direct formula for FIBONACCI NUMBERS (0 1 1 2 3 5.....)
let Un be the nth fibonacci number then
1) U(n-1) + U(n-2) = Un
2) (Un)^2 + ( U(n+1) )^2 = U(2n+1)
3) (Un)^2 - ( U(n-2) )^2 = U(2n-2)
4) (Un)^2 - ( U(n-1) )^2 = U(n-2) * U(n+1)
5) summation (Un)^2 =Un * U(n+1)
6) summation Un = U(n+2) - 1
CAT mei stats aya h kbi? 😛
anyone plz post that rule...a^n +- b^ n is always divisible by a-b or a + b...depending on even or odd..not getting what exactly it is.
Four men E, F, G, H and four women J, K, L, M are going on a hike under the guidance of four trainers U, V, W, X. The teams are formed under the following conditions:
Q)
If
the first two teams formed are (F, H, L, V) and (G, K, W), in how many
different ways can you form the third team if more than one trainer is
allowed in one team?
Can someone explain approach to questions on stocks n shares in profit n loss.
someone posted this on quant thread a few weeks ago..... a very useful stuff..
1) x+y+z+...(r terms) = n
Non negative solutions => (n+r-1)C(r-1)
Positive solns => (n-1)C(r-1)
2) ax+by= n
Non negative integeal solns => [n/lcm(a,b)]+1, if anyone of a or b is divisible by n, otherwise -1
For positive solns remove those including x/y=0 from non negative.
3) |x|+|y|= n has 4n solns
|x|+|y|+|z|=n has 4n^2+2 solns
where n => natural number
when n=0, only 1 soln
For n<0, no soln.
4) xy=N ,where N is natural number
Number of positive solns => Number of factors of N.
Integral soln => 2*Number of factors of N
5) xy= N
Number of unordered positive solns such that x and y are coprimes is 2^(n-1), where n is number of primes containing N.
6) x + y = N, where N => Natural number
Number of positive solutions such that x and y are coprime is Euler of N.
(If N=a^x*b^y, Euler(N)= N(1-1/a)(1-1/b)
7) i) a/x + b/y = 1/n
Number of positive integral solns => factors of a*b*n^2
Number of integral solns => 2*factors of a*b*n^2 - 1.
ii) a/x - b/y = 1/n
Number of integral solns => 2*factors of a*b*n^2 -1
Positive => factors of a*b*n^2 which lies below a*n
8) xyz= N = a^x*b^y
Number of ordered positive integral solns => (x+2)C2*(y+2)C2
Integqral solns => 4* (x+2)C2*(y+2)C2
9) x^2 - y^2 = N
Positive solns => Number of even*even or odd*odd factors if not perfect square otherwise -1
Integral = 4*positive solns
Zero solns if N = 4k+2 form as they are always odd*even form.
10) x^2 + y^2 = N
It will have integer solns only if N contains primes of the form 4k+1 type.
If all primes are 4k+1 type
Then positive solns => number of factors of N, (Be careful in case of perfect square) it will be -1 than
If it contains some 4k+3 primes with odd power then 0 solns
If it contains even powers of 4k+3 primes, then positive solns = number of factors of 4k+1 form only.
Integral solns = 4*positive solns
GEOMETRY
If the given quad is an isosceles trapezium ABCD then
AC*BD = AB*CD + AD*BC (ptolemy's theorem)
line of euler
for a non equilateral tri ABC be such that its centroid is at point G orthocenter at H and circumcenter at C
then all the tree points are collinear(lie on the same line called the euler line)
such that HG =2GC
Quant in Final Lap!
if quad ABCD is a square or a rectangle or a ||gm or a rhombus then area of tri PAB (where P is a point on CD) is always 1/2 the area of quad ABCD
pls tell the method to find nth digit when all natural no.s are written
in sequence from left to right..The
surprising thing isn't that so few people buy works of literature
nowadays, but that so many still do. The recent commercial success of
challenging novels, such as Roberto Bolaño's "2666" or "The Brief
Wondrous Life of Oscar Wao", by Junot Diaz, for example, proves that
American readers are hungry for serious, original writing. Yet it has
become almost impossible to find out what's actually good, short of
reading the books themselves. A book's very placement in a bookstore at
the moment is almost always paid for and fewer of us live anywhere near
an actual bookstore. ____________ .
Q 60-62
@eshanrock@SJ411@darchangel@rafaelnadal@HueyNot exactly Geometry but I've encountered such questions in a few mocks
https://drive.google.com/file/d/0B1zIq2LPoIbFYTYxQ1pyWHNpTWs/view?usp=sharing
A. Who can trace to its first beginnings the love of Damon for Pythias, of David for Jonathan, of Swan for Edgar?
B. Similarly with men.
C. There is about great friendships between man and man a certain inevitability that can only be compared with the age old association of ham and eggs.
D. One simply feels that it is one of the things that must be so.
E. No one can say what was the mutual magnetism that brought the deathless partnership of these
wholesome and palatable foodstuffs about.
Incorrect Usage:
Help
Insane Problem. Solve this if you can!
Two cars A and B start simultaneously from points P and Q with certain speeds towards each other. After reaching a point R, speed of A reduces by 1/3rd. It then meets B at a point S, where SQ=2PR. If the speed of A reduces by 1/3rd at the midpoint of RS, the cars would have met at T, where ST=PR/4. Find RS:PR.
Four alternative summaries are given below each text. Choose the option that best captures the essence of the text.
Some decisions will be fairly obvious - “no-brainers.” Your bank account is low, but you have a twoweek vacation coming up and you want to get away to some place warm to relax with your family. Will you accept your in-laws‟ offer of free use of their Florida beachfront condo? Sure. You like your employer and feel ready to move forward in your career. Will you step in for your boss for three weeks while she attends a professional development course? Of course.
A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the
hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the
triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square
inches) of the smaller triangle?
Two motorcyclists, Ajay and Vijay, start simultaneously from a point S on an oval track and drive around the track in the same direction, with speeds of 29 km/hr and 19 km/hr respectively. Every time Ajay overtakes Vijay (anywhere on the track), both of them decrease their respective speeds by 1 km/hr. If the length of the track is 1 km, how many times do they meet at the starting point before Vijay comes to rest?