Tuesday 1 December 2015

QA FUNDAS

‪#‎RattaMaro‬
Post all the shortcut formulas/techniques in Quants here.

Comments
Kartikey Sood
Kartikey Sood Area of |x+a|+|y+b|=k will be 2*k^2

Area of |px+a|+|qy+b|=k will be 2*k^2/(p*q)

like Area of |5x+4|+|3y+2|=4 will be 2*4^2/(5*3)=32/15
Kartikey Sood
Kartikey Sood What would be co-efficient of x^10 in ( 1 + x^2 - x^3)^8

{1+x^2(1-x)}^8
general term: 8Cr {x^2 (1-x)}^r
x^2r han yahaan...now (1-x)^r ka general term: rCt (-x)^t
so 2r+t=10, t<r. so (4,2) and (5,0) 
so 8C4*4C2 + 8C5*5C0= 420+56=476
Divyansh Bhateja
Divyansh Bhateja Bhai ye smjhaade...kbh smjh nh aata iska concept
Debarun Bhuyan
Debarun Bhuyan Binomial expand Karo 2 times
Limiting conditions lagao
Tanveer Iqbal Ahmed
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Kartikey Sood
Kartikey Sood Ptolemy's Theorem : 

AB × DC + BC × AD = BD × AC
Debarun Bhuyan
Debarun Bhuyan Only for cyclic quadrilateral na?
Tanveer Iqbal Ahmed
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Kartikey Sood
Kartikey Sood In an equilateral triangle,
1) sum of distances of any point from the 3 sides = height of triangle. (Viviani's Theorem)
2) Sum of distances of any point from the 3 vertices= side * root 3 approximately
Sudhanshu Ranjan
Sudhanshu Ranjan side *root(3)/2 hoga na ?
Tanveer Iqbal Ahmed
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Kartikey Sood
Kartikey Sood Distance between centroid and orthocenter = 2* distance between Centroid and circumcenter.
The line containing these points = Euler Line. 
If the triangle is isosceles/equilateral, then the Incenter also lies on this

Direct common tangents bewteen 2 circles = root (d^2-(r1-r2)^2 )
Transverse common tangent = root (d^2-(r1+r2)^2)
As is clear, DCT> TCT in length
Akul Chhillar
Akul Chhillar what is D here?
Kritika Sha
Kritika Sha Ofc distance between two centres
Tanveer Iqbal Ahmed
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Shubham Chopra
Shubham Chopra Sum of All digits made by 0,1,2,3,4 . 4!*11111*10 - 3!*1111*10 .
Like · Reply · 1 · 28 November at 15:24 · Edited
Ashish Porwal
Ashish Porwal It is only when repetition is nt allowed
Nishchay Nath
Nishchay Nath Number of ones should be n times and n-1 times
Tanveer Iqbal Ahmed
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Indrajeet Singh
Indrajeet Singh Ye i quanta batch se h na grin emoticon
Tanveer Iqbal Ahmed
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Debarun Bhuyan
Debarun Bhuyan |w|+|x|+|y|+|z|=N, integral solutions? 
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Shiv Mistri
Shiv Mistri Same
As nonnegative integral
Solution : n+r-1c r-1
Saurav Suman
Saurav Suman 8n/3 (n^2+2)
Tanveer Iqbal Ahmed
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Ashish Porwal
Ashish Porwal Anand Mittal ye dekh liyo free time mai ye wala formula kaam ka h
Tanveer Iqbal Ahmed
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Shiv Mistri
Shiv Mistri Hashtag mat maro .. Ye karo..
Shiv Mistri's photo.
Sharmaji Ka Ladka
Sharmaji Ka Ladka Ill delete all hashtags
Tanveer Iqbal Ahmed
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Saurav Suman
Saurav Suman Total no. Of planes/regions formed by n lines ka formula?
Priyanka Rani
Priyanka Rani n(n+1)/2 +1 -n non paralllel
n(n+1)/2 +1 + m (n+1) -n non paralllel nd m paralel
Saurav Suman
Saurav Suman Unbounded?
Tanveer Iqbal Ahmed
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Sharmaji Ka Ladka
Sharmaji Ka Ladka Area of a right triangle giver its inradius and outradius?
Shiv Mistri
Shiv Mistri Area : s*r 
Big area : abc/4R
Sharmaji Ka Ladka
Sharmaji Ka Ladka It was something else
I cant remember,but looked like r^2+2rR....?
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Sum of n natural numbers
-> The sum of first n natural numbers = n (n+1)/2

-> The sum of squares of first n natural numbers is n (n+1)(2n+1)/6

-> The sum of first n even numbers= n (n+1)

-> The sum of first n odd numbers= n^2
Rahul Sharma
Rahul Sharma Maximum/Minimum

-> If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4

-> If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .
Rahul Sharma
Rahul Sharma Mixtures

