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MATHS 1 Marks Question

PART - 1 CH - 7 Binomial Theorem · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 4 questions.

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Question 11 Mark
Write first 4 terms in the expansion of $(2 x-3 y)^4$.
Answer

$\begin{aligned}(2 x-3 y)^4 & =(2 x)^4-{ }^4 C _1(2 x)^3 \cdot(3 y)+{ }^4 C _2(2 x)^2  (3 y)^2-{ }^4 C _3(2 x)(3 y)^3 \\ & =16 x^4-96 x^3 y+216 x^2 y^2-216 x y^3\end{aligned}$
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Question 21 Mark
In binomial expansion, the coefficient of terms at equal distances from the beginning and the end are $\ldots\ldots\ldots$
Answer
equal, i.e., ${ }^n C _r={ }^n C _{n-r}$
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Question 41 Mark
Write the value of ${ }^{30} C _1+{ }^{30} C _2+{ }^{30} C _3+\ldots \ldots+{ }^{30} C _{30}$
Answer
We know that :
$\begin{array}{l}{ }^n C_1+{ }^n C_2+{ }^n C_3+{ }^n C_4+\ldots \ldots{ }^n C_n=2^n-1 \\\therefore \quad{ }^{30} C_1+{ }^{30} C_2+{ }^{30} C_3+\ldots \ldots+{ }^{30} C_{30}=2^{30}-1\end{array}$
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