⃗⋅(−i^+j^+k^)\vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k}) is equal to :

Options:

A)

-12

B)

-10

C)

-13

D)

-15

Question 14

For 0<θ<π/20<\theta<\pi / 2, if the eccentricity of the hyperbola

x2−y2cosec⁡2θ=5x^2-y^2 \operatorname{cosec}^2 \theta=5 is 7\sqrt{7} times eccentricity of the

ellipse x2cosec⁡2θ+y2=5x^2 \operatorname{cosec}^2 \theta+y^2=5, then the value of θ\theta is :

Options:

A)

π6\frac{\pi}{6}

B)

5π12\frac{5 \pi}{12}

C)

π3\frac{\pi}{3}

D)

π4\frac{\pi}{4}

Question 15

If the shortest distance between the lines

x−λ−2=y−21=z−11\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1} and x−31=y−1−2=z−21\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1} is 1 , then the sum of all possible values of λ\lambda is :

Options:

A)

0

B)

232 \sqrt{3}

C)

333 \sqrt{3}

D)

−23-2 \sqrt{3}

Numerical TypeQuestion 16

If x=x(t)x=x(t) is the solution of the differential equation (t+1)dx=(2x+(t+1)4)dt,x(0)=2(t+1) \mathrm{d} x=\left(2 x+(t+1)^4\right) \mathrm{dt}, x(0)=2, then, x(1)x(1) equals _________.

Numerical TypeQuestion 17

Let 3,7,11,15,…,4033,7,11,15, \ldots, 403 and 2,5,8,11,…,4042,5,8,11, \ldots, 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ___________.

Numerical TypeQuestion 18

Let A={1,2,3,…,20}A=\{1,2,3, \ldots, 20\}. Let R1R_1 and R2R_2 two relation on AA such that

R1={(a,b):bR_1=\{(a, b): b is divisible by a}a\}

R2={(a,b):aR_2=\{(a, b): a is an integral multiple of b}b\}.

Then, number of elements in R1−R2R_1-R_2 is equal to _____________.

Question 19

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

Options:

A)

511\frac{5}{11}

B)

1011\frac{10}{11}

C)

5011\frac{50}{11}

D)

12\frac{1}{2}

Question 20

A monochromatic light of wavelength 6000 A˚6000 ~\mathring{A} is incident on the single slit of width 0.01 mm0.01 \mathrm{~mm}. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm20 \mathrm{~cm}, the linear width of the central maximum is :

Options:

A)

12 mm12 \mathrm{~mm}

B)

24 mm24 \mathrm{~mm}

C)

60 mm60 \mathrm{~mm}

D)

120 mm120 \mathrm{~mm}

Question 21

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

Options:

A)

13.6eV13.6 \mathrm{eV}

B)

1.5eV1.5 \mathrm{eV}

C)

12.1eV12.1 \mathrm{eV}

D)

1.9eV1.9 \mathrm{eV}

Question 22

A particle moving in a circle of radius R\mathrm{R} with uniform speed takes time T\mathrm{T} to complete one revolution.

If this particle is projected with the same speed at an angle θ\theta to the horizontal, the maximum height attained by it is equal to 4R4 R. The angle of projection θ\theta is then given by :

Options:

A)

sin⁡−1[2gT2π2R]12\sin ^{-1}\left[\frac{2 \mathrm{gT}^2}{\pi^2 \mathrm{R}}\right]^{\frac{1}{2}}

B)

sin⁡−1[π2R2gT2]12\sin ^{-1}\left[\frac{\pi^2 \mathrm{R}}{2 \mathrm{gT}^2}\right]^{\frac{1}{2}}

C)

cos⁡−1[πR2gT2]12\cos ^{-1}\left[\frac{\pi \mathrm{R}}{2 \mathrm{gT}^2}\right]^{\frac{1}{2}}

D)

cos⁡−1[2gT2π2R]12\cos ^{-1}\left[\frac{2 \mathrm{gT}^2}{\pi^2 \mathrm{R}}\right]^{\frac{1}{2}}

Question 23

With rise in temperature, the Young's modulus of elasticity :

Options:

A)

changes erratically

B)

increases

C)

decreases

D)

remains unchanged

Numerical TypeQuestion 24

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ\theta with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 g/cc1.5 \mathrm{~g} / \mathrm{cc}, the dielectric constant of water will be __________.