If Q be the volume of a vessel q qty of a mixture of water and wine be removed each time from a mixture n be the number of times this operation be done and A be the final qty of wine in the mixture then ,
A/Q = (1-q/Q)^n
Rahul Sharma
Rahul Sharma Some Pythagorean triplets:

3,4,5----------(3^2=4+5)
5,12,13--------(5^2=12+13)
7,24,25--------(7^2=24+25)
8,15,17--------(8^2 / 2 = 15+17 )
9,40,41--------(9^2=40+41)
11,60,61-------(11^2=60+61)
12,35,37-------(12^2 / 2 = 35+37)
16,63,65-------(16^2 /2 = 63+65)
20,21,29-------(EXCEPTION)
Sudhanshu Ranjan
Sudhanshu Ranjan sum of a series whose general term is n(n+1)/2 is n(n+1)(n+2)/6. For example : 1+ 3+6+10+15 = 5*6*7/6=35 smile emoticon
Rahul Sharma
Rahul Sharma (m + n)! is divisible by m! * n!
Rahul Sharma
Rahul Sharma 145 is the 3-digit no. expressed as sum of factorials of the individual digits i.e.
145 = 1! + 4! + 5!
Shiv Mistri
Shiv Mistri And 5 digit is 40585 tongue emoticon
Sapna Keshari
Sapna Keshari 4 such numbers exist
and other numbers are 1! and 2!
Like · Reply · 2 · 28 November at 13:15 · Edited
Tanveer Iqbal Ahmed
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Sapna Keshari
Sapna Keshari Where a no. is of the form a^n – b^n, then,
The no. is always divisible by a – b
Further, the no. is divisible by a + b when n is even and not divisible by
a + b when n is odd
ü Where a no. is of the form a^n + b^n, then,
The no. is usually not divisible by a – b
However, the no. is divisible by a + b when n is odd and not divisible by
a + b when n is eve
Sapna Keshari
Sapna Keshari haha grin emoticon
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Where a no. is of the form a^n – b^n, then,

The no. is always divisible by a - b
Further, the no. is divisible by a + b when n is even and not divisible by a + b when n is odd

Where a no. is of the form a^n + b^n, then,

The no. is usually not divisible by a - b
However, the no. is divisible by a + b when n is odd and not divisible by a + b when n is even
Rahul Sharma
Rahul Sharma Pascal's Triangle for computing Compound Interest (CI)
The traditional formula for computing CI is
CI = P*(1+R/100)^N – P
Using Pascal's Triangle,
Number of Years (N) 
-------------------
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
… 1 .... .... ... ... ..1
Eg: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1:
Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331
The coefficients - 1,3,3,1 are lifted from the Pascal's triangle above.

Step 2:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331 (leaving out first term in step 1)
If N =2, we would have had,
Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs.1210
CI = 2 * 100 + 1* 10 = Rs.210
Abhishek Dangayach
Abhishek Dangayach Is this only applicable when R=10% ??
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Where 'P' represents principal and 'R' represents the rate of interest, then, the difference between 2 years' simple interest and compound interest is given by P * (R/100)^2
-> The difference between 3 years' simple interest and compound interest is given by (P * R2 *(300+R))/1003
Rahul Sharma
Rahul Sharma CALENDAR
-> Calendar repeats after every 400 years.
-> Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.
-> Century has 5 odd days and leap century has 6 odd days.
-> In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.
-> January 1, 1901 was a Tuesday.
Rahul Sharma
Rahul Sharma For any regular polygon, the sum of the exterior angles is equal to 360 degrees, hence measure of any external angle is equal to 360/n (where n is the number of sides)

