Class 12th

The number of stereoisomers formed in a reaction of

$(\pm) P h (C = O) C (O H) (C N) P h w i t h H C N i s____________.$

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Contributor-Level 10

Total 3 streo- isomers

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8 months ago

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors such that $\vec{a} * \vec{b} = 4 \vec{c}, \vec{b} * \vec{c} = 9 \vec{a}$ and $\vec{c} * \vec{a} = α \vec{b}, α > 0 .$ If $| \vec{a} | + | \vec{b} | + | \vec{c} | = \frac{1}{36},$ then a is equal to…….

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Contributor-Level 10

Data contradiction.

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8 months ago

A common tangent T to the curves $C_{1} : \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ and C₂ = $\frac{x^{2}}{42} - \frac{y^{2}}{143} = 1$ does not pass through the fourth quadrant. If T touches C₁ at (x₁, y₁) and C₂ at (x₂, y₂), then $| 2 x_{1} + x_{2} |$ is equal to………

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Contributor-Level 10

Common tangents

$T_{1} : y = m x \pm \sqrt[]{4 m^{2} + 9}$

$T_{2} : y = m x \pm \sqrt[]{42 m^{2} - 13}$

So, 4m² + 9 = 42 m² – 13 Þ m = $\pm 2$

$\Rightarrow c = \pm 5$

So tangent $y = \pm 2 x \pm 5$

y = 2x + 5 does not pass through 4^th quadrant compare this tangent with T = 0 to get pt. of intersection

$\frac{x x_{2}}{42} - \frac{y y_{2}}{143} = 1 \Rightarrow x_{2} = \frac{- 84}{5}$

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8 months ago

A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave 1.344mL of H₂ gas at STP. The number of alcoholic hydrogens present in compound 'X' is_________.

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Class 12th Differential Equations

Contributor-Level 10

Mole of polyhydric alcohol = $\frac{1.84 * 1 0^{- 3}}{92} = 2.0 * 1 0^{- 5} m o l e .$

Mole of H₂ gas produced = $\frac{1.344}{22400} = 6.0 * 1 0^{- 5} m o l e .$

No of -OH gp present = $\frac{6.0 * 1 0^{- 5}}{2.0 * 1 0^{- 5}} = 3$

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8 months ago

Let f be a differentiable function satisfying f(x) = $\frac{2}{\sqrt[]{3}} \int_{0}^{\sqrt[]{3}} f (\frac{λ^{2} x}{3}) d λ,$ x > 0 and f(1) = $\sqrt[]{3}$ . If y = f(x) passes through the point (a, 6), then a is equal to………….

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Contributor-Level 10

$f (x) = \frac{2}{\sqrt[]{3}} \int_{0}^{\sqrt[]{3}} f (\frac{λ^{2} x}{3}) d λ$

Substitute $\frac{λ^{2} x}{3} = t$ $\frac{^{}}{}$

$f (x) = \frac{1}{\sqrt[]{x}} \int_{0}^{x} \frac{f (t)}{\sqrt[]{t}} d t$

differentiate using leibneitz rule

$\sqrt[]{x} . f' (x) + f (x) . \frac{1}{2 \sqrt[]{x}} = \frac{f (x)}{\sqrt[]{x}}$

f (1) = $\sqrt[]{3} \Rightarrow f (x) = \sqrt[]{3 x}$

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8 months ago

Consider the following sulphur based oxoacids.

H₂SO₃, H₂SO₄, H₂S₂O₈ and H₂S₂O₇.

Amongst these oxoacids, the number of those with peroxo (O-O) bond is______________.

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Class 12th Chemistry Coordination Compounds

Contributor-Level 10

Only H₂S₂O₈ has per-oxo bond.

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8 months ago

Sum of oxidation state (magnitude) and coordination number of cobalt in $N a [C o (b p y) C l_{4}]$ is___________.

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Contributor-Level 10

Oxidation state of Co = 3

And co-ordination No = 6

Sum = 3 + 6 = 9

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8 months ago

For the curve C : $(x^{2} + y^{2} - 3) + {(x^{2} - y^{2} - 1)}^{5} = 0,$ the value of $3 y' - y^{3} y ",$ at the point (a, a), a > 0, on C, is equal to……….

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Contributor-Level 10

Find a, α

$(α^{2} + α^{2} - 3) + {(α^{2} - α^{2} - 1)}^{5} = 0$

$α = \sqrt[]{2}$

zx differentiate the curve

$2 x + 2 y . y^{1} + 5 {(x^{2} - y^{2} - 1)}^{4} (2 x - 2 y) = 0$ ……. (i)

differentiate equation (i)

$(α, α) \Rightarrow y'' = \frac{- 23}{4 \sqrt[]{2}}$

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8 months ago

Assuming 1 $μ g$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is __________* 10^-1 $μ g$

[Given: In 10 = 2.303; log 2 = 0.30]

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Contributor-Level 10

$λ t = l n \frac{N_{o}}{N_{t}}$

$\frac{0.693}{t_{1 / 2}} * t = l n \frac{1}{N_{t}}$

Or $\frac{0.693 * 100}{30} = l n \frac{1}{N_{t}}$

$\frac{1}{N_{t}} = 10$

$∴ N_{t} = \frac{1}{10} = 0.1$

Or N_t = 1 * 10^-1 $μ g$

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8 months ago

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $t a n^{- 1} \frac{3}{4} .$ Water is poured in it a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is……….

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