(Take density of water =1 g/cc=1 \mathrm{~g} / \mathrm{cc} )

Numerical TypeQuestion 25

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is 1000x\frac{1000}{x}, where xx is _______.

Numerical TypeQuestion 26

A regular polygon of 6 sides is formed by bending a wire of length 4π4 \pi meter.

If an electric current of 4π34 \pi \sqrt{3} A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be x×10−7 Tx \times 10^{-7} \mathrm{~T}.

The value of xx is _________.

Question 27

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :

Options:

A)

q=0,ΔT=0,w=0\mathrm{q}=0, \Delta \mathrm{T}=0, \mathrm{w}=0

B)

q=0,ΔT≠0,w=0\mathrm{q}=0, \Delta \mathrm{T} \neq 0, \mathrm{w}=0

C)

q≠0,ΔT=0,w=0\mathrm{q} \neq 0, \Delta \mathrm{T}=0, \mathrm{w}=0

D)

q=0,ΔT<0,w≠0\mathrm{q}=0, \Delta \mathrm{T}<0, \mathrm{w} \neq 0

Question 28

Given below are two statements :

Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution.

Statement (II) : In this titration phenolphthalein can be used as indicator.

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Both Statement I and Statement II are correct

B)

Statement I is incorrect but Statement II is correct

C)

Both Statement I and Statement II are incorrect

D)

Statement I is correct but Statement II is incorrect

Question 29

In case of isoelectronic species the size of F−,Ne\mathrm{F}^{-}, \mathrm{Ne} and Na+\mathrm{Na}^{+}is affected by :

Options:

A)

Nuclear charge (z)(\mathrm{z})

B)

None of the factors because their size is the same

C)

Electron-electron interaction in the outer orbitals

D)

Principal quantum number (n)

Question 30

Ionic reactions with organic compounds proceed through :

(A) homolytic bond cleavage

(B) heterolytic bond cleavage

(C) free radical formation

(D) primary free radical

(E) secondary free radical

Choose the correct answer from the options given below :

Options:

A)

(A) only

B)

(B) only

C)

(C) only

D)

(D) and (E) only

Question 31

Which of the following compound will most easily be attacked by an electrophile?

Options:

A)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Basics of Organic Chemistry Question 29 English Option 1

B)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Basics of Organic Chemistry Question 29 English Option 2

C)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Basics of Organic Chemistry Question 29 English Option 3

D)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Basics of Organic Chemistry Question 29 English Option 4

Question 32

Given below are two statements :

Statement (I) : A solution of [Ni(H2O)6]2+\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+} is green in colour.

Statement (II) : A solution of [Ni(CN)4]2−\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-} is colourless.

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Statement I is incorrect but Statement II is correct

B)

Both Statement I and Statement II are correct

C)

Both Statement I and Statement II are incorrect

D)

Statement I is correct but Statement II is incorrect

Question 33

Given below are two statements :

Statement (I) : Aminobenzene and aniline are same organic compounds.

Statement (II) : Aminobenzene and aniline are different organic compounds.

In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Both Statement I and Statement II are correct

B)

Statement I is incorrect but Statement II is correct

C)

Statement I is correct but Statement II is incorrect

D)

Both Statement I and Statement II are incorrect

Numerical TypeQuestion 34

Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is _______ .

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Basics of Organic Chemistry Question 28 English

Numerical TypeQuestion 35

Among the following oxides of p-block elements, number of oxides having amphoteric nature is ________.

Cl2O7,CO,PbO2, N2O,NO,Al2O3,SiO2, N2O5,SnO2\mathrm{Cl}_2 \mathrm{O}_7, \mathrm{CO}, \mathrm{PbO}_2, \mathrm{~N}_2 \mathrm{O}, \mathrm{NO}, \mathrm{Al}_2 \mathrm{O}_3, \mathrm{SiO}_2, \mathrm{~N}_2 \mathrm{O}_5, \mathrm{SnO}_2

Numerical TypeQuestion 36

The lowest oxidation number of an atom in a compound A2B\mathrm{A}_2 \mathrm{B} is -2 . The number of electrons in its valence shell is _______.

Numerical TypeQuestion 37

Ka\mathrm{K}_{\mathrm{a}} for CH3COOH\mathrm{CH}_3 \mathrm{COOH} is 1.8×10−51.8 \times 10^{-5} and Kb\mathrm{K}_{\mathrm{b}} for NH4OH\mathrm{NH}_4 \mathrm{OH} is 1.8×10−51.8 \times 10^{-5}. The pH\mathrm{pH} of ammonium acetate solution will be _________.