-> For any regular polygon, the sum of interior angles =(n-2)*180 degrees
So measure of one angle is (n-2)/n *180
-> If any parallelogram can be inscribed in a circle, it must be a rectangle.
-> If a trapezium can be inscribed in a circle it must be an isosceles trapezium (i.e. oblique sides equal).
Rahul Sharma
Rahul Sharma For an isosceles trapezium, sum of a pair of opposite sides is equal in length to the sum of the other pair of opposite sides (i.e. AB+CD = AD+BC, taken in order)
Ashish Porwal
Ashish Porwal Saksham Aggarwal He is champ of Quants so dont doubt
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma For any quadrilateral whose diagonals intersect at right angles, the area of the quadrilateral is
1/2*d1*d2, where d1, d2 are the length of the diagonals.
-> For a cyclic quadrilateral, area = root((s-a) * (s-b) * (s-c) * (s-d)), where s=(a + b + c + d)/2
Further, for a cyclic quadrilateral, the measure of an external angle is equal to the measure of the interior opposite angle.
-> Area of a Rhombus = Product of Diagonals/2
Rahul Sharma
Rahul Sharma Given the coordinates (a, b); (c, d); (e, f); (g, h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for
[(a + e)/2, (b + f)/2] = [(c + g)/2, (d + h)/2]
Putin Cat
Putin Cat Area of triangle when coordinates are given!
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Area of a triangle
-> 1/2*base*altitude
-> 1/2*a*b*sin C (or) 1/2*b*c*sin A (or) 1/2*c*a*sin B
-> root(s*(s-a)*(s-b)*(s-c)) where s=(a+b+c)/2
-> a*b*c/(4*R) where R is the circumradius of the triangle
-> r*s ,where r is the inradius of the triangle
Rahul Sharma
Rahul Sharma In any triangle
-> a=b*cos C + c*cos B
-> b=c*cos A + a*cos C
-> c=a*cos B + b*cos A
-> a/sin A=b/sin B=c/sin C=2R, where R is the circumradius
-> cos C = (a^2 + b^2 - c^2)/2ab
-> sin 2A = 2 sin A * cos A
-> cos 2A = cos^2 (A) - sin^2 (A)
Rahul Sharma
Rahul Sharma The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1
Rahul Sharma
Rahul Sharma Appollonius Theorem
In a triangle ABC, if AD is the median to side BC, then
AB2 + AC2 = 2(AD2 + BD2) or 2(AD2 + DC2)
Shiv Mistri
Shiv Mistri Arey Bhai turn on karo notification.. Kyu Hashtag post kar k.. Thread kharab kar rahe ho
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Let a be the side of an equilateral triangle, then, if three circles are drawn inside this triangle such that they touch each other, then each circle's radius is given by a/(2*(root(3)+1))
Saurav Suman
Saurav Suman Chicken nugget.. 
Maxm unattainable value : ab-a-b;
No. Of values that cannot be obtained: (a-1)(b-1)/2
Ashish Porwal
Ashish Porwal CAT level se upar h ye I feel
Saurav Suman
Saurav Suman Just in case tongue emoticon
Tanveer Iqbal Ahmed
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Rashmiranjan Nanda
Rashmiranjan Nanda Abe turn on notification karo # tag ki Maa behen mat karo
Saurav Suman
Saurav Suman Pythagorean triplet general form: n, (n^2-1)/2,(n^2-1)/2 +1. For odd values of n
And
n, (n^2-4)/4, (n^2-4)/4 +2.. when n is even 
Kaam ki cheej hai ratt lo
Rahul Sharma
Rahul Sharma DIVISIBILITY :

Divisibility by 2
-> A number is divisible by 2 if and only if the last digit is divisible by 2.
Divisibility by 3
-> A number is divisible by 3 if and only if the sum of the digits is divisible by 3.
Divisibility by 4
-> A number is divisible by 4 if and only if the last 2 digits is a number divisible by 4.
Divisibility by 5
-> A number is divisible by 5 if and only if the last digit is divisible by 5.
Divisibility by 6
-> A number is divisible by 6 if and only if it is divisible by 2 and 3.
Divisibility by 7
-> To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number, if the resulting number is divisible by 7 then original number is divisible by 7. If you don't know the new number's divisibility, you can apply the rule again.
Divisibility by 8
-> A number is divisible by 8 if and only if the last 3 digits of a number divisible by 8.
Divisibility by 9
-> A number is divisible by 9 if and only if the sum of the digits is divisible by 9.
Divisibility by 10
-> A number is divisible by 10 if and only if the number ends in n zeros.
Divisibility by 11
-> A number is divisible by 11 if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.
Divisibility by 12
-> A number is divisible by 12 if the number is divisible by both 3 and 4
Divisibility by 13
-> To find out if a number is divisible by 13 take the last digit of number and multiple it by 4 and add it to number formed with remaining digits check if the resultant number is divisible by 13. In case resultant number is big repeat process of multiplying last digit by 4 and adding it to number formed by remaining digits.
Sudhanshu Ranjan
Sudhanshu Ranjan ye sahi dala hai guru like emoticon
Tanveer Iqbal Ahmed
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Shubham Dahale
Shubham Dahale What is the formula for consecutive discounts given?
Shiv Mistri
Shiv Mistri CI wala but negative sign
Sharmaji Ka Ladka
Sharmaji Ka Ladka a+b+ab/100...
NOte:Discount is in negative
Tanveer Iqbal Ahmed
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Saurav Suman
Saurav Suman For trapezium abcd.. with ab and cd parallel sides : ( bd^2+ ca^2) = bc^2 + ad^2 + 2ab.cd
Anamika Singh
Anamika Singh should be ad in thhe rhs?
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.
Ashish Porwal
Ashish Porwal Please quote an example sir
Aspirant Cat
Aspirant Cat sign change nhi hogaa toh koi +ve root bhi nhi hoga
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.
Ashish Porwal
Ashish Porwal example please
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)
Rahul Sharma
Rahul Sharma ***VVI***

