The value of $({^{7} C}_{0} + {^{7} C}_{1}) + ({^{7} C}_{1} + {^{7} C}_{2}) + . . . . + ({^{7} C}_{6} + {^{7} C}_{7})$ is

2^{8} - 2

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2^{8} - 1

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2^{8} + 1

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2^{8}

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Solution

The correct option is D $2^{8} - 2$
The value of $({^{7} C}_{0} + {^{7} C}_{1}) + ({^{7} C}_{1} + {^{7} C}_{2}) + . . . . + ({^{7} C}_{6} + {^{7} C}_{7})$ is equal to
$= {^{8} C}_{1} + {^{8} C}_{2} + . . . . . . {^{8} C}_{7}$
$= {^{8} C}_{0} + {^{8} C}_{1} + . . . . {^{8} C}_{7} + {^{8} C}_{8} - ({^{8} C}_{0} + {^{8} C}_{8})$
$= 2^{8} - (1 - 1)$
$= 2^{8} - 2$

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Similar questions

Q. The value of

({^{7} C}_{0} + {^{7} C}_{1}) + ({^{7} C}_{1} + {^{7} C}_{2}) + . . . . . ({^{7} C}_{6} + {^{7} C}_{7})

Q. The value of

\frac{1}{2 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{10}} + . . . + \frac{1}{\sqrt{28} + \sqrt{31}}

is?

Question 109 (ii)

Observe the following patterns and fill in the blanks to make the statements true:
$7 \times 4 = 28$
$7 \times 3 =$ ___ $= 28 - 7$
$7 \times 2 =$ ___=___ $= - 7$
$7 \times 1 = 7 =$ ___ $- 7$
$7 \times 0 =$ ___ =___-___
$7 \times (- 1) = - 7 =$ ___-___
$7 \times (- 2) =$ ___=___-___
$7 \times (- 3)$ ___=___-___

Q. Find the value of
(−40) × (−1) + (−28) ÷ 7

Q. Find the value of
(−20) × (−1) + (−28) ÷ 7

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The value of (7C0+7C1)+(7C1+7C2)+....+(7C6+7C7) is

The correct option is D 28−2The value of (7C0+7C1)+(7C1+7C2)+....+(7C6+7C7) is equal to=8C1+8C2+......8C7=8C0+8C1+....8C7+8C8−(8C0+8C8)=28−(1−1)=28−2

The value of $({^{7} C}_{0} + {^{7} C}_{1}) + ({^{7} C}_{1} + {^{7} C}_{2}) + . . . . + ({^{7} C}_{6} + {^{7} C}_{7})$ is