Question 38

If A=[21−12],B=[1011],C=ABAT\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}} and X=ATC2 A\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}, then det⁡X\operatorname{det} \mathrm{X} is equal to :

Options:

A)

243

B)

729

C)

27

D)

891

Question 39

If n\mathrm{n} is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n\mathrm{n} is equal to :

Options:

A)

47

B)

53

C)

51

D)

43

Question 40

The area enclosed by the curves xy+4y=16x y+4 y=16 and x+y=6x+y=6 is equal to :

Options:

A)

28−30log⁡e228-30 \log _{\mathrm{e}} 2

B)

30−28log⁡e230-28 \log _{\mathrm{e}} 2

C)

30−32log⁡e230-32 \log _{\mathrm{e}} 2

D)

32−30log⁡e232-30 \log _{\mathrm{e}} 2

Numerical TypeQuestion 41

Let the line L:2x+y=α\mathrm{L}: \sqrt{2} x+y=\alpha pass through the point of the intersection P\mathrm{P} (in the first quadrant) of the circle x2+y2=3x^2+y^2=3 and the parabola x2=2yx^2=2 y. Let the line L\mathrm{L} touch two circles C1\mathrm{C}_1 and C2\mathrm{C}_2 of equal radius 232 \sqrt{3}. If the centres Q1Q_1 and Q2Q_2 of the circles C1C_1 and C2C_2 lie on the yy-axis, then the square of the area of the triangle PQ1Q2\mathrm{PQ}_1 \mathrm{Q}_2 is equal to ___________.

Numerical TypeQuestion 42

Let P={z∈C:∣z+2−3i∣≤1}\mathrm{P}=\{\mathrm{z} \in \mathbb{C}:|z+2-3 i| \leq 1\} and Q={z∈C:z(1+i)+zˉ(1−i)≤−8}\mathrm{Q}=\{\mathrm{z} \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \leq-8\}. Let in P∩Q\mathrm{P} \cap \mathrm{Q}, ∣z−3+2i∣|z-3+2 i| be maximum and minimum at z1z_1 and z2z_2 respectively. If ∣z1∣2+2∣z2∣2=α+β2\left|z_1\right|^2+2\left|z_2\right|^2=\alpha+\beta \sqrt{2}, where α,β\alpha, \beta are integers, then α+β\alpha+\beta equals _____________.

Numerical TypeQuestion 43

If ∫−π/2π/282cos⁡x dx(1+esin⁡x)(1+sin⁡4x)=απ+βlog⁡e(3+22)\int\limits_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \mathrm{~d} x}{\left(1+\mathrm{e}^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _{\mathrm{e}}(3+2 \sqrt{2}), where α,β\alpha, \beta are integers, then α2+β2\alpha^2+\beta^2 equals :

Numerical TypeQuestion 44

Let the line of the shortest distance between the lines

L1:r→=(i^+2j^+3k^)+λ(i^−j^+k^) and L2:r→=(4i^+5j^+6k^)+μ(i^+j^−k^) \begin{aligned} & \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}) \text { and } \\\\ & \mathrm{L}_2: \overrightarrow{\mathrm{r}}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k}) \end{aligned}

intersect L1\mathrm{L}_1 and L2\mathrm{L}_2 at P\mathrm{P} and Q\mathrm{Q} respectively. If (α,β,γ)(\alpha, \beta, \gamma) is the mid point of the line segment PQ\mathrm{PQ}, then 2(α+β+γ)2(\alpha+\beta+\gamma) is equal to ____________.

