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Class 12th Application of Integrals

8. The area between x = y² and x = 4 is divided into two equal parts by the line x = a find the value of a

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Vishal Baghel

Contributor-Level 10

Kindly go through the solution

\begin{array}{l} \Rightarrow {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{a} = {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{a}^{} \\ \Rightarrow \frac{2}{3} [a^{\frac{3}{2}} - 0] = \frac{2}{3} [4^{\frac{3}{2}} - a^{\frac{3}{2}}] \\ \Rightarrow a^{\frac{3}{2}} = 4^{\frac{3}{2}} - a^{\frac{3}{2}} \\ \Rightarrow 2 a^{\frac{3}{2}} = 4^{\frac{3}{2}} \end{array}

$\Rightarrow 4 a^{3} = 4^{3}$ (Squaring both sides)

$\Rightarrow a^{3} = 4^{2}$

$\Rightarrow a = 4^{\frac{2}{3}}$ (Taking cube on both sides)

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Class 12th General Principles and Isolation of Elements

38. Common impurities present in bauxite are

(i) CuO

(ii) ZnO

(iii) Fe₂O₃

(iv) SiO₂

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alok kumar singh

Contributor-Level 10

38. Option (iii) and (iv)

Bauxite consists of many impurities like hematite, goethite, Fe₂O₃, the sand SiO₂, etc.'

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Class 12th The d and f Block Elements

17. Although Cr³⁺ and Co²⁺ ions have same number of unpaired electrons but the magnetic moment of Cr³⁺ is 3.87 BM and that of Co²⁺is 4.87 BM. Why?

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Payal Gupta

Contributor-Level 10

17. Magnetic moment of an electron/dipole moment is caused by its intrinsic properties of spin and electric charge. It depends upon the number of unpaired electrons in its valence shell. The more the number of unpaired electrons, the greater will be the value of magnetic moment.

Cr³⁺ = [Ar] 3d³ = 3 unpaired electrons

Co²⁺ = [Ar] 3d⁷ = 3 unpaired electrons

But as both the ions have the same no. of unpaired electrons, there's one other factor called orbital contribution which also influences the magnetic moment. As, the three unpaired electronic configuration is sy

...more

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Class 12th General Principles and Isolation of Elements

37. In the Froth Floatation process, zinc sulfide and lead sulfide can be separated by

(i) Using collectors.

(ii) Adjusting the proportion of oil to water.

(iii) Using depression.

(iv) Using froth stabilizers.

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alok kumar singh

Contributor-Level 10

37. Option (ii) and (iii)

It is possible to separate two sulfide ores using the froth floatation process by adjusting the proportion of oil to water or by using 'depressants.' In the case of an ore containing ZnS and PbS, for example, the depressant used is NaCN.

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Class 12th Application of Integrals

7. Find the area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2

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Vishal Baghel

Contributor-Level 10

Kindly go through the solution

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New question posted

10 months ago

Class 12th Application of Integrals

7. Find the area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2

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New answer posted

10 months ago

Class 12th The d and f Block Elements

16. Although fluorine is more electronegative than oxygen, the ability of oxygen to stabilize higher oxidation states exceeds that of fluorine. Why?

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Payal Gupta

Contributor-Level 10

16. Fluorine - 1s²2s²2p⁵

Oxygen - 1s² 2s² 2p⁶ 3s² 3p⁶

As we can infer from the electronic configuration, fluorine only has one unpaired electron in its 2p-orbital which can be involved in formation of only one bond and fluorine lacks d-orbital.

While oxygen has d-orbitals in its configuration which allow the oxygen to form multiple bonds. Therefore, oxygen has greater stability to stabilise its oxidation states than fluorine.

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Class 12th General Principles and Isolation of Elements

36. Which of the following statements is correct about the role of substances added in the froth floatation process?

(i) Collectors enhance the non-wettability of the mineral particles.

(ii) Collectors enhance the wettability of gangue particles.

(iii) By using depressants in the process two sulfide ores can be separated.

(iv) Froth stabilizers decrease wettability of the gangue.

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alok kumar singh

Contributor-Level 10

36. Option (i) and (iii)

A suspension of powdered ore is made with water during the froth floatation process. Collectors and froth stabilizers are added to it. Collectors (e.g., pine oils, fatty acids, xanthates, etc.) improve the non wettability of the mineral particles, while froth stabilizers (e.g., cresols, aniline) keep the froth stable

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Class 12th Application of Integrals

6. Find the area of the region in the first quadrant enclosed by x-axis,line $x = \sqrt3y$ and the circle $x^{2} + y^{2} = 4$ .