For JEE-2016 (Concepts i forget in Mathematics)

Hello Guys who are giving Jee 2016.

Lets post Some of the things which we used to Forget every time.

Things That I always forget are:

1). Point from which Perpendicular Tangents can be drawn on a curve lies on Director Circle

2). Equation of Hyperbola (DistanceofpointP(x,y)fromconjugateAxis)2(LengthofsemiTransverseaxis)2(DistanceofpointP(x,y)fromtransverseAxis)2(LengthofsemiConjugateaxis)2=1 \frac { { \quad \left( \quad Distance\quad of\quad point\quad P(x,y)\quad from\quad conjugate\quad Axis \right) }^{ 2 } }{ { \left( \quad Length\quad of\quad semi\quad Transverse\quad axis \right) }^{ 2 } } -\frac { { \left( \quad Distance\quad of\quad point\quad P(x,y)\quad from\quad transverse\quad Axis \right) }^{ 2 } }{ { \left( \quad Length\quad of\quad semi\quad Conjugate\quad axis \right) }^{ 2 } } =1

3). In hyperbola PSPS=2b|PS-P{ S }^{ ' }|=2b Where P is a variable point , S,S,S,{ S }^{ , } are the focus and 2b= Length of transverse axis.

4). Standard deviation(σ)\left( \sigma \right) or Variance(σ)2{ \left( \sigma \right) }^{ 2 } Do no change on adding or subtracting a number from The observation.

5). Standard Deviation gets multiplied by the number "h""h" if we multiply the observations by a positive integer "h""h".

6). eax.sin(bx)dx=eaxa2+b2(asin(bx)bcos(bx))eax.cos(bx)dx=eaxa2+b2(bsin(bx)+acos(bx))\displaystyle \int { { e }^{ ax }.\sin { \left( bx \right) dx } } =\frac { { e }^{ ax } }{ { a }^{ 2 }+{ b }^{ 2 } } \left( a\sin { \left( bx \right) } -b\cos { \left( bx \right) } \right) \\ \displaystyle \int { { e }^{ ax }.\cos { (bx) } dx } =\frac { { e }^{ ax } }{ { a }^{ 2 }+{ b }^{ 2 } } \left( b\sin { \left( bx \right) } +a\cos { \left( bx \right) } \right)

7). d2xdy2=(dy2dy2)(dydx)3\frac { { d }^{ 2 }x }{ d{ y }^{ 2 } } =-\frac { \left( \frac { d{ y }^{ 2 } }{ d{ y }^{ 2 } } \right) }{ { \left( \frac { dy }{ dx } \right) }^{ 3 } }

8). aX(bXc)=(a.c)b(a.b)c\overrightarrow { a } X\left( \overrightarrow { b } X\overrightarrow { c } \right) =\left( \overrightarrow { a } .\overrightarrow { c } \right) \overrightarrow { b } -\left( \overrightarrow { a } .\overrightarrow { b } \right) \overrightarrow { c }

9). In a triangle ABC asin(A)=bsin(B)=csin(C)=abc2=2R\frac { a }{ \sin { \left( A \right) } } =\frac { b }{ \sin { \left( B \right) } } =\frac { c }{ \sin { \left( C \right) } } =\frac { abc }{ 2\triangle } =2R

10). In a triangle ABC tan(BC2)bc=tan(B+C2)b+c=cot(A2)b+c\frac { \tan { \left( \frac { B-C }{ 2 } \right) } }{ b-c } =\frac { \tan { \left( \frac { B+C }{ 2 } \right) } }{ b+c } =\frac { \cot { \left( \frac { A }{ 2 } \right) } }{ b+c }

Please share if you like it.

Also don't Forget to post your concepts that you used to forget at the Papers.

Note by Rishabh Deep Singh
3 years, 6 months ago

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1 vote

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I do understand 4 and 5, but you could rephrase it for clarity. Can you explain 7 in detail?

Agnishom Chattopadhyay Staff - 3 years, 6 months ago

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  1. Product of the lengths of perpendicular drawn from the focii(both) on any tangent to ellipse (or hyperbola) is b2b^2 b is the length of shorter axis

  2. A line that starts from one focus of ellipse after getting reflected from the ellipse , passes through the other focii..

  3. For the parabola ,directrix is the director circle.

I have just completed 11th , so, I can help you only with course of 11th, you may ask if you require

BEST OF LUCK! For JEE-ADVANCED

Which books are prefered to you in RESONANCE for all the subjects

Aniket Sanghi - 3 years, 6 months ago

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They give us Their Own study materials.

Rishabh Deep Singh - 3 years, 6 months ago

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I study in FIITJEE ..we are also given subject materials...but they also tell to refer some subject reference books...I was talking about these books

Aniket Sanghi - 3 years, 6 months ago

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@Aniket Sanghi S.L. Loney, Calculus in one variable .

But i dont do S.L. loney it is useless .

I like their study material And advanced level problems.

Rishabh Deep Singh - 3 years, 6 months ago

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