Question 45

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in ms−2\mathrm{ms}^{-2} is :

(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :

JEE Main 2024 (Online) 1st February Morning Shift Physics - Laws of Motion Question 8 English

Options:

A)

1.2

B)

4

C)

3

D)

2

Question 46

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

Options:

A)

32R\frac{3}{2} \mathrm{R}

B)

74R\frac{7}{4} \mathrm{R}

C)

52R\frac{5}{2} \mathrm{R}

D)

94R\frac{9}{4} \mathrm{R}

Question 47

The dimensional formula of angular impulse is :

Options:

A)

[ML2 T−2]\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]

B)

[ML−2 T−1]\left[\mathrm{M} \mathrm{L}^{-2} \mathrm{~T}^{-1}\right]

C)

[ML2 T−1]\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right]

D)

[MLT−1]\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-1}\right]

Question 48

The reading in the ideal voltmeter (V)(\mathrm{V}) shown in the given circuit diagram is :

JEE Main 2024 (Online) 1st February Morning Shift Physics - Current Electricity Question 23 English

Options:

A)

3 V3 \mathrm{~V}

B)

10 V10 \mathrm{~V}

C)

5 V5 \mathrm{~V}

D)

0 V0 \mathrm{~V}

Question 49

The pressure and volume of an ideal gas are related as PV32=K\mathrm{PV}^{\frac{3}{2}}=\mathrm{K} (Constant). The work done when the gas is taken from state A(P1,V1,T1)A\left(P_1, V_1, T_1\right) to state B(P2,V2,T2)B\left(P_2, V_2, T_2\right) is :

Options:

A)

2(P2V2−P1V1)2\left(\mathrm{P}_2 \sqrt{\mathrm{V}_2}-\mathrm{P}_1 \sqrt{\mathrm{V}_1}\right)

B)

2(P1 V1−P2 V2)2\left(\sqrt{\mathrm{P}_1} \mathrm{~V}_1-\sqrt{\mathrm{P}_2} \mathrm{~V}_2\right)

C)

2(P2 V2−P1 V1)2\left(\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right)

D)

2(P1 V1−P2 V2)2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)

Question 50

In series LCR circuit, the capacitance is changed from CC to 4C4 C. To keep the resonance frequency unchanged, the new inductance should be:

Options:

A)

increased by 2 L2 \mathrm{~L}

B)

reduced by 14 L\frac{1}{4} \mathrm{~L}

C)

reduced by 34 L\frac{3}{4} \mathrm{~L}

D)

increased to 4 L4 \mathrm{~L}

Numerical TypeQuestion 51

The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm20 \mathrm{~cm}. The focal length of the lens used is __________ cm\mathrm{cm}.

Numerical TypeQuestion 52

A tuning fork resonates with a sonometer wire of length 1 m1 \mathrm{~m} stretched with a tension of 6 N6 \mathrm{~N}. When the tension in the wire is changed to 54 N54 \mathrm{~N}, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ Hz\mathrm{Hz}.

Question 53

Identify AA and BB in the following sequence of reaction

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 15 English

Options:

A)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 15 English Option 1

B)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 15 English Option 2

C)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 15 English Option 3

D)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 15 English Option 4

Question 54

Which of the following complex is homoleptic?

Options:

A)

[Ni(NH3)2Cl2]\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]

B)

[Co(NH3)4Cl2]+\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}

C)

[Fe(NH3)4Cl2]+\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^{+}

D)

[Ni(CN)4]2−\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}

Question 55

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron (λ)(\lambda) and momentum of electron (p)(p) ?

Options:

A)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Structure of Atom Question 8 English Option 1

B)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Structure of Atom Question 8 English Option 2

C)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Structure of Atom Question 8 English Option 3

D)

JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Structure of Atom Question 8 English Option 4

Question 56

In acidic medium, K2Cr2O7\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 shows oxidising action as represented in the half reaction:

Cr2O72−+XH++Ye⊖→2 A+ZH2O \mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}+\mathrm{XH}^{+}+\mathrm{Ye}^{\ominus} \rightarrow 2 \mathrm{~A}+\mathrm{ZH}_2 \mathrm{O}

X,Y,Z\mathrm{X}, \mathrm{Y}, \mathrm{Z} and A\mathrm{A} are respectively are :

Options:

A)

14,7,614,7,6 and Cr3+\mathrm{Cr}^{3+}

B)

14,6,714,6,7 and Cr3+\mathrm{Cr}^{3+}

C)

8,4,68,4,6 and Cr2O3\mathrm{Cr}_2 \mathrm{O}_3

D)

8,6,48,6,4 and Cr2O3\mathrm{Cr}_2 \mathrm{O}_3

Question 57

Match List - I with List - II.

