The value of 1-1-a 1-1-a-1 1-1-a-2 1-1-a-3 1-1-a-4 is

The correct option is B a+1/a 4 ( 1+1/a ) ( 1+1/a 1 ) ( 1+1/a 2 ) ( 1+1/a 3 ) ( 1+1/a 4 ) = ( a+1/a ) ( a 1+1/a 1 ) ( a 2+1/a 2 ) ( a 3+1/a 3 ) ( ...

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Standard XII

Mathematics

Applications of Dot Product

The value of ...

Question

The value of $(1 + \frac{1}{a}) (1 + \frac{1}{a - 1}) (1 + \frac{1}{a - 2}) (1 + \frac{1}{a - 3}) (1 + \frac{1}{a - 4})$ is

\frac{a - 3}{a}

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\frac{a + 1}{a - 4}

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\frac{a + 1}{a - 1}

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\frac{a - 1}{a - 4}

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Solution

The correct option is B $\frac{a + 1}{a - 4}$
$(1 + \frac{1}{a}) (1 + \frac{1}{a - 1}) (1 + \frac{1}{a - 2}) (1 + \frac{1}{a - 3}) (1 + \frac{1}{a - 4})$
= $(\frac{a + 1}{a}) (\frac{a - 1 + 1}{a - 1}) (\frac{a - 2 + 1}{a - 2}) (\frac{a - 3 + 1}{a - 3}) (\frac{a - 4 + 1}{a - 4})$
= $(\frac{a + 1}{a}) (\frac{a}{a - 1}) (\frac{a - 1}{a - 2}) (\frac{a - 2}{a - 3}) (\frac{a - 3}{a - 4}) = \frac{a + 1}{a - 4}$

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The value of (1+1a)(1+1a−1)(1+1a−2)(1+1a−3)(1+1a−4) is

The correct option is B a+1a−4(1+1a)(1+1a−1)(1+1a−2)(1+1a−3)(1+1a−4)=(a+1a)(a−1+1a−1)(a−2+1a−2)(a−3+1a−3)(a−4+1a−4)=(a+1a)(aa−1)(a−1a−2)(a−2a−3)(a−3a−4)=a+1a−4

The value of $(1 + \frac{1}{a}) (1 + \frac{1}{a - 1}) (1 + \frac{1}{a - 2}) (1 + \frac{1}{a - 3}) (1 + \frac{1}{a - 4})$ is