The value of 50-6 - 5-1 40-6 - 5-2 30-6 - 5-3 20-6 - 5-4 10-6 where n-r denotes nCr is

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Implicit Differentiation

The value of ...

Question

The value of $(\frac{50}{6}) - (\frac{5}{1}) (\frac{40}{6}) + (\frac{5}{2}) (\frac{30}{6}) - (\frac{5}{3}) (\frac{20}{6}) + (\frac{5}{4}) (\frac{10}{6}) w h e r e (\frac{n}{r}) d e n o t e s^{n} C_{r}$ is

15625

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1000000

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2250000

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Solution

The correct option is D
2250000

$^{50} C_{6} -^{5} C_{1}^{40} C_{6} +^{5} C_{2}^{30} C_{5} -^{5} C_{3}^{20} C_{6} +^{5} C_{4}^{10} C_{6}$ =

coefficient of $x^{6}$ in

[ $^{5} C_{0} (1 + x)^{50} -^{5} C_{1} (1 + x)^{40} +^{5} C_{2} (1 + x)^{30} -^{5} C_{3} (1 + x)^{20} +^{5} C_{4} (1 + x)^{10} -^{5} C_{5} (1 + x)^{0}]$

coefficient $x^{6}$ in [(1+x)^{10} - 1]^{5} \)

= coefficient of $x^{6}$ in ({}^{10} C_1 x + {}^{10} C_2x^2 + ....)^5 = {}^5C_1 ({}^{10} C_{(b):} ({}^{10}C_1)^4 \) = 2250000

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Q. Let

N = \frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{3^{5} + 3^{5} + 3^{5}} . \frac{6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}}

, then the value of

{log}_{2} N =

Let N = $\frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{3^{5} + 3^{5} + 3^{5}} \cdot \frac{6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}}$ then the value of ${log}_{2} N$ =

50 \times 5 \div 2 + 24

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Q. The value of

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is ____.

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, the value of x is :

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The value of (506)−(51)(406)+(52)(306)−(53)(206)+(54)(106) where (nr) denotes nCr is

The value of $(\frac{50}{6}) - (\frac{5}{1}) (\frac{40}{6}) + (\frac{5}{2}) (\frac{30}{6}) - (\frac{5}{3}) (\frac{20}{6}) + (\frac{5}{4}) (\frac{10}{6}) w h e r e (\frac{n}{r}) d e n o t e s^{n} C_{r}$ is