List I (Reactions) List II (Reagents)
(A) JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 14 English 1 (I) CH3MgBr, H2O
(B) C6H5COC6H5 ⟶ C6H5CH=C6H5 (II) Zn(Hg) and conc. HCl
(C) C6H5CHO ⟶ C6H5CH(OH)CH3 (III) NaBH4, H+
(D) JEE Main 2024 (Online) 1st February Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 14 English 2 (IV) DIBAL-H, H2O


Choose the correct answer from the options given below :

Options:

A)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

B)

(A)-(IV), (B)-(II), (C)-(III), (D)-(I)

C)

(A)-(IV), (B)-(II), (C)-(I), (D)-(III)

D)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Question 58

Arrange the bonds in order of increasing ionic character in the molecules. LiF\mathrm{LiF}, K2O,N2,SO2\mathrm{K}_2 \mathrm{O}, \mathrm{N}_2, \mathrm{SO}_2 and ClF3\mathrm{ClF}_3 :

Options:

A)

N2<SO2<ClF3<K2O<LiF\mathrm{N}_2<\mathrm{SO}_2<\mathrm{ClF}_3<\mathrm{K}_2 \mathrm{O}<\mathrm{LiF}

B)

ClF3<N2<SO2<K2O<LiF\mathrm{ClF}_3<\mathrm{N}_2<\mathrm{SO}_2<\mathrm{K}_2 \mathrm{O}<\mathrm{LiF}

C)

LiF<K2O<ClF3<SO2<N2\mathrm{LiF}<\mathrm{K}_2 \mathrm{O}<\mathrm{ClF}_3<\mathrm{SO}_2<\mathrm{N}_2

D)

N2<ClF3<SO2<K2O<LiF\mathrm{N}_2<\mathrm{ClF}_3<\mathrm{SO}_2<\mathrm{K}_2 \mathrm{O}<\mathrm{LiF}

Numerical TypeQuestion 59

Number of optical isomers possible for 2-chlorobutane ________.

Numerical TypeQuestion 60

The ratio of 14C12C\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}} in a piece of wood is 18\frac{1}{8} part that of atmosphere. If half life of 14C{ }^{14} \mathrm{C} is 5730 years, the age of wood sample is ________ years.

Question 61

If tan⁡A=1x(x2+x+1),tan⁡B=xx2+x+1\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan \mathrm{B}=\frac{\sqrt{x}}{\sqrt{x^2+x+1}} and

tan⁡C=(x−3+x−2+x−1)1/2,0<A,B,C<π2\tan \mathrm{C}=\left(x^{-3}+x^{-2}+x^{-1}\right)^{1 / 2}, 0<\mathrm{A}, \mathrm{B}, \mathrm{C}<\frac{\pi}{2}, then A+B\mathrm{A}+\mathrm{B} is equal to :

Options:

A)

C\mathrm{C}

B)

π−C\pi-C

C)

2π−C2 \pi-C

D)

π2−C\frac{\pi}{2}-\mathrm{C}

Question 62

Let f:R→Rf: \mathbf{R} \rightarrow \mathbf{R} and g:R→Rg: \mathbf{R} \rightarrow \mathbf{R} be defined as

f(x)={log⁡ex,x>0e−x,x≤0f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right. and

g(x)={x,x⩾0ex,x<0g(x)=\left\{\begin{array}{ll}x, & x \geqslant 0 \\ \mathrm{e}^x, & x<0\end{array}\right.. Then, gof : R→R\mathbf{R} \rightarrow \mathbf{R} is :

Options:

A)

one-one but not onto

B)

neither one-one nor onto

C)

onto but not one-one

D)

both one-one and onto

Question 63

Let f:R→Rf: \mathbf{R} \rightarrow \mathbf{R} be defined as :

f(x)={a−bcos⁡2xx2;x<0x2+cx+2;0≤x≤12x+1;x>1 f(x)= \begin{cases}\frac{a-b \cos 2 x}{x^2} ; & x<0 \\\\ x^2+c x+2 ; & 0 \leq x \leq 1 \\\\ 2 x+1 ; & x>1\end{cases}

If ff is continuous everywhere in R\mathbf{R} and mm is the number of points where ff is NOT differential then m+a+b+c\mathrm{m}+\mathrm{a}+\mathrm{b}+\mathrm{c} equals :

Options:

A)

1

B)

4

C)

3

D)

2

Numerical TypeQuestion 64

If the Coefficient of x30x^{30} in the expansion of (1+1x)6(1+x2)7(1−x3)8;x≠0\left(1+\frac{1}{x}\right)^6\left(1+x^2\right)^7\left(1-x^3\right)^8 ; x \neq 0 is α\alpha, then ∣α∣|\alpha| equals ___________.

