Class 12th

Identify the major products A and B for the below given reaction sequence.

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Class 12th Physics

Two identical positive charge Q each are fixed at a distance of '2a' apart from each other. Another point charge q₀ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q₀ executes SHM. The time period of oscillation of charge q₀ will be:

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$F_{R} = {\frac{k Q q_{0}}{{(a - x)}^{2}} - \frac{k Q q_{0}}{{(a + x)}^{2}}}$

$= - k Q q_{0} {\frac{a^{2} + x^{2} + 2 a x - a^{2} - x^{2} + 2 a x}{(a^{2} - x^{2})}}$

$F_{R} = - \frac{k Q q_{0} (4 a x)}{{(a^{2} - x^{2})}^{2}}$

$T = 2 π \sqrt[]{\frac{a^{3} m}{4 k Q q_{0}} = \sqrt[]{\frac{4 π^{2} a^{3} m * 4 π ε_{0}}{4 Q q_{0}}}} = \sqrt[]{\frac{4 π^{3} ε_{0} m a^{3}}{Q q_{0}}}$

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Among the following marked proton of which compound shows lowest pK_a value?

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Compound 'A' undergoes following sequence of reactions to give compound 'B'. The correct structure and chirality of compound 'B' is

[where Et is -C₂H₅]

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Choose the correct option for the following reactions.

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Correct structure of $γ - m e t h y l c y c l o h e x a n e$ carbaldehyde is

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Match List-I with List-II

Choose the correct answer from the options given below

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Class 12th Maths

Let [t] denote the greatest integer less than or equal to t. Then the value of the integral $\int_{- 3}^{101} ([s i n (π x)] + e^{[c o s (2 π x)]}) d x i s e q u a l t o$

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Payal Gupta

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$l = \int_{- 3}^{103} ([s i n (π x)] + e^{[c o s (2 π x)]}) d x$

$[s i n π x]$ is periodic with period 2 and

$e^{[c o s 2 π x]}$ is periodic with period 1.

So,

$I = 52 \int_{0}^{2} ([s i n (π x)] + e^{[c o s 2 π x]}) d x$

= $\frac{52}{e}$

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Class 12th Maths

If A and B are two events such that P(A) = $\frac{1}{3}$ , P(B) = $\frac{1}{5}$ and $P (A \cup B) = \frac{1}{2},$ then $P (A | B') + P (B | A')$ is equal to

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Payal Gupta

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$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

$\Rightarrow \frac{1}{2} = \frac{1}{3} + \frac{1}{5} - P (A \cap B)$

$P (\frac{A}{B'}) + P (\frac{B}{A'})$

$= \frac{P (A) - P (A \cap B)}{1 - P (B)} + \frac{P (B) - P (A \cap B)}{1 - P (A)} = \frac{5}{8}$

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Which of the following 3d- metal ion will give the lowest enthalpy of hydration $(Δ_{h y d} H)$ when dissolved in water?

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