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]]>The post Line of Intersection of Two Planes appeared first on MyRank.

]]>**Line of Intersection of Two Planes: **Let two non-parallel planes be \(\vec{r}.{{\vec{n}}_{1}}={{d}_{1}}\)
and \(\vec{r}.{{\vec{n}}_{2}}={{d}_{2}}\) now line of
intersection of planes is perpendicular to vectors \({{\vec{n}}_{1}}\) and \({{\vec{n}}_{2}}\). Therefore, line of intersection is parallel to vector \({{\vec{n}}_{1}}\times
{{\vec{n}}_{2}}\).

find the equation of the of intersection of plane \({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z-{{d}_{1}}=0\) and \({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z-{{d}_{2}}=0\), then we find any point on the line by putting z = 0(say), then we can find corresponding values of x and y by solving equations \({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z-{{d}_{1}}=0\) and \({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z-{{d}_{2}}=0\). Thus, by fixing the value of z = λ, we can find the corresponding value of x and y in terms of λ.

**Example: **Reduce
the equation of line x – y + 2z = 5 and 3x + y + z = 6 in symmetrical form.

**Solution:**

Given x – y + 2z = 5 and 3x + y + z = 6

Let z = λ

x – y + 2λ = 5…(1) and

3x + y + λ = 6…(2)

Solving equation (1) and (2)

x – y + 2λ = 5

3x + y + λ = 6

______________

4x + 3λ = 11

______________

4x = 11 – 3λ

And

From equation (1)

x – y + 2λ = 5

4x – 4y + 8λ = 20

(11 -3λ) – 4y + 8λ = 20

4y = 5λ – 9

4x = 11 -3λ and 4y = 5λ – 9

The equation of the line is \(\frac{4x-11}{-3}=\frac{4y+9}{5}=\frac{z-0}{1}\)

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]]>The post AIIMS-B.Sc (H) Nursing/B.Sc Nursing (Post-Basic)/B.Sc (Paramedical Courses)-2020 appeared first on MyRank.

]]>- All India Institute of Medical Sciences, New Delhi Online applications (Basic Registration followed by Generation of Code and Final Registration) for Entrance Examinations leading to admission in B.Sc(H) Nursing/B.Sc Nursing (Post-Basic)/B.Sc(Paramedical Courses)-2020 of AIIMS, New Delhi and Other AIIMS

Who can apply for Basic Registration and are eligible for B.Sc (H) Nursing course 2020 sesssion |
Candidates who have Passed the 12th Class under the 10+2 scheme/Senior School Certificate Examination or Intermediate Science or an equivalent examination from a recognized University/Board of any Indian State with English, Physics, Chemistry and Biology and has a minimum aggregate marks required in qualifying examination i.e.10+2 or equivalent is 55% for Gen/EWS/OBC and 50% in case of SCs/STs categories |

Who can apply for Basic Registration and are eligible for B.Sc (Paramedical Courses) 2020 session |
Candidate who have Passed 10+2 or equivalent examination with English, Physics, Chemistry and either Biology or Mathematics with 50% for Gen/ EWS/OBC and 45% in case of SCs/ STs Categories |

Who can apply for Basic Registration and are eligible for B.Sc Nursing (Post-Basic) course 2020 session | The candidate who have : (i) Passed 12th class under 10+2 system of education or an equivalent examination from a recognized Board/University (Those who have passed 10+1 on or before 1986 are also eligible). (For BSc Nursing Post-Basic) (ii) Diploma in General Nursing and Midwifery from any institution recognized by the Indian Nursing Council. (For BSc Nursing Post-Basic) (iii) Registration as nurse, RN, RM (registered nurse, registered midwife) with any State Nursing Council (For BSc Nursing Post-Basic) (iv) In case of male nurses, (if passed before implementation of new integrated course in 2003), beside being registered as a nurse with the State Nursing Council, should have obtained a certificate in General Nursing and instead of Training in Midwifery, training in any subject out of following, for a period of six months: i) O.T. Techniques, ii) Ophthalmic Nursing, iii) Leprosy Nursing, iv) TB Nursing, v) Psychiatric Nursing, vi) Neurological and Neuro Surgical Nursing, vii) Community Health Nursing, viii) Cancer Nursing, ix) Orthopaedic Nursing (For BSc Nursing Post-Basic) |