Numerical TypeQuestion 65

Let {x}\{x\} denote the fractional part of xx and f(x)=cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3,x≠0f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0. If L\mathrm{L} and R\mathrm{R} respectively denotes the left hand limit and the right hand limit of f(x)f(x) at x=0x=0, then 32π2( L2+R2)\frac{32}{\pi^2}\left(\mathrm{~L}^2+\mathrm{R}^2\right) is equal to ___________.

Question 66

If R\mathrm{R} is the radius of the earth and the acceleration due to gravity on the surface of earth is g=π2 m/s2g=\pi^2 \mathrm{~m} / \mathrm{s}^2, then the length of the second's pendulum at a height h=2R\mathrm{h}=2 R from the surface of earth will be, :

Options:

A)

19 m\frac{1}{9} \mathrm{~m}

B)

89 m\frac{8}{9} \mathrm{~m}

C)

29 m\frac{2}{9} \mathrm{~m}

D)

49 m\frac{4}{9} \mathrm{~m}

Question 67

A ball of mass 0.5 kg0.5 \mathrm{~kg} is attached to a string of length 50 cm50 \mathrm{~cm}. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N400 \mathrm{~N}. The maximum possible value of angular velocity of the ball in rad/s\mathrm{rad} / \mathrm{s} is, :

Options:

A)

1600

B)

20

C)

40

D)

1000

Question 68

A galvanometer has a resistance of 50 Ω50 ~\Omega and it allows maximum current of 5 mA5 \mathrm{~mA}. It can be converted into voltmeter to measure upto 100 V100 \mathrm{~V} by connecting in series a resistor of resistance :

Options:

A)

19500Ω19500 \Omega

B)

5975Ω5975 \Omega

C)

20050Ω20050 \Omega

D)

19950Ω19950 \Omega

Question 69

A parallel plate capacitor has a capacitance C=200 pF\mathrm{C}=200~ \mathrm{pF}. It is connected to 230 V230 \mathrm{~V} ac supply with an angular frequency 300 rad/s300~ \mathrm{rad} / \mathrm{s}. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

Options:

A)

14.3 μA14.3 ~\mu \mathrm{A} and 143 μA143 ~\mu \mathrm{A}

B)

13.8 μA13.8 ~\mu \mathrm{A} and 13.8 μA13.8 ~\mu \mathrm{A}

C)

13.8 μA13.8 ~\mu \mathrm{A} and 138 μA138 ~\mu \mathrm{A}

D)

1.38 μA1.38 ~\mu \mathrm{A} and 1.38 μA1.38 ~\mu \mathrm{A}

Question 70

Two identical capacitors have same capacitance CC. One of them is charged to the potential VV and other to the potential 2 V2 \mathrm{~V}. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

Options:

A)

14CV2\frac{1}{4} \mathrm{CV}^2

B)

34CV2\frac{3}{4} \mathrm{CV}^2

C)

12CV2\frac{1}{2} \mathrm{CV}^2

D)

2CV22 \mathrm{CV}^2

Question 71

We have three aqueous solutions of NaCl\mathrm{NaCl} labelled as ' A\mathrm{A} ', ' B\mathrm{B} ' and ' C\mathrm{C} ' with concentration 0.1M0.1 \mathrm{M}, 0.01M0.01 \mathrm{M} and 0.001M0.001 \mathrm{M}, respectively. The value of van 't Hoff factor(i) for these solutions will be in the order :

Options:

A)

iA<iC<iB\mathrm{i}_{\mathrm{A}}<\mathrm{i}_{\mathrm{C}}<\mathrm{i}_{\mathrm{B}}

B)

iA<iB<iC\mathrm{i}_{\mathrm{A}}<\mathrm{i}_{\mathrm{B}}<\mathrm{i}_{\mathrm{C}}

C)

iA>iB>iC\mathrm{i}_{\mathrm{A}}>\mathrm{i}_{\mathrm{B}}>\mathrm{i}_{\mathrm{C}}

D)

iA=iB=iC\mathrm{i}_{\mathrm{A}}=\mathrm{i}_{\mathrm{B}}=\mathrm{i}_{\mathrm{C}}

Question 72

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is :

Options:

A)

25\frac{2}{5}

B)

27\frac{2}{7}

C)

