Question and Answers Forum

A party of 7 members is to be chosen from a group of 6 ladies and 5 gents. In how many ways can the party be formed if it is to contain (i) exactly 4 ladies (i) at least 4 ladies (i) at most 4 ladies ?

$A party of 7 members is to be chosen$ $from a group of 6 ladies and 5 gents .$ $In how many ways can the party be$ $formed if it is to contain$ $(i) exactly 4 ladies$ $(i) at least 4 ladies$ $(i) at most 4 ladies ?$

Question Number 6111 Answers: 1 Comments: 0

log^2 x+logx^2 −3=0 , x=?

${l o g}^{2} x + {l o g x}^{2} - 3 = 0, x = ?$

Question Number 6146 Answers: 1 Comments: 0

Determine the value of sin ((Π/3)+p)cos ((Π/6)+p)−cos ((Π/3)+p)sin ((Π/6)+p)

$D e t e r m i n e t h e v a l u e o f \sin (\frac{Π}{3} + p) \cos (\frac{Π}{6} + p) - \cos (\frac{Π}{3} + p) \sin (\frac{Π}{6} + p)$

Question Number 6145 Answers: 1 Comments: 0

show that sin 64^(° ) ×cos 26^° + cos 64^(° ) × sin 26^° =1

$s h o w t h a t \sin 64^{°} \times \cos 26^{°} + \cos 64^{°} \times \sin 26^{°} = 1$

Question Number 6090 Answers: 1 Comments: 0

Question Number 6086 Answers: 1 Comments: 0

Find the solution of the differential equation (y − x + 1)dy − (y + x + 2)dx = 0

$F i n d t h e s o l u t i o n o f t h e d i f f e r e n t i a l e q u a t i o n$ $(y - x + 1) d y - (y + x + 2) d x = 0$

Question Number 6087 Answers: 0 Comments: 2

Given the terms a_k and a_(k + r ) of an A.P find a_1 and a_(k + r) in terms of a_(k ) and a_(k + r)

$G i v e n t h e t e r m s a_{k} a n d a_{k + r} o f a n A . P$ $f i n d a_{1} a n d a_{k + r} i n t e r m s o f a_{k} a n d a_{k + r}$

Question Number 6071 Answers: 0 Comments: 2

SHARING: Martin Gardner (famous mathematician) found a way to write his name so that it can also be read upside down. See the comment below

$SHARING :$ $Martin Gardner (famous mathematician)$ $found a way to write his name so that it can$ $also be read upside down .$ $See the comment below$

Question Number 6058 Answers: 0 Comments: 1

sin(a)=sin(−a) For what values of a is the statement true?

$\sin (a) = \sin (- a)$ $For what values of a is the statement true ?$

Question Number 6056 Answers: 1 Comments: 3

Question Number 6055 Answers: 1 Comments: 0

ln(x)+x=a x=?

$l n (x) + x = a$ $x = ?$

Question Number 6054 Answers: 1 Comments: 2

Determine distance between opposite corners of a cubic room of dimention x units.

$D e t e r m i n e d i s t a n c e b e t w e e n$ $o p p o s i t e c o r n e r s o f a c u b i c$ $r o o m o f d i m e n t i o n x u n i t s .$

Question Number 6045 Answers: 1 Comments: 1

4^x = 2x find x

$4^{x} = 2 x$ $f i n d x$

Question Number 6044 Answers: 0 Comments: 2

Find the locus in the complex plain such that arg ((z/(z + 2))) = (Π/2) please help.

$F i n d t h e l o c u s i n t h e c o m p l e x p l a i n s u c h t h a t$ $a r g (\frac{z}{z + 2}) = \frac{Π}{2}$ $p l e a s e h e l p .$

Question Number 6043 Answers: 1 Comments: 0

The number of positive integral pairs satisfying the equation tan^(−1) a + tan^(−1) b = tan^(−1) 3 is

$The number of positive integral pairs$ $satisfying the equation$ $\tan^{- 1} a + \tan^{- 1} b = \tan^{- 1} 3 is$

Question Number 6042 Answers: 0 Comments: 4

Can you solve the indefinite integral: ∫e^(−u) u^n du

$Can you solve the indefinite integral :$ $\int e^{- u} u^{n} d u$

Question Number 6028 Answers: 0 Comments: 2

Can you please show me how to solve: L=lim_(n→∞) (x^n /(n!))

$Can you please show me how to solve :$ $L = \lim_{n \to \infty} \frac{x^{n}}{n!}$

Question Number 6027 Answers: 0 Comments: 3

x^x =e^(xln x) e^x =1+x+(x^2 /(2!))+(x^3 /(3!))+... ∴ e^(xln x) = 1+xln(x)+(((xln x)^2 )/(2!))+... e^(xln x) = (((xln x)^0 )/(0!))+(((xln x)^1 )/(1!))+(((xln x)^2 )/(2!))+... x^x =e^(xln x) =Σ_(n=0) ^∞ ((x^n (ln x)^n )/(n!)) Question: ∫_0 ^( 1) x^x dx=Σ_(i=0) ^∞ ∫_0 ^1 ((x^n (ln x)^n )/(n!))dx by substituting: x=exp(−(u/(n+1))), 0<u<∞ show that: ∫_0 ^( 1) x^n (ln x)^n =(−1)^n (n+1)^(−(n+1)) ∫_0 ^( ∞) u^n e^(−u) du

$x^{x} = e^{x \ln x}$ $e^{x} = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . .$ $∴ e^{x \ln x} = 1 + x \ln (x) + \frac{{(x \ln x)}^{2}}{2!} + . . .$ $e^{x \ln x} = \frac{{(x \ln x)}^{0}}{0!} + \frac{{(x \ln x)}^{1}}{1!} + \frac{{(x \ln x)}^{2}}{2!} + . . .$ $x^{x} = e^{x \ln x} = \underset{n = 0}{\sum^{\infty}} \frac{x^{n} {(\ln x)}^{n}}{n!}$ $Question :$ $\int_{0}^{1} x^{x} d x = \underset{i = 0}{\sum^{\infty}} \int_{0}^{1} \frac{x^{n} {(\ln x)}^{n}}{n!} d x$ $by substituting :$ $x = \exp (- \frac{u}{n + 1}), 0 < u < \infty$ $show that :$ $\int_{0}^{1} x^{n} {(\ln x)}^{n} = {(- 1)}^{n} {(n + 1)}^{- (n + 1)} \int_{0}^{\infty} u^{n} e^{- u} d u$

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