If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)
Ridhi Arora
Ridhi Arora plz xplain in detail using eg
Sahil Gupta
Sahil Gupta x+x3+x5+x7=has no real roots except x=0
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma (n!)^2 > n^n
Rahul Sharma
Rahul Sharma When a three digit number is reversed and the difference of these two numbers is taken, the middle number is always 9 and the sum of the other two numbers is always 9.
Shiv Mistri
Shiv Mistri Ye sab sum the.. _/\_
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Total no. of prime numbers between 1 and 50 is 15
Total no. of prime numbers between 51 and 100 is 10
Total no. of prime numbers between 101 and 200 is 21
Rahul Sharma
Rahul Sharma The number of squares in n*m board is given by 
= m*(m+1)*(3n-m+1)/6
The number of rectangles in n*m board is given by 
= n+1C2 * m+1C2
Aim Cat
Aim Cat between 1 and 1000 - 168 primes
Vidushi Naudiyal
Vidushi Naudiyal Formula clear nai h. cn u please type?
Shiv Mistri
Shiv Mistri In question whatever is the value of n.. Put in the answer
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma If A can finish a work in X time and B can finish the same work in Y time then both of them together can finish that work in (X*Y)/ (X+Y) time.

If A can finish a work in X time and A & B together can finish the same work in S time then B can finish that work in (XS)/(X-S) time.

If A can finish a work in X time and B in Y time and C in Z time then all of them working together will finish the work in (XYZ)/ (XY +YZ +XZ) time

If A can finish a work in X time and B in Y time and A, B & C together in S time then

· C can finish that work alone in (XYS)/ (XY-SX-SY)

· B+C can finish in (SX)/(X-S); and

· A+C can finish in (SY)/(Y-S)
Rahul Sharma
Rahul Sharma Where a rectangle is inscribed in an isosceles right angled triangle, then, the length of the rectangle is twice its breadth and the ratio of area of rectangle to area of triangle is 1:2.
Saurav Suman
Saurav Suman Side of the square with maxm possible area inside a triangle is base×height/(base+height); 
Works for cube in cone as well
Like · Reply · 6 · 28 November at 13:56 · Edited
Tanya Tewari
Tanya Tewari For selection of non consecutive things in a row n-r+1Cr
Priyanka Rani
Priyanka Rani in a circle its n-r+1Cr - n-r-1Cr-2
Tanveer Iqbal Ahmed
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Anuj Kumar Sinha
Anuj Kumar Sinha Mobile ka poora screenshot chipka de aaj tongue emoticon
Shiv Mistri
Shiv Mistri Train bus rickshaw diaries tongue emoticon
Tanveer Iqbal Ahmed
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Shubham Dahale
Shubham Dahale √(k√(k..... N times)= k^(1-(1/2^n))
Same case but infinite tyms. =k
Sharmaji Ka Ladka
Sharmaji Ka Ladka Perimeter of triangle=N(say 20)
No. of possible triangles shortcut?
Shiv Mistri
Shiv Mistri Matlab tune mera uper wala photo save kia or frame ghar pe lgayega?
Tanveer Iqbal Ahmed
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Mukul Sharma
Mukul Sharma A^n+1 ,B^n-1 hcf???
Rahul Sharma
Rahul Sharma The fifth power of any number has the same
units place digit as the number itself.
Rahul Sharma
Rahul Sharma * If a, b and c give remainders p, q and r
respectively, when divided by the same number H,
then H is HCF of (a-p), (b-q), (c-r) 
* If the HCF of two numbers 'a' and 'b' is H, then,
the numbers (a+b) and (a-b) are also divisible by H.
* If a number N always leaves a remainder R
when divided by the numbers a, b and c, then N = LCM
(or a multiple of LCM) of a, b and c + R.
Shashank Sharma
Shashank Sharma Pratik Sahoo aao bhaiyya. Revision krlo
Rahul Sharma
Rahul Sharma * If N = x^a*y^b*z^c where x, y, z are prime factors. Then,
Number of factors of N = P = (a + 1)(b + 1)(c + 1)

* Number of ways N can be written as product of two
factors = P/2 or (P+1)/2 if P is even or odd respectively

*The number of ways in which a composite number can be
resolved into two co-prime factors is 2^(m-1), where m is the
number of different prime factors of the number.