17\frac{1}{7}

D)

15\frac{1}{5}

Question 73

The value of the integral ∫0π/4x dxsin⁡4(2x)+cos⁡4(2x)\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)} equals :

Options:

A)

2π28\frac{\sqrt{2} \pi^2}{8}

B)

2π216\frac{\sqrt{2} \pi^2}{16}

C)

2π232\frac{\sqrt{2} \pi^2}{32}

D)

2π264\frac{\sqrt{2} \pi^2}{64}

Question 74

Let S={x∈R:(3+2)x+(3−2)x=10}\mathbf{S}=\left\{x \in \mathbf{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}. Then the number of elements in S\mathrm{S} is :

Options:

A)

4

B)

0

C)

2

D)

1

Question 75

If the system of equations

2x+3y−z=5x+αy+3z=−43x−y+βz=7 \begin{aligned} & 2 x+3 y-z=5 \\\\ & x+\alpha y+3 z=-4 \\\\ & 3 x-y+\beta z=7 \end{aligned}

has infinitely many solutions, then 13αβ13 \alpha \beta is equal to :

Options:

A)

1110

B)

1120

C)

1210

D)

1220

Question 76

Let y=y(x)y=y(x) be the solution of the differential equation

dy dx=2x(x+y)3−x(x+y)−1,y(0)=1\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x(x+y)^3-x(x+y)-1, y(0)=1.

Then, (12+y(12))2\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2 equals :

Options:

A)

44+e\frac{4}{4+\sqrt{\mathrm{e}}}

B)

33−e\frac{3}{3-\sqrt{\mathrm{e}}}

C)

21+e\frac{2}{1+\sqrt{\mathrm{e}}}

D)

12−e\frac{1}{2-\sqrt{\mathrm{e}}}

Question 77

Let x2a2+y2b2=1,a>b\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a}>\mathrm{b} be an ellipse, whose eccentricity is 12\frac{1}{\sqrt{2}} and the length of the latusrectum is 14\sqrt{14}. Then the square of the eccentricity of x2a2−y2b2=1\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 is :

Options:

A)

3

B)

72{7 \over 2}

C)

32{3 \over 2}

D)

52{5 \over 2}

Question 78

Let 3,a,b,c3, a, b, c be in A.P. and 3,a−1,b+1,c+93, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of a,ba, b and cc is :

Options:

A)

-4

B)

-1

C)

13

D)

11

Question 79

Let C:x2+y2=4C: x^2+y^2=4 and C′:x2+y2−4λx+9=0C^{\prime}: x^2+y^2-4 \lambda x+9=0 be two circles. If the set of all values of λ\lambda so that the circles C\mathrm{C} and C\mathrm{C} intersect at two distinct points, is R−[a,b]\mathrm{R}-[\mathrm{a}, \mathrm{b}], then the point (8a+12,16 b−20)(8 \mathrm{a}+12,16 \mathrm{~b}-20) lies on the curve :

Options:

A)

x2+2y2−5x+6y=3x^2+2 y^2-5 x+6 y=3

B)

5x2−y=−115 x^2-y=-11

C)

x2−4y2=7x^2-4 y^2=7

D)

6x2+y2=426 x^2+y^2=42

Question 80

If 5f(x)+4f(1x)=x2−2,∀x≠05 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0 and y=9x2f(x)y=9 x^2 f(x), then yy is strictly increasing in :

Options:

A)

(0,15)∪(15,∞)\left(0, \frac{1}{\sqrt{5}}\right) \cup\left(\frac{1}{\sqrt{5}}, \infty\right)

B)

(−15,0)∪(15,∞)\left(-\frac{1}{\sqrt{5}}, 0\right) \cup\left(\frac{1}{\sqrt{5}}, \infty\right)

C)

(−15,0)∪(0,15)\left(-\frac{1}{\sqrt{5}}, 0\right) \cup\left(0, \frac{1}{\sqrt{5}}\right)

D)

(−∞,15)∪(0,15)\left(-\infty, \frac{1}{\sqrt{5}}\right) \cup\left(0, \frac{1}{\sqrt{5}}\right)

Numerical TypeQuestion 81

The number of elements in the set S={(x,y,z):x,y,z∈Z,x+2y+3z=42,x,y,z⩾0}\mathrm{S}=\{(x, y, z): x, y, z \in \mathbf{Z}, x+2 y+3 z=42, x, y, z \geqslant 0\} equals __________.

