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Question Number 22618 Answers: 1 Comments: 0

If (1 + x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + ... + C_n x^n , prove that (2^2 /(1.2))C_0 + (2^3 /(2.3))C_1 + (2^4 /(3.4))C_2 + ... + (2^(n+2) /((n + 1)(n + 2)))C_n = ((3^(n+2) − 2n − 5)/((n + 1)(n + 2)))

$I f {(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3}$ $+ . . . + C_{n} x^{n}, p r o v e t h a t$ $\frac{2^{2}}{1.2} C_{0} + \frac{2^{3}}{2.3} C_{1} + \frac{2^{4}}{3.4} C_{2} + . . . +$ $\frac{2^{n + 2}}{(n + 1) (n + 2)} C_{n} = \frac{3^{n + 2} - 2 n - 5}{(n + 1) (n + 2)}$

Question Number 22640 Answers: 0 Comments: 0

With usual notation, show that (C_0 /x) − (C_1 /(x+1)) + (C_2 /(x+2)) − .... + (−1)^n (C_n /(x+n))= ((n!)/(x(x + 1)(x + 2)....(x + n)))

$W i t h u s u a l n o t a t i o n, s h o w t h a t$ $\frac{C_{0}}{x} - \frac{C_{1}}{x + 1} + \frac{C_{2}}{x + 2} - . . . . + {(- 1)}^{n} \frac{C_{n}}{x + n} =$ $\frac{n!}{x (x + 1) (x + 2) . . . . (x + n)}$

Question Number 23796 Answers: 1 Comments: 0

∫((2sinx+3cosx)/(3sinx+4cosx)) dx

$\int \frac{2 sinx + 3 cosx}{3 sinx + 4 cosx} dx$

Question Number 23793 Answers: 1 Comments: 1

Question Number 22598 Answers: 0 Comments: 4

Wow guys. You people are amazing.Its my pleasure to be a part of this forum. :)

$W o w g u y s . Y o u p e o p l e a r e$ $a m a z i n g . I t s m y p l e a s u r e t o$ $b e a p a r t o f t h i s f o r u m . :)$

Question Number 22594 Answers: 1 Comments: 0

ΔH_f ^o of water is −285.8 kJ mol^(−1) . If enthalpy of neutralization of monoacid strong base is −57.3 kJ mol^(−1) , ΔH_f ^o of OH^− ion will be

$Δ H_{f}^{o} of water is - 285.8 kJ {mol}^{- 1} . If$ $enthalpy of neutralization of monoacid$ $strong base is - 57.3 kJ {mol}^{- 1}, Δ H_{f}^{o} of$ ${OH}^{-} ion will be$

Question Number 22599 Answers: 0 Comments: 5

Question Number 22612 Answers: 2 Comments: 0

In the binomial expasion of (a − b)^5 , the sum of 2^(nd) and 3^(rd) term is zero, then (a/b) is

$I n t h e b i n o m i a l e x p a s i o n o f {(a - b)}^{5},$ $t h e s u m o f 2^{n d} a n d 3^{r d} t e r m i s z e r o,$ $t h e n \frac{a}{b} i s$

Question Number 22582 Answers: 1 Comments: 2

A chain consisting of 5 links each of mass 0.1 kg is lifted vertically with a constant acceleration of 2 m/s^2 . The force of interaction (in newton) between the top link and the link immediately below it will be : Take g = 10 m/s^2 .

$A chain consisting of 5 links each of$ $mass 0.1 kg is lifted vertically with a$ $constant acceleration of 2 m / s^{2} . The$ $force of interaction (in newton) between$ $the top link and the link immediately$ $below it will be :$ $Take g = 10 m / s^{2} .$

Question Number 22576 Answers: 1 Comments: 1

Question Number 22574 Answers: 1 Comments: 1

The system is initially at origin and is moving with a velocity (3 m/s) k^∧ . A force (120t newton) i^∧ acts on mass m_2 , where t is time in seconds. The man throws a light ball, at the instant when m_1 starts slipping on m_2 , with a velocity 5 m/s vertically up w.r.t himself. Taking the masses of blocks and man as 60 kg each and assuming that the man never slips on m_2 , find (a) The time at which man throws the ball and (b) The coordinates of the point where ball lands. Neglect the dimensions of the system. (g = 10 m/s^2 )

