Ronit-Maths-problems
On Tue, Feb 9, 2010 at 3:18 PM, Ronit Sen wrote:
Dear Sir,
I am sending you some.Please try for it.
They are as follows:
1)Prove that for all real values of x, the expression 3x^2-6x+10 is always greater that 7.
2)If a^2+b^2+c^2=1 then prove that bc+ca+ab≥-1/2.
3)Find the equation to the straight line which passes through the point (-4,3)
and is such that the portion of the line between the axes is divided at the
point internally in the ratio 5:3.
I did the height and distance sum while giving you the sum.
Please send it to me as fast as possible..
Sir please send it fast.
Our Reply:
Hi Ronit,Find the solutions as below:
1) we can write the expression as 3(x-1)^2+7, since (x-1)^2 will
always be positive, the minimum value of the expression will always be
7, even if x=1, ie, (x-1)^2 is zero.So, your solution is:
3x^2-6x+10
=3(x-1)^2+7Since a square is always positive, the minimum value of the exprssion
will always be 7.2) (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
Now since (a+b+c) is a square, the value has to be greater than zero.
So, a^2+b^2+c^2+2(ab+bc+ca)>0,
So, 2(ab+bc+ca)>-(a^2+b^2+c^2)
So, ab+bc+ca>-1/2.3) The formula to be used here is :
y2-y1/x2-x1=m/n
since it is dividing internally,(y-3)/(x+4)=5/3
so the equation is: 5x-3y+29=0
Thanks
The Target ICSE team
SIR PLEASE SEND ME THE SOLUTIONS OF THESE QUESTIONS….
Q1. What is conversion in java ?
Q2. Differentiate between :
1) p = 6 & p = = 6
2)SDA & DDA
Q3) Answer the following :
1)System.out.println(c=a+b); if a=5,b=6,c=10
2)Debug: short z = (a + b)/2; if int a=6, b= 9;
3)System.out.println(“CTC”+“supports”.substring(4));
4)System.out.println(5 & 6);
5)What is the difference between throw and throws?
6)What are instance variable and instance methods
7)math.rint(38.96)
1. checkAmicable(int,int) – this function returns true if the two arguments are amicable otherwise it returns false.
2. main(int,int) – this function invokes the above function and prints whether the parameters passed to it are amicable or not.
I SHALL BE GRATEFUL TO YOU…..
2)
i) (p = 6)
This means that the integral value of ‘6′ is assigned to the variable ‘p’.This is an assignment operator.
(p == 6)
These type of statements are used when we are checking a condition.Here we are checkinhg whether the value of the variable ‘p’ is ‘6′ or not.