*Number of numbers which are less than N and co-prime to 
N = N(1-1/a)(1-1/b)(1-1/c)

*If N = (2)^a(y)^b(z)^c where x, y, z are prime factors
Number of even factors of N = (a)(b+1)(c+1)
Number of odd factors of N = (b+1)(c+1)
Rahul Sharma
Rahul Sharma Any single digit number written (P-1) times is
divisible by P, where P is a prime number >5.
Examples: 222222 is divisible by 7
444444….. 18 times is divisible by 19
Rahul Sharma
Rahul Sharma AM ≥ GM ≥ HM is always true. They will be
equal if all elements are equal to each other. If you have
just two values then GM^2 = AM x HM
Sharmaji Ka Ladka
Sharmaji Ka Ladka Shortcut method for finding Rank of word(with and without repetition)
Photo or link
Rahul Sharma
Rahul Sharma SI and CI are same for a certain sum of money
(P) at a certain rate (r) per annum for the first year. The
difference after a period of two years is given by
Δ = PR^2/100^2
Anuj Kumar Sinha
Anuj Kumar Sinha Rahul Sharma bhaiya book likh do _/\_ tongue emoticon
Shashank Sharma
Shashank Sharma Sach m. Rahul Sharma on Aag-The Fire hai tongue emoticon
Anuj Kumar Sinha
Anuj Kumar Sinha Iske que ni kiye tongue emoticon u missed the oppurtunity
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Hands of a clock coincide (or make 180 ) 11
times in every 12 hours. Any other angle is made 22
times in every 12 hours.
Sudhanshu Ranjan
Sudhanshu Ranjan Shiv Mistri ye thoda heavy ho gya tongue emoticon
Tanveer Iqbal Ahmed
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Shiv Mistri
Shiv Mistri Zhellar- don't know how to
Pronounce.
Shiv Mistri's photo.
Rashmiranjan Nanda
Rashmiranjan Nanda Charansparsh gurudev
Shiv Mistri
Shiv Mistri Maine nahi likha hai ye.. Kisi Ne likha hua hai uska dhaap mara:)
Tanveer Iqbal Ahmed
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Harsh Agarwal
Harsh Agarwal No side common Wala kaise hua?
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma If the sum of two or more positive quantities is
constant, their product is greatest when they are equal
and if their product is constant then their sum is the
least when the numbers are equal.
If x + y = k, then xy is greatest when x = y
If xy = k, then x + y is least when x = y
Sahil Singhal
Sahil Singhal are these 6 different different series?
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma Centroid and Incenter will always lie inside the triangle.
- For an acute angled triangle, the Circumcenter and the Orthocenter will lie inside the triangle.
- For an obtuse angled triangle, the Circumcenter and the Orthocenter will lie outside the triangle.
- For a right angled triangle the Circumcenter will lie at the midpoint of the hypotenuse and the
Orthocenter will lie at the vertex at which the angle is 90°.

The orthocenter, centroid, and circumcenter always lie on the same line known as Euler Line.
- The orthocenter is twice as far from the centroid as the circumcenter is.
- If the triangle is Isosceles then the incenter lies on the same line.
- If the triangle is equilateral, all four are the same point.
Rahul Sharma
Rahul Sharma If a circle can be inscribed in a quadrilateral, its
area is given by = √abcd
Like · Reply · 1 · 28 November at 15:21 · Edited
Shiv Mistri
Shiv Mistri Semi perimeter find kiye bina chalega ?
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma A parallelogram inscribed in a circle is always a
Rectangle. A parallelogram circumscribed about a
circle is always a Rhombus.
Debarun Bhuyan
Debarun Bhuyan Set A has m elements, B has n 
Total no of functions 
Onto 
Into ??
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Rahul Sharma
Rahul Sharma Total number of functions : same as distributing n balls into m boxes : n^m ways 

Total onto functions : same as distributing balls into boxes such that no box remains empty : ( inclusion exclusion ) 

INTO : Atleast one empty = Total - Onto
Tanveer Iqbal Ahmed
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Rahul Sharma
Rahul Sharma *Each diagonal divides a parallelogram in two triangles of equal area.

*Sum of squares of diagonals = Sum of squares of four sides
AC^2 + BD^2 = AB^2 + BC^2 + CD^2 + DA^2

*A Rectangle is formed by intersection of the four angle bisectors of a parallelogram
Rahul Sharma
Rahul Sharma NOTE : From all quadrilaterals with a given area, the square has the least perimeter. For all quadrilaterals with a given perimeter, the square has the greatest area.
Rahul Sharma
Rahul Sharma *If a sphere is inscribed in a cube of side a, the radius of the sphere will be a/2. If a sphere is circumscribed about a cube of side a, the radius of the sphere will be √ 3 a/2.