Question 82

The de Broglie wavelengths of a proton and an α\alpha particle are λ\lambda and 2λ2 \lambda respectively. The ratio of the velocities of proton and α\alpha particle will be :

Options:

A)

8:18: 1

B)

1:21: 2

C)

1:81: 8

D)

4:14: 1

Question 83

The radius (r)(\mathrm{r}), length (l)(l) and resistance (R)(\mathrm{R}) of a metal wire was measured in the laboratory as

r=(0.35±0.05) cmR=(100±10) ohml=(15±0.2) cm \begin{aligned} & \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\ & \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\ & l=(15 \pm 0.2)~ \mathrm{cm} \end{aligned}

The percentage error in resistivity of the material of the wire is :

Options:

A)

37.3%37.3 \%

B)

25.6%25.6 \%

C)

35.6%35.6 \%

D)

39.9%39.9 \%

Question 84

A simple pendulum of length 1 m1 \mathrm{~m} has a wooden bob of mass 1 kg1 \mathrm{~kg}. It is struck by a bullet of mass 10−2 kg10^{-2} \mathrm{~kg} moving with a speed of 2×102 ms−12 \times 10^2 \mathrm{~ms}^{-1}. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )

Options:

A)

0.20 m0.20 \mathrm{~m}

B)

0.40 m0.40 \mathrm{~m}

C)

0.30 m0.30 \mathrm{~m}

D)

0.35 m0.35 \mathrm{~m}

Question 85

In the given circuit if the power rating of Zener diode is 10 mW10 \mathrm{~mW}, the value of series resistance RsR_s to regulate the input unregulated supply is :

JEE Main 2024 (Online) 1st February Morning Shift Physics - Semiconductor Question 9 English

Options:

A)

10kΩ10 \mathrm{k} \Omega

B)

10Ω10 \Omega

C)

1kΩ1 \mathrm{k} \Omega

D)

37kΩ{3\over7} \mathrm{k} \Omega

Numerical TypeQuestion 86

A rectangular loop of sides 12 cm12 \mathrm{~cm} and 5 cm5 \mathrm{~cm}, with its sides parallel to the xx-axis and yy-axis respectively, moves with a velocity of 5 cm/s5 \mathrm{~cm} / \mathrm{s} in the positive xx axis direction, in a space containing a variable magnetic field in the positive zz direction. The field has a gradient of 10−3 T/cm10^{-3} \mathrm{~T} / \mathrm{cm} along the negative xx direction and it is decreasing with time at the rate of 10−3 T/s10^{-3} \mathrm{~T} / \mathrm{s}. If the resistance of the loop is 6 mΩ6 \mathrm{~m} \Omega, the power dissipated by the loop as heat is __________ ×10−9 W\times 10^{-9} \mathrm{~W}.

Numerical TypeQuestion 87

A plane is in level flight at constant speed and each of its two wings has an area of 40 m240 \mathrm{~m}^2. If the speed of the air is 180 km/h180 \mathrm{~km} / \mathrm{h} over the lower wing surface and 252 km/h252 \mathrm{~km} / \mathrm{h} over the upper wing surface, the mass of the plane is ___________ kg.

(Take air density to be 1 kg m−31 \mathrm{~kg} \mathrm{~m}^{-3} and g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2} )

Numerical TypeQuestion 88

A particle is moving in one dimension (along xx axis) under the action of a variable force. It's initial position was 16 m16 \mathrm{~m} right of origin. The variation of its position (x)(x) with time (t)(t) is given as x=−3t3+18t2+16tx=-3 t^3+18 t^2+16 t, where xx is in m\mathrm{m} and t\mathrm{t} is in s\mathrm{s}.

The velocity of the particle when its acceleration becomes zero is _________ m/s\mathrm{m} / \mathrm{s}.

Numerical TypeQuestion 89

The identical spheres each of mass 2M2 \mathrm{M} are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m4 \mathrm{~m} each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is 42x\frac{4 \sqrt{2}}{x}, where the value of xx is ___________ .

Numerical TypeQuestion 90

The current in a conductor is expressed as I=3t2+4t3I=3 t^2+4 t^3, where II is in Ampere and tt is in second. The amount of electric charge that flows through a section of the conductor during t=1 st=1 \mathrm{~s} to t=2 st=2 \mathrm{~s} is __________ C.