Class 12th

The nature of charge on resulting colloidal particles when FeCl₃ is added to excess of hot water is:

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Contributor-Level 10

$F e C l_{3} \to_{}^{h y d r o l y s i s} F e {(O H)}_{3} ↓ \to_{A d s o r p t i o n}^{F e^{3 +}} F e {(O H)}_{3} | F e^{3 +} (c o l l o i d a l p a r t i c l e)$

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5 months ago

Match List with List II.

List I List II

(Monomer Unit)

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alok kumar singh

Contributor-Level 10

Caprolactum is monomer of nylon-6

Isoprene is polymer of natural rubber

2 – chloro-1,3-butadiene or chloroprene is the polymer of neoprene which is a synthetic rubber

Acrylonitrite is one of the monomer of Buna-N

Acrylonitrile

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Class 12th Maths

Let m, n $\in$ N and gcd (2, n) = 1. If 30 $(\begin{matrix} 30 & 0 \end{matrix}) + 29 (\begin{matrix} 30 & 1 \end{matrix}) + . . . . . + 2 (\begin{matrix} 30 & 28 \end{matrix}) + 1 (\begin{matrix} 30 & 29 \end{matrix})$ = n. 2m, then n + m is equal to--------.

$(H e r e (\begin{matrix} n & k \end{matrix}) =^{n} ? C_{k})$

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$30^{30} C_{0} + 29^{30} C_{1} + . . . . . + 2^{30} C_{28} + 1 .^{30} C_{29} = n . 2^{m}$

$∴ n = 15, m = 0$

$∴ n + m = 15 + 30 = 45$

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Identify A in the following chemical reaction.

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Contributor-Level 10

Kindly consider the following figure

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Class 12th Maths

The sum of 162^th power of the roots of the equation $x^{3} - 2 x^{2} + 2 x - 1 = 0 i s$ -------------.

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Class 12th Inverse Trigonometric Functions

Contributor-Level 10

$(x - 1) (x^{2} - x + 1) = 0$

$x = 1, x = \frac{1 \pm \sqrt[]{3} i}{2} = \frac{1}{2} + \frac{\sqrt[]{3}}{2} i, \frac{1}{2} - \frac{\sqrt[]{3}}{2} i = e^{i \frac{π}{3}}, e^{- i \frac{π}{3}}$

Sum of 162th power of roots = $1 + e^{i 54 π} + e^{- i 54 π} = 1 + 1 + 1 = 3$

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The number of integral values of 'k' for which the equation 3sinx + 4cos x = k + 1 has a solution, k $\in$ R is------------.

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Contributor-Level 10

$3 s i n x + 4 c o s x = k + 1, c o s α = \frac{3}{5}, s i n α = \frac{4}{5}$

$5 s i n (x + α) = k + 1,$

$∴ - 5 \leq k + 1 \leq 5 \Rightarrow - 6 \leq k \leq 4$

$∴$ total number of integral values of k is 11.

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In Freundlich adsorption isotherm, slope of AB line is:

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alok kumar singh

Contributor-Level 10

Freundlich adsorption isotherm

$\frac{x}{m} = k p^{1 / n}$

$l o g \frac{x}{m} = \frac{1}{n} l o g p + l o g k$

Comparing with y = mx + C

so, slope of given graph is $\frac{1}{n}$ whose value varies from 0 to 1.

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Identify A in the given reaction.

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Contributor-Level 10

Since SOCl₂ is used to covert aliphatic (R-OH) into chlorides. It will not react with aromatic alcohol

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Class 12th Maths

Let $(λ, 2, 1)$ be a point on the plane which passes which through the point (4, 2, 2). If the plane is perpendicular to the line joining the points (2, 21, 29) and (1, 16, 23), then ${(\frac{λ}{11})}^{2} - \frac{4 λ}{11} - 4$ is equal to----------.

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Contributor-Level 10

Let $A (- 2, - 21, 29), B (- 1, - 16, 23), P (λ, 2, 1), Q (4, - 2, 2)$

Given $\vec{A B} ⊥ \vec{P Q}$

$∴ \vec{A B} . \vec{P Q} = 0$

$(\hat{i} + 5 \hat{j} - 6 \hat{k}) . ((4 - λ) \hat{i} - 4 \hat{j} + \hat{k}) = 0$

$4 - λ - 20 - 6 = 0$

$λ = - 22$

$∴ {(\frac{λ}{11})}^{2} + (\frac{- 4 λ}{11}) - 4 = 4 + 8 - 4 = 8$

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5 months ago

Match List – I with List – II.

List – I List – II

(A) Siderite (i) Cu

(B) Calamine (ii) Ca

(C) Malachite &nb

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