Basic Registration (PAAR) for B.Sc(H) Nursing/B.Sc Nursing (PostBasic)/B.Sc(Paramedical Courses) -2020 | Start Date:12.12.2019 Closing Date:16.01.2020 (5.00 PM) | ||

Status update (Accepted & Not Accepted) of Basic Registration | 20.01.2020 | ||

Correction of deficiencies in Basic Registration that are not Accepted | 21.01.2020 – 30.01.2020 | ||

Final status (Accepted & Rejected) of Basic Registration for B.Sc(H) Nursing/B.Sc Nursing (Post-Basic)/B.Sc(Paramedical Courses) -2020 | 04.02.2020 | ||

Uploading of Prospectus | 12.03.2020 | ||

Generation of Code for Final Registration for B.Sc(H) Nursing/B.Sc Nursing (Post-Basic)/B.Sc(Paramedical courses) -2020 only for those whose Basic Registration is accepted. | Start date: 14.03.2020 Closing date: 15.04.2020 (05:00 PM) | ||

Final Status of B.Sc (H) Nursing application & Rejected application with reason for rejection | 22.04.2020 | ||

Final Status of B.Sc Nursing(Post Basic) and B.Sc (Paramedical Courses) application & Rejected application with reason for rejection | 24.04.2020 | ||

Last date for submission of required documents for B.Sc (H) Nursing/B.Sc Nursing (Post-Basic)/B.Sc (Paramedical Courses)-2020 for Regularization of Rejected Application. No Correspondence will be entertained after 04.05.2020 under any circumstances and candidates are requested not to contact the Examination Section. | 04.05.2020 (05:00 PM) | ||

Hosting/uploading of Admit Cards of B.Sc(H) Nursing on AIIMS website | 13.05.2020 (Tentative) | ||

Hosting/uploading of Admit Cards of B.Sc Nursing (Post-Basic)/ B.Sc(Paramedical courses) on AIIMS website | 15.05.2020 (Tentative) | ||

Date & Timing of Examination of B.Sc Nursing (Post-Basic) | 06th June, 2020 (10.00-11.30 AM) | ||

Date& Timing of Examination of B.Sc (Paramedical courses) | 20th June, 2020 (10.00 – 11.30 AM) | ||

Date & Timing of Examination of B.Sc(H) Nursing | 28th June, 2020 (10.00 – 12.00 Noon) |

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]]>The post Emissive Power, Absorptive Power and Emissivity appeared first on MyRank.

]]>If temperature of a body is more than its surrounding then body emits thermal radiation.

**1) Monochromatic Emittance or Spectral
emissive power\(\left( {{e}_{\lambda }} \right)\): **For a given
surface it is defined as the radiant energy emitted per sec per unit area of
the surface with in a unit wavelength around \(\lambda \) i.e. lying between \(\left(
\lambda -\frac{1}{2} \right)\) to\(\left(
\lambda +\frac{1}{2} \right)\).

Spectral emissive power\(\left( {{e}_{\lambda }} \right)=\frac{Energy}{Area\times Time\times Wavelength}\)

**2) Total Emittance (or) Total Emissive
Power\(\left( e \right)\): **It is defined as
the total amount of thermal energy emitted per unit time, per unit area of the
body for all possible wavelengths.

**3) Monochromatic absorptance or
spectral absorptive power\(\left( {{a}_{\lambda }} \right)\): **It is defined as
the ratio of the amount of the energy absorbed in a certain time to the total
heat energy incident upon it in the same time, both in the unit wavelength
interval. It is dimensionless and unit less quantity.

**4) Total absorptance (or) Total
absorpting power\(\left( a \right)\): **It is defined as
the total amount of thermal energy absorbed per unit time, per unit area of the
body for all possible wavelengths.

**5) Emissivity**\(\left(\varepsilon \right)\): Emissivity of a body at a given temperature is defined as the ratio of the total emissive power of the body\(\left( e \right)\) to the total emissive power of a perfect black body\(\left( E \right)\) at that temperature, i.e. \(\varepsilon =\frac{e}{E}\)

(i) For perfectly black body, \(\varepsilon =1\)

(ii) For highly polished body, \(\varepsilon =0\)

(iii) For practical bodies emissivity \(\left( \varepsilon \right)\) lies between zero and one \(\left( 0<\varepsilon <1 \right)\)

** **

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]]>The post Leibnitz’s Rule appeared first on MyRank.

