Class 12th

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A relation R is defined as ARB if PAP? ¹ = B for a non-singular matrix P.

· Reflexive: ARA requires PAP? ¹ = A. This holds if P is the identity matrix I, as IAI? ¹ = A. Assuming P can be I, the relation is reflexive.

· Symmetric: We need to show that if ARB, then BRA.
ARB ⇒ PAP? ¹ = B.
To get the reverse, we need to express A in terms of B.
From PAP? ¹ = B, pre-multiply by P? ¹ and post-multiply by P:
P? ¹ (PAP? ¹)P = P? ¹BP ⇒ A = P? ¹BP. This shows BRA where the matrix is P? ¹. Thus, the relation is symmetric.

· Trans

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Class 12th Chemistry

Given below are two statements:
Statement I: Non-biodegradable wastes are generated by the thermal power plants.
Statement II: Bio-degradable detergents leads to eutrophication.
In the light of the above statements, choose the most appropriate answer from the options given below:

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Contributor-Level 9

Non- biodegradable wastes are generated by thermal power plants which produce fly ash. Bio-degradable detergents leads to eutrophication by decreasing oxygen level in water.

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Class 12th Chemistry

A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/ an:

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Class 12th Ncert Solutions Chemistry Class 12th

Contributor-Level 9

Covalent solids have high melting point due to strong covalent bonds, also they are insulator in both solid as well as in molten state.

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2 months ago

In basic medium H?O? exhibits which of the following reactions?
(A) Mn²? → Mn?
(B) I? → I?
(C) PbS → PbSO?
Choose the most appropriate answer from the options given below:

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Contributor-Level 9

In basic medium H? O? can behaves as both oxidizing and reducing agent, so it can oxidize Mn²? to Mn? and reduce I? to I?

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An infinite number of point charges, each carrying 1 μC charge, are placed along y-axis at y = 1 m, 2 m, 4 m, 8 m, . The total force on a 1 C point charge, placed at the origin is x*10³ N. The value of x, to the nearest integer, is.
[Take 1/(4πε?) = 9*10⁹ Nm²/C²]

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Contributor-Level 10

F = (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + .

⇒ F = (qQ)/ (4πε? ) [1/1² + 1/2² + 1/4² + 1/8² + .]

⇒ F = (qQ)/ (4πε? ) [1/ (1 - 1/4)]

⇒ F = (qQ)/ (4πε? ) [4/3] = 10? * 1 * 9 * 10? * (4/3) = 12 * 10³ N

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2 months ago

A galaxy is moving away from the earth at a speed 286 kms^-1. The shift in wavelength of a redline at 630 nm is x*10^-10 m. The value of x, to the nearest integer, is.
[Take the value of speed of light c, as 3*10⁸ ms^-1]

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Contributor-Level 10

Δλ = (v/c)λ = (286/3000000) * 630 * 10? = 6.006 * 10? ¹? ≈ 6 * 10? ¹? m

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Class 12th Chemistry

Given below are two statements:
Statement I: C?H?OH and AgCN both can generate nucleophile.
Statement II: KCN and AgCN both will generate nitrile nucleophile with all reaction conditions.
Choose the most appropriate option:

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Contributor-Level 9

Both C? H? OH and AgCN can generate nucleophile.
KCN generate nitrile as nucleophile while AgCN generate isonitrile as nucleophile in nucleophilic substitution reaction.

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Two wires of same length and thickness having specific resistance 6 Ω cm and 3 Ω cm respectively are connected in parallel. The effective resistivity is ρ Ω cm. The value of ρ, to the nearest integer, is.

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Contributor-Level 10

R_eq = (R? )/ (R? +R? ) ⇒ p (l)/ (2A) = [ (p? l/A) (p? l/A)] / [ (p? l/A) + (p? l/A)]

⇒ ρ/2 = (p? )/ (p? +p? ) ⇒ ρ = (2p? p? )/ (p? +p? ) = (2 * 6 * 3)/9 = 4 Ωcm

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2 months ago

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection.

The value of x, to nearest integer, is.

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Class 12th Electromagnetic Waves

Contributor-Level 10

12/x = 6/ (72-x) ⇒ x = 144 - 2x ⇒ x = 144/3 = 48cm

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2 months ago

A TV transmission tower antenna is at a height of 20m. Suppose that the receiving antenna is at
(i) ground level
(ii) a height of 5m
The increase in the antenna range in case (ii) relative to case (i) is n %.
The value of n, to the nearest integer, is.

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