@iLoveTorres said:Bhai awesome status. superlikes!!
ohh.thx.. :)
@scrabbler said:What if Hockey is student 1 to 40 and 71-100?Look at the attached doc please.regardsscrabbler
Thanks @scrabbler for correction, got your point!
13. If a^2 + b^2 + c^2 = 1, then ab + bc + ca lies in
(A) [1/2,1]
(B) [ā1, 1],
(C) [ā1/2,1/2]
(D) [ā1/2, 1] .
(A) [1/2,1]
(B) [ā1, 1],
(C) [ā1/2,1/2]
(D) [ā1/2, 1] .
@ishu1991 said:13. If a2 + b2 + c2 = 1, then ab + bc + ca lies in(A) [1/2,1](B) [ā1, 1],(C) [ā1/2,1/2](D) [ā1/2, 1] .
option D..??
@sbharadwaj said:option D..??
@ishu1991 :
Range of : ab+bc+ca
Consider a=b=c. you'll get it as 1. Hence, option C ruled out.
Consider a=b=0; c=1; you'll get 0. Option A ruled out.
Now b/w B and D.., ab+bc+ca cannot be -1. Hence, D.
PS: Correct me if I'm wrong. Also tag me if any other approach is mentioned.
Range of : ab+bc+ca
Consider a=b=c. you'll get it as 1. Hence, option C ruled out.
Consider a=b=0; c=1; you'll get 0. Option A ruled out.
Now b/w B and D.., ab+bc+ca cannot be -1. Hence, D.
PS: Correct me if I'm wrong. Also tag me if any other approach is mentioned.
@sbharadwaj said:@ishu1991 :
Range of : ab+bc+ca
Consider a=b=c. you'll get it as 1. Hence, option C ruled out.
Consider a=b=0; c=1; you'll get 0. Option A ruled out.
Now b/w B and D.., ab+bc+ca cannot be -1. Hence,D.PS: Correct me if I'm wrong. Also tag me if any other approach is mentioned.
U used option elimination approach-
but the basic approach is like:
(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
Since (a+b+c)^2>=0
=>a^2+b^2+c^2+2(ab+bc+ca)>=0
but a^2+b^2+c^2=1(given)
=>1+2(ab+bc+ca)>=0
or ab+bc+ca>=-1/2
and max occurs for a=b=c
thus (ab+bc+ca)=(a^2+b^2+c^2)
=1
So the range is[-1/2,1]
The value of
nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)
equals
(A) 2^n + n2^(nā1)
(B) 2^n ā n2^(nā1),
(C) 2^n,
(D) 2^(n+2)
nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)
equals
(A) 2^n + n2^(nā1)
(B) 2^n ā n2^(nā1),
(C) 2^n,
(D) 2^(n+2)
@ishu1991 said:The value of
nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)
equals
(A) 2^n + n2^(nā1)
(B) 2^n ā n2^(nā1),
(C) 2^n,
(D) 2^(n+2)
option A??
@ishu1991 said:The value of
nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)
equals
(A) 2^n + n2^(nā1)
(B) 2^n ā n2^(nā1),
(C) 2^n,
(D) 2^(n+2)
put n=2
you would get nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)=8
put n=2 in the options ,only A would give the correct answer
@ishu1991 said:The value ofnc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)equals(A) 2^n + n2^(nā1)(B) 2^n ā n2^(nā1),(C) 2^n,(D) 2^(n+2)
option a?
@ishu1991 said:The value ofnc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)equals(A) 2^n + n2^(nā1)(B) 2^n ā n2^(nā1),(C) 2^n,(D) 2^(n+2)
A??
@ishu1991 @ishu1991
@ishu1991 said:13. If a^2 + b^2 + c^2 = 1, then ab + bc + ca lies in(A) [1/2,1](B) [ā1, 1],(C) [ā1/2,1/2](D) [ā1/2, 1] .
it should be given in the question that a,b,c are real no
if a,b,c are real no then
(a+b+c)^2 >= 0
so a^2 + b^2 + c^2 +2(ab + bc +ca) >= 0
put value
1 + 2(ab + bc +ca) >=0
ab+bc+ca >= -1/2
and
(a-b)^2 + (b-c)^2 + (c-a)^2 >= 0 (bcs a,b,c are real no)
then 2(a^2+b^2+c^2) - 2(ab+bc+ca) >=0
=> (a^2+b^2+c^2) > =(ab+bc+ca)
=> 1 >= (ab+bc+ca)
so range [-1/2, 1]
if a,b,c are real no then
(a+b+c)^2 >= 0
so a^2 + b^2 + c^2 +2(ab + bc +ca) >= 0
put value
1 + 2(ab + bc +ca) >=0
ab+bc+ca >= -1/2
and
(a-b)^2 + (b-c)^2 + (c-a)^2 >= 0 (bcs a,b,c are real no)
then 2(a^2+b^2+c^2) - 2(ab+bc+ca) >=0
=> (a^2+b^2+c^2) > =(ab+bc+ca)
=> 1 >= (ab+bc+ca)
so range [-1/2, 1]
anil can make 5 books in 2 hrs nd 6 pens in 3 hrs bimal takes 2 hrs to make 6 pens nd 3 hrs to make 5 books..to make 100 books nd 100 pens together ,what is the minimum time they take?
@falcao said:anil can make 5 books in 2 hrs nd 6 pens in 3 hrs bimal takes 2 hrs to make 6 pens nd 3 hrs to make 5 books..to make 100 books nd 100 pens together ,what is the minimum time they take?
Options? I am getting something like 37hrs 20 min...by letting B make all the pens and then join A to finish the books...
regards
scrabbler
regards
scrabbler
@falcao said:anil can make 5 books in 2 hrs nd 6 pens in 3 hrs bimal takes 2 hrs to make 6 pens nd 3 hrs to make 5 books..to make 100 books nd 100 pens together ,what is the minimum time they take?
Anil.
1 Hour - 2.5 Books and 2 Pens.
Bimal.
1 Hour - 5/3 Books and 3 Pens.
Bimal 32 hours => 96 Pens.
Anil 32 hours => 80 Books.
Rest 4 Pens in 2 hours by Anil.
2 hours Bimal makes 10/3 Pens.
So next 4 hours => 4*25/6 = 50/3 Pens.
Thus, 32 + 2 + 3.3 = 37 Hours 20 Minutes.
@scrabbler said:Give him 33 hours na? 99 pens ho jayega....or even better 33hrs 20 min, 100 pens ho jayega.regardsscrabbler
Haan! :)
Got it Sir. /m\
@ishu1991 said:The value of
nc0+ 2(nc1)+ 3(nc2)+ . . . + (n + 1)(ncn)
equals
(A) 2^n + n2^(nā1)
(B) 2^n ā n2^(nā1),
(C) 2^n,
(D) 2^(n+2)
Differentiate binomial expansion of (1+x)^n w.r.t. x and put x=1
Now put x=1 in binomial expansion of (1+x)^n and add the two....
|a|+|b|+|c|+|d| = 10
a,b,c,d are integers.
How many solns possible??