# 1. The mean and median of the data a,b,c are 50 and 35 respectively, where a 2. if sin theta = 3/5 belongs to 2nd quadrant , then cos theta ? 3.there are n Arithmetic mean's between 11 and 53 such that each each of them is an integer. how many distinct arithmetic progressions are possible from above data ? 4.four bells toll at intervals of 10 seconds , 15 seconds, 20 seconds , 30 seconds respectively. if they together at 10.00 A.M. at what time will they toll together for the first time after 10.00 A.M. ? 5. if a-b , b-c are roots of general form of quadratic equation , then (a-b)(b-c)/(c-a) ?

1
by Bindu09

2015-04-15T01:10:48+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
1)  let  a >= b >= c
mean =  (a+b+c) /3  =  50
a+b+c = 150
median is the middle one ,  b = 35
hence,    a + c =  115 .
if we know  one quantity  we can find the other quantity.
=============================
2.    Sin Ф  =  3/5      2nd quadrant.
Cos² Ф = 1 -  sin² Ф = 1 - 9/25 =  16/25
cos Ф =  - 4/5          we put a minus sign because in 2nd quadrant Cosine is negative.
=========
3.    AP  series:    11 , a₁ , a₂ , a₃ ..... a_n  , 53
number of terms = n + 2                first term = 11
common difference :  d
53 = 11 + (n+1) d

(n+1) d = 42  =  7 * 6 = 21 * 2  =  3 * 14  =  1 * 42

So there are 8 combinations possible.  then there could be 8  different series,

all terms are integers,  means that  common difference d  is  an integer.
n is an integer .

case 1:  d = 1   and  n+1 = 42    so n =41,          AP:  11,12,13,14....
case 2:  d = 42  and  n+1 = 1   so  n = 0,        AP:  11, 53, .....
case 3: d = 2  and n+1 = 21  , n = 20,      AP:  11,13,15,..51, 53
case 4: d = 21  and  n +1 = 2,  n = 1,    AP  :  11,  32,  53 , ....
case 5:  d = 3  and  n+1 = 14  , n = 13,    AP :    11,14, 17,...., 50, 53
case 6:  d= 14  and n+1 = 3      n = 2,    AP = 11, 25, 39, 53, ...
case 7 : d = 7  and  n+1 = 6      so n = 5,    AP =  11,18,25,32,39,46, 53,...
case 8:  d = 6,  n+1 = 7,...        so n = 6,    AP :  11, 17,23,29,35,41,47,53,
=======================================
4.    four bells: toll at  intervals of 10, 15 , 20 , 30 seconds ....
the interval between two times that they will toll all togehter will be the LCM of the time intervals of each.

LCM of 10, 15 , 20 , 30 seconds =  2 * 5 * 3  * 2 = 60
So it is one minute.
They will all together at  10 : 01 AM,
==============================
5.        a x² + b x + c = 0  is the general form of quadratic equation.
sum of roots :  - b/a        product :  c/a    --- (3)

[x - (a - b) ] [ x - (b - c) ] = 0  is the quadratic equation.
=>     x² + (c-a) x + (a-b)(b-c) = 0        is the quadratic equation.

It means that  product of roots is  (a - b) (b - c)
sum of the roots = a - b + b - c =   - (c - a)

- b / a  = - (c - a)    =>  b = a (c - a)            ---- (1)
(a - b) (b - c)  = c/a
a b - a c - b² + b c = c/a    --- (2)

given (a-b)(b-c) / (c-a)  = - product / sum  =  - c / -b = c/b    ,,,,,   by using (3)

thanks a lot
:) u are welcome.