MET Mock Test - 6 - JEE MCQ

Let ρ₁ and ρ₂ be the charge densities of two spheres.
Then,

The given P-V graph of an ideal gas is reproduced below:

As the given process is cyclic, change in internal energy of the gas, 

Using the first law of thermodynamics,  

Thus, total work done by the gas is 

Now, work done by the gas for any path is given as  

From the figure, we get 

 is an isochoric process, thus 
Therefore, total work done by the gas is given as 

The average power consumed/cycle in an ideal capacitor is 0.
The average power consumed in an ideal capacitor is given as based on the instantaneous power which is supplied to the capacitor:
p_c = iv= (i_m cos ωt)(v_m sin ωt)
p_c = i_mv_m (cos ωt sin ωt)
pc=(i_mv_m/2)sin2ωt
We know that sin ωt = 0
Therefore, average power = 0

The linear mass density,

Current in AB = (V_AB/R_AB) = (1/2.5) = 0.4 A
I₁ = I₂
I₁ + I₂ = 0.4
I, = 0.4/2 = 0.2 A

σ = 0.424 nC m^-2

For the concave lens made up of liquid

now for equivalent lens


or f_e = 10 cm

u = -15 m

v = mu

v = (-2) × (-15) = 30 cm

Hence,

f = 10 cm

The strongest oxidising agent has the highest reduction potential value.

The most stable trihalide is NF₃.
Order of stability: NF₃ > NCl₃ > NBr₃ > NI₃
NCl₃ is explosive is nature.
NBr₃ and NI₃ are known only as ammoniates. The stability of trihalides decreases down the group due to weakening of N-X bond and inability of N to accommodate large sized halogen atoms (Cl, Br, I) around it.

Among methanol, phenol and p-ethoxyphenol, C-OH bond length is least in phenol due to resonance and highest in methanol due to lack of resonance, whereas it will have some intermediate value in p-ethoxyphenol.
∴ The increasing order of C-OH bond length is:
Phenol < p-ethoxyphenol < methanol

PCl₅(g) ⇋ PCl₃(g) + Cl₂(g)

α = deree of dissociation
Total moles = 5(1 - α) + 5α + α = 5(1 + α)
2 moles of N₂ are present, so total moles at equilibrium = 5(1 + α) + 2 ...(1)
By gas equation,
PV = nRT
P = 2.46 atm; V = 200 L
R = 0.082 L atm K^-1; T = 600 K

So, n = 10 moles
From equation (1),
5(1 + α) + 2 = 10

Degree of dissociation = α = 3/5 = 0.60

= 1107 × 10^-3

∴ Slope of the graph = 
∴ E_a = 18.5 × 8.31 × 1000 ≌ 154 kJ mol^-1

[Fe(H₂O)₃Cl₃] → Outer-orbital complex
K₃[Fe(CN)₆] → Inner-orbital complex
[Co(NH₃)₆]Cl₃ → Inner-orbital complex
Since CN^- is a strong filed ligand than NH₃. Hence, K₃[Fe(CN)₆] is the inner-orbital complex that absorbs light at shortest wavelength.
Fe(III)  Valence shell configuration 3d⁵
Since CN^- will do pairing, so unpaired electron = 1

y = e^x and y = sin x
We can solve this question by graphing.



From the graph and the tables, it is clear that for x > 0, there is no solution for y = e^x and y = sin x.

Sum of the roots = 3/2
Sum of product (two at a time) of roots = 6/2 = 3
Required Answer = (3/2)² - 2 x 3
= -15/4
(Note : Answer is negative, It means there must be 2 roots which are imaginary. This is because the sum of square of real number can never be negative.
Imaginary roots are always in pair. )
Correct answer is Option (a)

= 18 square units

Put cos^-1 (e-x) = θ,  θ ∈ [0, π]
cos θ = e^-x ⇒ 2 cos² θ/2  - 1 = e^-x 


2(1 - e-x)^1/2 = √2y + c (put given condition)

The word ‘otherwise’ can be used in several different ways. ‘Otherwise’ can be used to introduce the possible outcome of a given situation. ‘Otherwise’ can also be used as an ordinary adverb. It is used for saying that if one thing does not happen, something else (usually bad) will happen. Otherwise can also be used after an order or suggestion to show what the result will be if you do not follow that order or suggestion
The correct sentence is – Our team must work hard on this project, otherwise, we will not get the desired funding from the respective client on time.

Given letters are R, T, A, N, U, E.
We have to arrange the letters so that it becomes a meaningful word.
The sequence of the letters is 4, 3, 2, 5, 1, 6.
Thus, the word becomes NATURE.
Therefore, the correct answer is 432516.

The word given in option D is incorrect. The correct spelling is controversial. It is an adjective that means something that causes public discussions. It is a topic that causes controversy and people argue about it. Different people have different opinions about things.

In this question, the two terms of the given pair are related to each other in the following way;
The second number is obtained by adding 11 to the thrice of the first number.
The pattern is shown below,
9 : 9 × 3 + 1 = 9 : 28
Similarly,
56 : 56 × 3 + 1 = 56 :169
Hence, the correct answer is 169.

Here, the cut made near the lower-left corner will appear only once in the opened paper but the other cut will appear twice. Thus, there will be three cuts when the folded paper will be opened. It has been shown below-

Given Venn diagram:

From the above diagram, we can see that Square represents Mothers and circle represents Racers, DFG is the set of letters represents Mothers who are not Racers.
Hence, the correct answer is DFG.