]]>**Leibnitz’s
Rule:** If f is a
continuous function on [a, b], and u(x) and v(x) are differentiable function of
x whose values lie in [a, b], then \(\frac{d}{dx}\left\{
\int\limits_{u(x)}^{v(x)}{f(t).dt} \right\}=f\left( v\left( x \right)
\right)\frac{dv\left( x \right)}{dx}-f\left( u\left( x \right)
\right)\frac{du\left( x \right)}{dx}\).

**Proof:**

Let d/dx(F(x)) = f(x)

\(\int\limits_{u(x)}^{v(x)}{f(t)dt}=F\left( v(x) \right)-F\left( u(x) \right)\),

\(\frac{d}{dx}\left\{ \int\limits_{u(x)}^{v(x)}{f(t)dt} \right\}=\frac{d}{dx}\left( F\left( v(x) \right)-F\left( u(x) \right) \right)\),

\(\frac{d}{dx}\left\{ \int\limits_{u(x)}^{v(x)}{f(t)dt} \right\}=F’\left( v(x) \right)\frac{d(v(x))}{dx}-F’\left( u(x) \right)\frac{d(u(x))}{dx}\),

\(\frac{d}{dx}\left\{ \int\limits_{u(x)}^{v(x)}{f(t)dt} \right\}=f\left( v(x) \right)\frac{d(v(x))}{dx}-f\left( u(x) \right)\frac{d(u(x))}{dx}\).

**Example:** If \(y=\int\limits_{{{x}^{2}}}^{{{x}^{3}}}{\frac{1}{\log
t}}.dt\) (where x > 0), then
find dy/dx.

Solution:

\(y=\int\limits_{{{x}^{2}}}^{{{x}^{3}}}{\frac{1}{\log t}}.dt\),

\(\frac{dy}{dx}=\frac{d}{dx}\left( {{x}^{3}} \right)\frac{1}{\log {{x}^{3}}}-\frac{d}{dx}\left( {{x}^{2}} \right)\frac{1}{\log {{x}^{2}}}\),

\(\frac{dy}{dx}=\left( 3{{x}^{2}} \right)\frac{1}{\log {{x}^{3}}}-\left( 2x \right)\frac{1}{\log {{x}^{2}}}\),

\(\frac{dy}{dx}=\left( 3{{x}^{2}} \right)\frac{1}{3\log x}-\left( 2x \right)\frac{1}{2\log x}\)\(\frac{dy}{dx}=\left( 3{{x}^{2}} \right)\frac{1}{3\log x}-\left( 2x \right)\frac{1}{2\log x}\),

\(\frac{dy}{dx}=\frac{3{{x}^{2}}}{3\log x}-\frac{2x}{2\log x}\),

\(\frac{dy}{dx}=\frac{{{x}^{2}}}{\log x}-\frac{x}{\log x}\),

\(\frac{dy}{dx}={{x}^{2}}\log {{x}^{-1}}-x\log {{x}^{-1}}\),

\(\frac{dy}{dx}=\log {{x}^{-1}}\left( {{x}^{2}}-x \right)\),

\(\frac{dy}{dx}=\log {{x}^{-1}}x\left( x-1 \right)\).

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]]>The post Streamline, Laminar and Turbulent Flow appeared first on MyRank.

]]>**1)**
**Stream Line Flow: **Stream line flow
of a liquid is that flow in which each element of the liquid passing through a
point travels along the same path and with the same velocity as the preceding
element passes through that point.

A streamline may be defined as the path, straight or curved the tangent to which at any point gives the direction of the flow of liquid at that point. The two streamlines can’t cross each other and the greater is the crowding of streamlines at a place, the greater is the velocity of liquid particles at that place. Path ABC is streamline as shown in the above figure and\({{v}_{1}}\), \({{v}_{2}}\) and \({{v}_{3}}\) are the velocities of the liquid at A, B and C point respectively.

**2)**
**Laminar Flow: **If a liquid is flowing
over a horizontal surface with a steady flow and moves in the form of layers of
different velocities which do not mix with each other, the flow of liquid is
called laminar flow.

