The value of 15C0- 15C1- 15C2- - 15C7 is

Let S= ^15C_0+ ^15C_1+ ^15C_2+… + ^15C_7 We know that, ^15C_0+ ^15C_1+ ^15C_2+…+ ^15C_15 =2^15 ⇒ S+ ^15C_8+… + ^15C_15 = 2^15 ⇒ 2S = 2^15 (∵ ^15C_r = ^15C_15 ...

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Standard XII

Mathematics

Sum of Coefficients of All Terms

The value of ...

Question

The value of $^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}$ is

2^{14}

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2^{15}

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2^{13}

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2^{7}

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Solution

The correct option is A $2^{14}$
Let $S =^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}$
We know that,
$^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{15} = 2^{15} \Rightarrow S +^{15} C_{8} + \dots +^{15} C_{15} = 2^{15} \Rightarrow 2 S = 2^{15} (∵^{15} C_{r} =^{15} C_{15 - r}) ∴ S = 2^{14}$

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Q. The value of

^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}

\frac{^{15} C_{1}}{^{15} C_{0}} + 2. \frac{^{15} C_{2}}{^{15} C_{1}} + 3. \frac{^{15} C_{3}}{^{15} C_{2}} + \dots + 15. \frac{^{15} C_{15}}{^{15} C_{14}} =

Q. The value of

-^{15} C_{1} + 2 \times^{15} C_{2} - 3 \times^{15} C_{3} + . . . - 15 \times^{15} C_{15} +^{14} C_{1} +^{14} C_{3} +^{14} C_{5} + . . . +^{14} C_{11}

is :

Q. The value of ¹⁵C₈ = ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ is ___________.

Find the value of $^{15} C_{2}$ + 2 $^{15} C_{3}$ + 3 $^{15} C_{4}$ . . . . . 14 $^{15} C_{15}$

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Sum of Coefficients of All Terms

Standard XII Mathematics

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The value of 15C0+ 15C1+ 15C2+…+ 15C7 is

The correct option is A 214 Let S= 15C0+ 15C1+ 15C2+…+ 15C7 We know that, 15C0+ 15C1+ 15C2+…+ 15C15=215⇒S+ 15C8+…+ 15C15=215⇒2S=215 (∵ 15Cr= 15C15−r)∴S=214

The value of $^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}$ is