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Maths Solve the following Question.(1 Marks)

Methods of Induction and Binomial Theorem · Maharashtra Board STD 11 Science (MSBSHSE - English Medium). 18 questions.

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Solve the following Question.(1 Marks)

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18 questions · timed · auto-graded

Question 91 Mark
Show that $C_1+C_2+C_3+\ldots . .+C_6=63$
Answer
Since $C_0+C_1+C_2+C_3+\ldots . .+C_n=2^n$
Putting n = 6, we get
$C_0+C_1+C_2+\ldots . .+C_6=2^6$
$\therefore C_0+C_1+C_2+\ldots \ldots+C_6=64$
But, $C_0=1$
$\therefore 1+C_1+C_2+\ldots . .+C_6=64$
$\therefore C_1+C_2+\ldots . .+C_6=64-1=63$
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Question 101 Mark
Show that $C_1+C_2+C_3+\ldots . .+C_7=127$
Answer
Since $C_0+C_1+C_2+C_3+\ldots . .+C_n=2^n$
Putting $n = 7,$ we get
$C_0+C_1+C_2+\ldots . .+C_7=2^7$
$\therefore C_0+C_1+C_2+\ldots . .+C_7=128$ But, C0 = 1
$\therefore 1+C_1+C_2+\ldots . .+C_7=128$
$\therefore C_1+C_2+\ldots . .+C_7=128-1=127$
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Question 111 Mark
Show that $C_0+C_1+C_2+\ldots \ldots+C_9=512$
Answer
Since $C_0+C_1+C_2+C_3+\ldots . .+C_n=2^n$
Putting n = 9, we get
$C_0+C_1+C_2+\ldots . .+C_9=2^9$
$\therefore C_0+C_1+C_2+\ldots . .+C_9=512$
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Question 121 Mark
Show that $C_0+C_1+C_2+\ldots . .+C_8=256$
Answer
Since $C_0+C_1+C_2+C_3+\ldots . .+C_n=2^n$
Putting n = 8, we get
$C_0+C_1+C_2+\ldots . .+C_8=2^8$
$\therefore C_0+C_1+C_2+\ldots . .+C_8=256$
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Question 161 Mark
State, by writing the first four terms, the expansion of the following, where |x| < 1.

$\left(1+x^2\right)^{-1}$

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Question 171 Mark
State, by writing the first four terms, the expansion of the following, where |x| < 1.

$\left(1-x^2\right)^{-3}$

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Solve the following Question.(1 Marks) - Maths STD 11 Science Questions - Vidyadip