$The system is initially at origin and is$ $moving with a velocity (3 m / s) \overset{\land}{k} . A$ $force (120 t newton) \overset{\land}{i} acts on mass m_{2},$ $where t is time in seconds .$ $The man throws a light ball, at the$ $instant when m_{1} starts slipping on m_{2},$ $with a velocity 5 m / s vertically up w . r . t$ $himself . Taking the masses of blocks$ $and man as 60 kg each and assuming$ $that the man never slips on m_{2}, find$ $(a) The time at which man throws the$ $ball and$ $(b) The coordinates of the point where$ $ball lands . Neglect the dimensions of$ $the system . (g = 10 m / s^{2})$

Question Number 22562 Answers: 0 Comments: 0

solve∫_0 ^1 ln(x)dx/x^2 −x−1 dx

$s o l v e {\int^{1}}_{0} l n (x) d x / x^{2} - x - 1 d x$

Question Number 22561 Answers: 1 Comments: 0

Solve for all integer x,y ∈Z x^2 +y^2 =19

$Solve for all integer x, y \in Z$ $x^{2} + y^{2} = 19$

Question Number 22547 Answers: 1 Comments: 0

If α = (5/(2!3)) + ((5.7)/(3!3^2 )) + ((5.7.9)/(4!3^3 )) ,... then find the value of α^2 + 4α.

$If α = \frac{5}{2! 3} + \frac{5.7}{3! 3^{2}} + \frac{5.7.9}{4! 3^{3}}, . . . then find$ $the value of α^{2} + 4 α .$

Question Number 22545 Answers: 2 Comments: 0

∫(x^(1/2) /(x^(1/2) −x^(1/3) ))dx=

$\int \frac{x^{\frac{1}{2}}}{x^{\frac{1}{2}} - x^{\frac{1}{3}}} dx =$

Question Number 22567 Answers: 3 Comments: 0

Question Number 22537 Answers: 0 Comments: 22

Mr. Ajfour, you are very good at solving difficult questions.How do you do that ? Please tell us something about yourself.

$M r . A j f o u r, y o u a r e v e r y$ $g o o d a t s o l v i n g d i f f i c u l t$ $q u e s t i o n s . H o w d o y o u$ $d o t h a t ? P l e a s e t e l l u s$ $s o m e t h i n g a b o u t y o u r s e l f .$

Question Number 22536 Answers: 1 Comments: 1

show that (((a+b+c)^2 )/(a^2 +b^2 +c^2 ))= ((cot (1/2)A+cot (1/2)B+cot (1/2)C)/(cot A+cot B+cot C)) please help

$s h o w t h a t \frac{{(a + b + c)}^{2}}{a^{2} + b^{2} + c^{2}} =$ $\frac{\cot \frac{1}{2} A + \cot \frac{1}{2} B + \cot \frac{1}{2} C}{\cot A + \cot B + \cot C}$ $p l e a s e h e l p$

Question Number 22535 Answers: 0 Comments: 0

How to solve this homogeneous equation. Can u help me plz Q. solve (x sin (y/x))dy −(y sin^(−1) (y/x))dx=0

$H o w t o s o l v e t h i s h o m o g e n e o u s e q u a t i o n . C a n u h e l p m e p l z$ $Q . s o l v e (x s i n \frac{y}{x}) d y - (y {s i n}^{- 1} \frac{y}{x}) d x = 0$

Question Number 22525 Answers: 0 Comments: 4

Question Number 22524 Answers: 0 Comments: 1

toutes lessolutions du systeme

$t o u t e s l e s s o l u t i o n s d u s y s t e m e$

Question Number 22522 Answers: 0 Comments: 1

Happy Diwali Friends !! :)

$H a p p y$ $D i w a l i$ $F r i e n d s!! :)$

Question Number 22518 Answers: 2 Comments: 1

Question Number 22517 Answers: 0 Comments: 0

Find the coefficient of x in the expansion of [(√(1 + x^2 )) − x]^(−1) in ascending power of x when ∣x∣ < 1.

$Find the coefficient of x in the expansion$ $of {[\sqrt{1 + x^{2}} - x]}^{- 1} in ascending power$ $of x when ∣ x ∣ < 1 .$

Question Number 22516 Answers: 0 Comments: 1

toutes les solutions ?

$t o u t e s l e s s o l u t i o n s ?$

Question Number 22515 Answers: 0 Comments: 0

In a quadrilateral ABCD, it is given that AB is parallel to CD and the diagonals AC and BD are perpendicular to each other. Show that (a) AD.BC ≥ AB.CD; (b) AD + BC ≥ AB + CD.

$In a quadrilateral A B C D, it is given$ $that A B is parallel to C D and the$ $diagonals A C and B D are perpendicular$ $to each other .$ $Show that$ $(a) A D . B C ⩾ A B . C D;$ $(b) A D + B C ⩾ A B + C D .$

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