*If a largest possible sphere is inscribed in a cylinder of radius 'a' and height h, its radius r will be r = h/2 {If 2a > h} & r = a {If 2a < h}

*If a largest possible sphere is inscribed in a cone of radius r and slant height equal to 2r, then the radius of sphere = r/rt3

*If a cube is inscribed in a hemisphere of radius
r, then the edge of the cube = r * rt(2/3)
Rahul Sharma
Rahul Sharma If we know three points A(x1,y1), B(x2,y2 ) and C(x2,y2) of a parallelogram, the fourth point is given by (x1 + x3 – x2, y1 + y3 – y2)
Tanveer Iqbal Ahmed
Write a reply...
Rahul Sharma
Rahul Sharma Any set is a subset of itself, but not a proper subset. The empty set, denoted by , is also a subset of any given set X. The empty set is always a proper subset, except of itself. Every other set is then a subset of the universal set.

A set with 'n' elements will have 2^n subsets (2^n – 1 proper subsets)
Rahul Sharma
Rahul Sharma Union of two sets is represented as A B and consists of elements that are present in either Set A or Set B or both. Intersection of two sets is represented as A B and consists of elements that are present in both Set A and Set B. 
n(AUB) = n(A) + n(B) — n(AintersectionB)
Similarly,
n(AUBUC) = n(A) + n(B) + n(C) — n(AintB) — n(AintC) -
n(BintC) + n(AintBintC)
Rahul Sharma
Rahul Sharma Binomial :

*There is one more term than the power of the exponent, n. That is, there are terms in the expansion of (a + b)^n.

*In each term, the sum of the exponents is n, the power to which the binomial is raised.

*The exponents of a start with n, the power of the binomial, and decrease to 0. The last term has no factor of a. The first term has no factor of b, so powers of b start with 0 and increase to n.

*The coefficients start at 1 and increase through certain values about "half"-way and then decrease through these same values back to 1.

*To find the remainder when (x + y)^n is divided
by x, find the remainder when y^n is divided by x.

*(1+x)^n ≅ 1 + nx, when x<<1
Rahul Sharma
Rahul Sharma Circular arrangement of 'n' distinct items: Fix the first item and then arrange all the other items linearly with respect to the first item. This can be done in (n — 1)! ways.

NOTE : In a necklace, it can be done in (n-1)!/2 ways
Rahul Sharma
Rahul Sharma Number of ways of arranging 'n' items out of which `p' are alike, 'q' are alike, 'r' are alike in a line is given by n!/(p!*q!*r!)
Rahul Sharma
Rahul Sharma If all terms of an AP are multiplied with k or divided with k, the resultant series will also be an AP with the common difference dk or d/k respectively.
Rahul Sharma
Rahul Sharma *Range is a subset of Co-Domain. Co-domain may or may not have values which do not have a preimage in the domain.

*It is not a function if for some value in the domain, the relationship gives more than one value.
Eg: f(x) = √x (At x = 4, f(x) could be both +2 and -2)

*Domain cannot have any extra value ie the values at which the function does not exist.

*Even Function: f(x) is even if and only if f(-x) = f(x) for all values of x. The graph of such a function is symmetric about the Y-Axis

*Odd Function: f(x) is odd if and only if f(-x) = - f(x) for all
values of x. The graph is symmetric about the origin

*If f(x) is an odd function and f(0) exists then f(0) = 0
Rahul Sharma
Rahul Sharma Distance between 2 parallel lines ax+by+c1=0 and ax+by+c2=0
is c1-c2/sqrt(a^2 +b^2)
Debarun Bhuyan
Debarun Bhuyan Rahul ,cubes ka de do, no of ways,painted etc
Abhishek Bhardwaj
Abhishek Bhardwaj No of cubes with 3 side painted =8
No of cubes with 2 sides painted = 12(a-2)
No of cubes with 1 side painted = 6(a-2)^2
No of cubes with 0 side painted = (a-2)^3
Like · Reply · 3 · 28 November at 16:15 · Edited
Raghav Grover
Raghav Grover can someone tell the formula for crease formed when a rectangle opposite sides are joined?'
Sharmaji Ka Ladka
Sharmaji Ka Ladka Equilateral triangle inside a circle
Circle inside eq. triangle
Circle inside hexagon
post useful formulas in reply
Anuj Kumar Sinha
Anuj Kumar Sinha Khtm hogye kya formulas? tongue emoticon
Abhishek Agrawal
Abhishek Agrawal Ye bhi yaad rakho
Simple h but imp
Abhishek Agrawal's photo.
Anuj Kumar Sinha
Anuj Kumar Sinha How to solve these types of series que:
Q-2,15,32,53,78,...
Find 20th term

Soln: Look at the series 
2 15 32. 53. 78
Find diffences of terms u get
13. 17. 21. 25
So whenever u get a series whose differences r in AP remember nth term must be of form An^2+Bn+C 
Now how to find that Tn
Let Tn=An^2+Bn+c
Put values 
At n=1
T1=A+B+C=2
At n=2
T2=4A+2B+C=15
At n=3
T3=9A+3B+C=32
3 eqn 3 variable solve u will get 
A=2 B=7 C=-7
Hence Tn= 2n^2+7n-7
Sn=sigma Tn
2*n*(n+1)*(2n+1)/6 + 7*n(n+1)/2 - 7*n
Where n=20
5740+1470 - 140
=7070 