In this flow, the velocity of liquid flow is always less than the critical velocity of the liquid. The laminar flow is generally used synonymously with streamlined flow.

**3)**
**Turbulent Flow: **When a liquid moves
with a velocity greater than its critical velocity, the motion of the particles
of liquid becomes disordered or irregular. Such a flow is called a turbulent
flow.

In a turbulent flow, the path and the velocity of the particles of the liquid change continuously and haphazardly with time from point to point. In a turbulent flow, most of the external energy maintaining the flow is spent in producing eddied in the liquid and only a small fraction of energy is available for forward flow. For example, eddies are seen by the sides of the pillars of a river bridge.

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]]>The post Limits – Part2 appeared first on MyRank.

]]>1. \(\underset{x\to 0}{\mathop{\lim }}\,{{\left( 1+x \right)}^{\frac{1}{x}}}=e\ \ (or)\ \ \ \ \ \underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{1}{x} \right)}^{x}}=e\)

\(=\underset{x\to 0}{\mathop{\lim }}\,\left( 1+\frac{1}{x}x+\frac{\frac{1}{x}\left( \frac{1}{x}-1 \right)}{2!}{{x}^{2}}+\frac{\frac{1}{x}\left( \frac{1}{x}-1 \right)\left( \frac{1}{x}-2 \right)}{2!}{{x}^{3}}+…. \right)\)\(=\underset{x\to 0}{\mathop{\lim }}\,\left( 1+1+\frac{1(1-x)}{2!}+\frac{1(1-x)(1-2x)}{3!}+… \right)\),

\(=\left( 1+1+\frac{1}{2!}+\frac{1}{3!}+…. \right)=e\)2. \(L=\underset{x\to a}{\mathop{\lim }}\,f{{\left( x \right)}^{g(x)}}\). If \(\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=1\ \ and\ \ \underset{x\to a}{\mathop{\lim }}\,g\left( x \right)=\infty \)

Then \(L=\underset{x\to a}{\mathop{\lim }}\,f{{\left( x \right)}^{g(x)}}\),

\(L=\underset{x\to a}{\mathop{\lim }}\,{{\left\{ 1+\left( f\left( x \right)-1 \right) \right\}}^{\frac{1}{f\left( x \right)-1}\left( f\left( x \right)-1 \right)\times g\left( x \right)}}\),

\(L=\underset{x\to a}{\mathop{\lim }}\,{{\left\{ {{\left( 1+\left( f\left( x \right)-1 \right) \right)}^{\frac{1}{f\left( x \right)-1}}} \right\}}^{\underset{x\to a}{\mathop{\lim }}\,}}^{\left( f\left( x \right)-1 \right)\times g\left( x \right)}\),

\(={{e}^{\underset{x\to a}{\mathop{\lim }}\,\left( f\left( x \right)-1 \right)\times g\left( x \right)}}\).

**Example**: Evaluate \(\underset{x\to 0}{\mathop{\lim
}}\,{{\left( 1+x \right)}^{\cos ecx}}\)

**Solution: **

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left( 1+x \right)}^{\cos ecx}}\),

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left( 1+x \right)}^{\frac{1}{\sin x}}}\),

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left( 1+x \right)}^{\frac{1}{\sin x}\times \frac{x}{x}}}\),

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ \left( 1+x \right) \right\}}^{\frac{x}{\sin x}\times \frac{1}{x}}}\),

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ {{\left( 1+x \right)}^{\frac{1}{x}}} \right\}}^{\frac{x}{\sin x}}}\),

\(\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ {{\left( 1+x \right)}^{\frac{1}{x}}} \right\}}^{\underset{x\to 0}{\mathop{\lim }}\,\ \ \frac{x}{\sin x}}}\),

\(\because \underset{x\to 0}{\mathop{\lim }}\,{{\left( 1+x \right)}^{\frac{1}{x}}}=e\),

\({{e}^{\underset{x\to 0}{\mathop{\lim }}\,\ \ \frac{x}{\sin x}}}\),

\(={{e}^{1}}\).

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]]>The post Specific Heat of a Gas appeared first on MyRank.

]]>For solids and liquids, we define the specific heat capacity as the quantity of energy that will raise the temperature of unit mass of the body by 1K. For gases, however, it is necessary to specify the conditions under which the change of temperature takes place, since a change of temperature will also produce large changes in pressure and volume.

