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techack

Hi friends, why don't we use this thread to share shortcut tips n techniques on various Topics. This will be quite helpful to other forum members too.

So let's start sharing!

nunoxic

Here Are 2 (which most of u already know i think)

1. when a matrix is given and its inverse is asked for (along with 4 options) instead of solving the matrix to find the inverse, its much easier to multiply the matrix to the 4 options... AxA^Inverse=1 there is no need to multiply entirely...if u get some number which is not 1 in a₁₁ stop and goto next option or else continue
2.similarly when 3 equations are to be solved using matrices and options r given best way is to substitute values of x,y,z.....

saket_brutus

Hi,

I have a few that u guys may already know. Here goes :-

1) loss of energy in an inelastic collision

= [m₁m₂ (v₁-v₂)²(1-e)²] / 2(m₁+m₂)

2) fraction of KE transferred in an elastic collision where ,m₁=m; m₂=xm

=4x / (1+x)²

3) if a bullet or any body loses f fraction of velocity after every collision with a plank, then no. of planks required to stop the bullet=1 / (1-(1-f)²)

4) a body is projected from a step (stair has 'n' steps) of height 'h'and breadth 'b'. if the body hits the nth step, then square of projection velocityu²=ngb²/ 2h

5)

dx / x(1+xⁿ) = (1/n) log(xⁿ/1+xⁿ) +c

6) IF cos^-1x + cos^-1y + cos^-1z=pi, then x²+y²+z²+2xyz = 1

7) IF sin^-1x + sin^-1y + sin^-1z=pi, then x(1-x²)+y(1-y²)+z(1-z²) = 2xyz

8) IF tan^-1x + tan^-1y + tan^-1z=pi, then x+y+z=xyz

9) tan^-1(x/y) + tan^-1(y-x / y+x) = pi/4

10) IF tan^-1x + tan^-1y =pi/2 or cot^-1x + cot^-1y = pi/2, then xy=1

Cheers.

AAKRITI

It would be really helpful if experts also contribute.

techack

Thanks for ur contribution saket_brutus & nunoxic

techack

hey long time...no new contributions??

chimanshu_007

well i have posted some good shrtcts...but many of u havent seen them...

so here m posting (pasting them 1ce more)

shrtct to find eqn of tangent to ellipse

eg. take this

Q)find the eqn of ellipse if its eqn of chord is 2x² + 5y² = 20 which is bisected at (2,1) ??????????

Sol....first write eqn in terms of xx₁ and yy₁

like 2xx₁+ 5yy₁= 20

now satisfy this pt. (2,1) here

it will bcome 4x + 5y = 20 now subtract coeff. of x and y (given in very first eqn) frm the rt. hand side's const. term

final ans is 4x + 5y = 13

chimanshu_007

1)The value of 2.357 (bar on 357) is?

in these typeof qs look at the no. of terms having bar on them (here three)
so denominator will b 999 (if 2 terms hav bar then it will b 990 etc....)

then write 2357 and subtract the no. bfore decimal i.e

2357-2 = 2355
so the ans will be 2355 / 999

2) an + bn / an-1 + bn-1

= o then it is Harmonic mean
= 1 then it is Arthmetic mean
=1/2 then it is Geometric mean

3) If in a GP of +ive terms any term is = to sum of next 2 terms then common ratio is........................2sin18 degrees

4)Image of interval ( functions)

Image of interval ( -1 , 3 )
f (x) = 4x3 - 12x is.............................
jst satisfy both the values ans comes out to b 8 and 72 but..................
look at coeff. of intervals i.e. -1 and +1
so ans is (-8 , 72)

chimanshu_007

1)

= 2pi (

x) / lamda

= phase diff. ................del. x is path diff.

2)normal shift

S = t (1 - 1/

).....................(

is not whole divided)

S_water = t/4

S_glass = t/3

3)wen a lens is cut into 2 = parts perpendicular to its principal axis , focal length gets doubled and power gets halved

4)wen a lens is cut into 2 = parts parallel to its P. Axis , no change in focal length or power takes place

5)Goggles donot hav any power coz R1 = R2 = R for them

so p = (

- 1) (1/R1 - 1/R2)

6)wen a lens is submerged in a denser medium its focal length inc and power dec.

7)wen a lens is submerged in water its focal length inc by 4 times and power dec. by 4 times

8)wen a lens is submerged in a medium of greater R.I then its nature reverses

9)Min. length of a plane mirror reqired to see full image of the object of ht. 'h' is h/2

10)* formula to calculate no. of images frmed b/w 2 mirrors is given by

n = 360/theta - 1

eg. if theta is 60.

then n = 5

Plz donot rate me here....m not pasting them to earn rates plzz....its to help u all...

if u wish to rate , then rate where i have posted this article...u have to find it , sorry...

cheers!!!!!!

Selvaganesh_i

finding adjoint of 2X2 matrix is easy.....

eg:

A = a b

c d

Adj(A) = d -b

-c a

Selvaganesh_i

finding adjoint of 2X2 matrix is easy.....

eg:

A = a b

c d

Adj(A) = d -b

-c a

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