Now generalising it 
When a series is given
1- new series obtained from differences of terms are in ap then u get quadratoc soln
2- if new series obtained from difference is not ap but again u repeat same step and find differences and new series is in ap then its soln will b of 3rd degree that is an^3 + bn^2 + cn + d

So if series is ap after finding difference Kth time, then its soln will have order of degree (K+1)

Though cat exam me max 2 wala hi ayega....worst case me 3rd degree possible...
Anuj Kumar Sinha
Anuj Kumar Sinha Copy pasting my previous post 

Since so many ppl are asking.. m making a post here...
#Chicken_McNugget
For 2 variable- you know the direct formula mn-m-n
Example-Find largest integral amount which can not b paid using denominations 23 and 31 rupee notes.
Ans- 23*31 -23 -31
=659Ans

But for 3 variable there is no such direct formula. Let's see how to solve then.
Q1- Largest integer that can't be formed using denominations of 6, 9 and 20 rupee notes is?
Approach:
6,9,20 
Sabse chota no=6
So write all no of form 6k,6k+1,...6k+5 which can b made using 6,9,20
Ab made ka kya mtlb he..chicken mcnugget is pieces of chicken
Aise smjho KFC gye waha 3 boxes hai ek me 6 chicken hai ek me 9 ek me 20piece
BT they won't sell any loose piece..jab v denge packet bechenge
To Tm kitne kitne khareed skte?
U can never buy 1,2,3..5 chicken pieces..BT 6 kharid skte ho 6 wala packet de denge..
Usi tarah 9 khareeda skte,12 khareed skte n so on...que is max kitna wala nai khareed skte?
Ab approach pe aao. Write all smallest possible no of these form which u can buy
6k=>6 (simply buy 6 wala packet)
6k+1=>49(20+20+9 ye 3 packets buy krne padenge)
6k+2=>20(direct 20 wala)
6k+3=>9(direct 9 wala packet khareedo)
6k+4=>40(20+20 Waale lelo)
6k+5=>29(20+9 wale lelo)
Ab in no me highest kitna hai? 49
Just substract the base packet(6) on which we were working so far
49-6=43Ans

one more Question 
Q2-Largest integeral amount that can't be formed using denominations of 5, 10 and 17 rupee note is?

Soln:
5,10,17
Lowest no lo
Yaha 5
Now write lowest no possible of form which can be made using 5,10,17
5k,5k+1,5k+2...
5k=>5
5k+1=>51(17+17+17)
5k+2=>17
5k+3=>68(17+17+17+17)
5k+4=>34(17+17)
5k+5=5k so yahi tk likhna tha
Ab in sab form ne highest kitna hai?
68 right?
Just do 68-5 =63 Ans
Jo v smallest no tha jisko humne base leke uske form nikale the...WO minus kr denge last me highest no se

lowest possible Jo in 3 no se bana skte us form me
5k+1 jaise
1 not possible
6 not possible
But 17+17+17=51 ye bana skte

5k+3=68 ye wale me
Is form ka 3,8,13... Ye sab nai banta 
But 17+17+17+17 krke 68 bana skte

This is General method. aie 3,4,5, to kya 20 denominations bhi dede thn also u can solve.

I hope it's clear now.
If not then contact guruji jinhone meko sikhaya tha Atul Gandhi sir tongue emoticon
Anuj Kumar Sinha
Anuj Kumar Sinha ok so since yesterday I have got more than 20 msgs asking ki chicknet mcnugget mn-m-n hota hai ya (m-1)(n-1)/2 
Aap log bina smjhe formula rat lete ho.. let's see whats the difference
#Chicken_Mcnugget_2
For any two coprime +ve integers m,n greatest number that can not be written in form am+bn is given by mn-m-n 
and there are exactly (m-1)(n-2)/2 +ve integers that can not be written in that form
Example-You have coins of denomination 23INR and 31INR
1)largest amount that can not be paid using these denominations
Ans- mn-m-n = 23*31-23-31=659
2)No of such integeral amount that can not be paid using these denominations
Ans-(m-1)(n-1)/2 = 22*30/2=330

