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 ankur gupta's messages in the community 1 2 3 ... 11 12 13 GO Go to Page...
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 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

e^(-y)dy = (e^x) dx

integrating both sides

-e^(-y)= e^x + c

e^x + e^(-y) +c =0

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
i think tmh is best book for maths ,i used it nd i like it very mch ......u shoud do all the different ques of tmh and examples also it wl make maths very strong for sure....nudge me if u want to knw morethanks.........
 Discussion Forums -> This Post 2 points    (0    in 1 votes )   [?]

a(n)= 1+ (1/2+1/3)+ (1/4+1/5+1/6+1/7)+....... < 1+ (1/2+1/2)+ (1/4+1/4+1/4+1/4) +..............

put n=100

a(100) < 1+(1)+(1)+..........upto 100 terms

a(100)<100

so option a is correct

again ,

a(n) = 1+ (1/2+1/3)+ (1/4+1/5+1/6+1/7) +......  > 1 + (1/4+1/4)+ (1/8+1/8+1/8+1/8)..........

put n= 200

a(200) > 1+ [(1/2)+(1/2) + .......upto 199 terms]

a(200) > 1+ 99.5a(200) > 100.5

so option d is also correct

thus , a and d are the ans

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

focii = (0,be) and (0,-be)

eq of directrix :- y=b/e , y= -b/e

eq of major axis :- y=0

eq of minor axis :- x=0

length of latus rectum = 2a^2/b

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

2)Total no. of arrangements  =  No of possible arrangements when the delegates of the countries A and B r  seated nxt 2 each other  -  No of possible arrangements when the delegates of the countries A and B r  seated nxt 2 each other and C and D r also seated next 2 each other

so, Total no of arrangements   = 8!*2! - 7!2!2!

hopeu gt it

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

2) i m just correcting nikhil's sol....

nikhil method is correct till p=9

now , a = p/cos60 = 18and b= p/sin60 = 18/sqrt(3)

so, the equation of line is

x/18 + ysqrt(3)/18 =1

x + ysqrt(3) = 18

hope u gt it .....in case of ny problem tl me...

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
let max. speed be v
so, total time (t) = v/A +v/B

v = (A+B)t/2 --------(1)

for the first half when car acc with A
s1= distance travelled = v^2/(2A)
s2=distance travelled in second half = v^2/( 2B)

total distance travelled = v^2 (1/2A + 1/2B)
s= v^2 (A+B)/2AB
s = (A+B)^3 (t) /8AB

average velocity = s/t = (A+B)^3/8AB
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
let rate of diffusion of hydrogen = r
and rate of difffusion of oxygen = d

nw r=50/20
d= 45/t

and r/d = sqrt(mol mass of oxygen/mol mass of hydrogen)
r/d= sqrt(32/2)

r=4d
50/20 =4(45/t)

t=72 mins
 Discussion Forums -> This Post 7 points    (1    in 2 votes )   [?]
let the g.p be
a,ar,ar^2,..........upto (2n) terms

sum of all terms (S1) = a(1-r^(2n)) / (1-r)

terms occuping odd places wl also be g.p
with first term a and commomn ratio r^2 and upto n terms

sum of terms occuping odd places (S2) = a[1-(r^2)^n] / (1-r^2)

nw S1 = 5(S2)
a/(1-r) = 5a/(1-r^2)
1-r^2 = 5 - 5r
r^2 -5r +4 =0
r=4 , r= 1(not possible )

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
the pts at which ordinate decrease at the same rate at which the absicssa increase ,
dy/dx = -1

now differentiating the ellipse equation
32x + 18y.(dy/dx)=0
put dy/dx=-1 to get those pts.

so , we get 18y=32x
9y=16x
put this in the ellipse equation ,
we get the pt (3,16/3) and (-3 , -16/3)
hope u gt it ...........
 Discussion Forums -> This Post 4 points    (0    in 2 votes )   [?]
this ques can be solved by using limit as a sum

= (1/n) (summation ) [n^3 / (3n+r)^3]

= integration (from 0 to 3 ) (3+x)^(-3)

integrate it and dput the limits and u wl get the answer.......
hope u gt it ....
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
let its general term = an^2 +bn +c
now put n=1 , n=2 , n=3
a+b+c = 2 ----------(1)
4a+2b+c = 5 ------------(2)
9a+3b+c = 9 ------------(3)
solving (1), (2) , (3)

a=1/2 , b=3/2 , c=0

so general term = (n^2+3n)/2
sum to n terms = [n(n+1)(2n+1)/6 + 3(n)(n+1)/2 ]/2
= (n)(n+1)(n+5)/6

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
solution:-
(1,1,z) where z belongs to whole nos.
(1,y,0) where y belongs to natural nos.
(2,3,1)
(3,3,2)
(3,9,1)

 Discussion Forums -> This Post 15 points    (3    in 3 votes )   [?]
Tk = [(k+1)-1](k!)
= (k+1)! - (k!)
as we hv expressed general term as diff of two consecutive terms ,

thus Sn = (n+1)! - 1
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
n{x} = {x}+2[x]
{x} = 2[x] / (n-1) where n-1 >0

0<= 2[x]/(n-1) <1
so,0<= [x] < (n-1)/2
as x has exactly five solutions so [x]can take 5 values
so , [x] =0 ,1 ,2,3,,4
so, 0 <= [x] <5
thus, (n-1)/2 = 5
n = 11

if n= 12
then 12{x} = {x} +2[x]
{x} = 2[x] /11
then [x] can take values = 0,1,2,3,4,5
so six solutions .
thus the only answer is n=11
 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]
1) put 10^x +x^10 = t
10x^9 + (10^x) (log10) = dt
then,
integral dt/ t
= ln (t)
= ln ( 10^x +x^10)

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]
2) f(x) = lim (n tends to infinity ) (x^2n - 1) / (x^2n + 1)
as 0thus , f(x) = -1 [as lim (n tends to infinity) (x^2n) =0 ]

nw integral -sin^(-1)x dx

which can be easily calculated by appplying by parts........
 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]
1) integral [2^(x+1) -3^(x-1)] / (2^x.3^x)

integral 2/ (3^x) - 1/ 3.(2^x)

= -2ln(3) / 3^x + ln(2) / 3.(2^x)

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]
4) put ln(ln(lnx)) = t
dx/ (xln(lnx) lnx) = dt
then
=integral tdt
= t^2/2

 Discussion Forums -> This Post 7 points    (1    in 2 votes )   [?]
xdx(y+1) = (x^2+1)(y^2+1)dy

xdx/ (x^2+1) = (y^2+1)dy/ (y+1)

xdx/ (x^2+1) = (y^2-1)dy / (y+1) + 2dy/(y+1)

xdx / (x^2+1) = (y-1)dy +2dy/(y+1)

1/2 log(x^2+1) = [(y-1)^2]/ 2 +2log(y+1) +c

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