The specific heat of gas can have many values, but out of them following two values are very important.

1)
**Specific heat at constant volume\(\left(
{{C}_{V}} \right)\): **

The specific heat of a gas at constant volume is defined as the quantity of heat required to raise the temperature of unit mass of gas through \({{1}^{0}}C\) (or) 1K when its volume is kept constant, i.e. \({{c}_{V}}=\frac{{{\left( \Delta Q \right)}_{V}}}{m\,\Delta T}\)

If instead of unit mass, 1 mole of gas is considered, the specific heat is called molar specific heat at constant volume and is represented by\({{C}_{V}}\).

\({{C}_{V}}=M{{c}_{V}}=\frac{M{{\left( \Delta Q \right)}_{V}}}{m\,\Delta T}=\frac{1}{\mu }\frac{{{\left( \Delta Q \right)}_{V}}}{\Delta T}\,\,\,\,\,\left( As,\,\mu =\frac{m}{M} \right)\)2)
**Specific heat at constant pressure\(\left(
{{C}_{P}} \right)\):**

The specific heat of a gas at constant pressure is defined as the quantity of heat required to raise the temperature of unit mass of gas through 1K when its pressure is kept constant, i.e.

\({{c}_{P}}=\frac{{{\left( \Delta Q \right)}_{P}}}{m\,\Delta T}\)If instead of unit mass, 1 mole of gas is considered, the specific heat is called molar specific heat at constant pressure and is represented by\({{C}_{P}}\).

\({{C}_{P}}=M{{c}_{P}}=\frac{M{{\left( \Delta Q \right)}_{P}}}{m\,\Delta T}=\frac{1}{\mu }\frac{{{\left( \Delta Q \right)}_{P}}}{\Delta T}\,\,\,\,\,\left( As,\,\mu =\frac{m}{M} \right)\)The post Specific Heat of a Gas appeared first on MyRank.

]]>The post Limits – Part 1 appeared first on MyRank.

]]>**Limits of the Form \(\underset{x\to a}{\mathop{\lim
}}\,{{\left( f(x) \right)}^{g(x)}}\)– Form: \({{0}^{0}},{{\infty }^{0}}\):**

Let \(L\text{ }=\underset{x\to a}{\mathop{\lim }}\,{{\left( f(x) \right)}^{g(x)}}\) then

Taking log on both sides

\({{\log }_{e}}L\text{ }={{\log }_{e}}\left[ \underset{x\to a}{\mathop{\lim }}\,{{\left( f(x) \right)}^{g(x)}} \right]\),

\({{\log }_{e}}L\text{ }=\left[ {{\log }_{e}}\underset{x\to a}{\mathop{\lim }}\,{{\left( f(x) \right)}^{g(x)}} \right]\),

\({{\log }_{e}}L\text{ }=\left[ \underset{x\to a}{\mathop{\lim }}\,{{\log }_{e}}{{\left( f(x) \right)}^{g(x)}} \right]\),

\({{\log }_{e}}L\text{ }=\left[ \underset{x\to a}{\mathop{\lim }}\,g(x){{\log }_{e}}\left( f(x) \right) \right]\),

\(L\text{ }={{e}^{\left[ \underset{x\to a}{\mathop{\lim }}\,g(x){{\log }_{e}}\left( f(x) \right) \right]}}\).

**Example:** Evaluate
\(\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\)

**Solution:**

Given that \(\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\)

Let us consider\(L=\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}\)

Taking log on both sides

\({{\log }_{e}}L={{\log }_{e}}\left( \underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}} \right)\),

\({{\log }_{e}}L=\left( \underset{x\to \infty }{\mathop{\lim }}\,{{\log }_{e}}{{x}^{1/x}} \right)\),

\({{\log }_{e}}L=\left( \underset{x\to \infty }{\mathop{\lim }}\,\ \frac{1}{x}\times {{\log }_{e}}x \right)\),

\(L={{e}^{\left( \underset{x\to \infty }{\mathop{\lim }}\,\ \frac{1}{x}\times {{\log }_{e}}x \right)}}\),

\(L={{e}^{0}}=1\).

The post Limits – Part 1 appeared first on MyRank.

]]>