If ( 1 − 3 x ) 1 2 + ( 1 − x ) 5 3 √ 4 − x is approximately equal to a + bx for small values of x, then (a, b) = Options: A . &nbsp (1, 35 24 ) B . &nbsp (1, - 35 24 ) C . &nbsp (2, 35 12 ) D . &nbsp (2, - 35 12 )

Answer: Option B : B ( 1 − 3 x ) 1 / 2 + ( 1 − x ) 5 / 3 2 [ 1 − x 4 ] 1 / 2 1 2 [ ( 1 − 3 2 x ) + ( 1 − 5 x 3 ) ] ( 1 + x 8 ) 1 2 [ 2 − 19 6 x ] ] ( 1 + x 8 ) = 1 2 [ 2 − ( − 1 4 + 19 6 ) x ] = 1 − 35 24 x ∴ ( a , b ) = ( 1 , − 35 24 )

If (1−3x)12+(1−x)53√4−x is approximately equ

Discussion Forum : Binomial Theorem

Question -

If $\frac{(1 - 3 x)^{\frac{1}{2}} + (1 - x)^{\frac{5}{3}}}{\sqrt{4 - x}}$ is approximately equal to a + bx for small values of x, then (a, b) =

Options:

A . (1,

\frac{35}{24}

)

B . (1, -

\frac{35}{24}

)

C . (2,

\frac{35}{12}

)

D . (2, -

\frac{35}{12}

)

Answer: Option B
:
B

$\frac{(1 - 3 x)^{1 / 2} + (1 - x)^{5 / 3}}{2 [1 - \frac{x}{4}]^{1 / 2}} \frac{1}{2} [(1 - \frac{3}{2} x) + (1 - \frac{5 x}{3})] (1 + \frac{x}{8}) \frac{1}{2} [2 - \frac{19}{6} x]] (1 + \frac{x}{8}) = \frac{1}{2} [2 - (- \frac{1}{4} + \frac{19}{6}) x] = 1 - \frac{35}{24} x ∴ (a, b) = (1, - \frac{35}{24})$

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