I hope now u know which formula is used when.
Anuj Kumar Sinha
Anuj Kumar Sinha max no of regions in which plane is divided when m non-parallel lines and n parallel lines are drawn
{1 + m(m+1)/2 } + n(m+1)
Anuj Kumar Sinha
Anuj Kumar Sinha no of times a digit repeats itself while listing integers from 1 to 10^n is n*10^(n-1)

example- no of times digit 8 is repeated from 1- 1000
here 1 to 10^3 so n =3
so 3*10^2=300 times
Like · Reply · 4 · 28 November at 17:20 · Edited
Anuj Kumar Sinha
Anuj Kumar Sinha no of times a no N can be expressed as product of 3 factors-
***special rule
if N can be represented as product of ditinct primes then no of ways are {3^(n-1) +1}/2 where n is no of different primes

example- no of ways 2310 can b expressed as product of 3 factors
2310= 2*3*5*7*11
5 distinct primes so n=5
so 3^4+1/2 = 41Ans
Anuj Kumar Sinha
Anuj Kumar Sinha picks theorem I+ B/2 - 1 = A
I= no of integral pts inside 
B= no of pts on boundary
A= area
Anuj Kumar Sinha
Anuj Kumar Sinha sum upto n terms of fionacci = f(n+2) - f(2)
Anuj Kumar Sinha
Anuj Kumar Sinha 1) X=√(n+ √(n - (√n + (√n - (√n +.... Find X
X= {√(4n-3) + 1}/2

2) X=√(n- √(n + (√n - (√n + (√n -.... Find X
X={√(4n-3) -1}/2

3) X=√(n+ √(n + (√n + (√n + (√n +.... Find X
Just express n=k(k+1) that is write prod of 2 consecutive +ve integer form then X=k+1
Ex- 1) X=√(30+ √(30+(√30 + (√30 + (√30 +.... Find X
N=30=5*6
So X=6

4) X=√(n- √(n - (√n - (√n - (√n -.... Find X

Ex- 1) X=√(30- √(30-(√30 -(√30 -(√30 - ... Find X
N=30=5*6
So X=5
Anuj Kumar Sinha
Anuj Kumar Sinha No of diaginals in a n sided polygon = nc2 - n

Max no of pts of intersection of diagonals in a n sided polygon =nc4 for n>6
Yash Verma
Yash Verma Cauchy ke formula anyone? For max min
Aditya Kranti
Aditya Kranti F(x+1)+F(x-1)=Fx...then cyclicity 6
If - in place of + then cyclicity 3
Rishabh Kumar
Rishabh Kumar Yhi to chahiye tha...... smile emoticon
Sudhanshu Ranjan
Sudhanshu Ranjan Bhai saare formulae yaad hain , IIM A ko bolo questions badha de tongue emoticon
Aditya Tonage
Aditya Tonage Sharmaji Ka Ladka n all those who have shared their knowledge and those who will share further, dil se best of luck for all you guys. Dil khush kar diya tum logo ne.. smile emoticon
Like · Reply · 7 · 28 November at 19:48 · Edited
Zanabe Ali
Zanabe Ali If two bodies A and B start from two opposite ends of a linear track with the speed of X and Y respectively and they take x seconds and y seconds respectively to reach their opposite ends after meeting, then X/Y=[x/y]^(1/2)
Abhishek Dhawan
Abhishek Dhawan nCr + nC(r-1) = (n+1)Cr
Anuj Kumar Sinha
Anuj Kumar Sinha If no of trailing 0s in n! In any base
Multiply no of zeroes * (p-1)
Where p is highest prime factor of given no. In system base and exact no will b slightly more than that...
Ex- 24 zeroes in base 10
10=2*5
So p=5 hence 
24*4=96 se thoda upar...
Exact answr is 100!

Same u can do in any base...
Dipesh Monga
Dipesh Monga if f(x)+f(1/x)=f(x).f(1/x) then f(X)= x^n+1 or-x^n+1
Madhav Srimohan
Madhav Srimohan If the probability of an event occurring is P, then the probability of that event occurring 'r' times in
'n' trials is = nCr x Pr x (1-P)n-r
Sudhanshu Ranjan
Sudhanshu Ranjan if A and B complete a job and individually they take a and b hours respectively , more than the time their combination would have taken , then they do the job together in Root(ab) hours. I think ye chhut gya tha tongue emoticon
Preetika Tayal
Preetika Tayal Rashi Jain Real last minute tips tongue emoticon
Sudhanshu Ranjan
Sudhanshu Ranjan Anuj Kumar Sinha If a thief is running at a m/s and a cop is following at b m/s and he is some D distance behind. There is a dog with the cop having speed speed c m/s. The dog runs from the cop to the thief and turns back and comes back to the cop and goes again to the thief and comes back and so on till the thief is caught (c>b>a obviously tongue emoticon ) . Then if the forward distance by the dog is F and backward is B, F+B = distance traversed by the dog, F-B = distance traversed by the cop.Thus F and B can be found out.
Sourabh Singh Vball
Sourabh Singh Vball Feeling tans for cat exam....
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