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PART - 1 CH - 7 Binomial Theorem MATHS - PART - 1 CH - 7 Binomial Theorem

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 25 questions in this chapter.

Question types

PART - 1 CH - 7 Binomial Theorem question types

25 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

25
Questions
6
Question groups
5
Question types
Sample Questions

PART - 1 CH - 7 Binomial Theorem questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If the sum of even and odd terms of the expansion of $(x+a)^n$ are A and B respectively, $(x+a)^{2 n}-(x$ $-a)^{2 n}$ is equal to :
  • A
    $4 (A + B)$
  • B
    $AB$
  • C
    $4 (A – B)$
  • ✓
    $4AB$

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
If $C _0, C _1, C _2 \ldots . . C _n$ are the coefficients of different terms of the expansion of $(1+x)^n$, then $C _0+ C _2+$ $C _4+\ldots .$. is equal to :
  • A
    $2^n$
  • B
    $2^n-1$
  • ✓
    $2^{n-1}$
  • D
    $2^{n+1}$

Answer: C.

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Q 182 Marks Questions2 Marks
If $C _0, C _1, C _2, \ldots \ldots . C _n$ are the binomial coefficients in the expansion of $(1+x)^n$, then prove that :
$C_0-\frac{C_1}{2}+\frac{C_2}{3}-\frac{C_3}{4}+\ldots \ldots \ldots+\frac{(-1)^n \cdot C_n}{n+1}=\frac{1}{n+1}$
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Q 192 Marks Questions2 Marks
If $C_0, C_1, C_2, \ldots \ldots \ldots . C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then prove that :
$2 C_0+\frac{2^2 C_1}{2}+\frac{2^3 C_2}{3}+\ldots \ldots  +\frac{2^{n+1} \cdot C_n}{n+1}=\frac{3^{n+1}-1}{n+1}$
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Q 202 Marks Questions2 Marks
If the expansion of $\left(1+x-2 x^2\right)^6$ is $1+a_1 x+$ $a_2 x^2+a_3 x^3+$ $\ldots\ldots\ldots$ $+a_{12} x^{12}$, then prove that $a_2$ $+a_4+a_6+\ldots \ldots \ldots .+a_{12}=31$.
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Q 23Match the following.5 Marks
Part (a)Part (b)
1. Number of terms in the expansion of $\left(4 x^2+12 x y+9 y^2\right)^9$(a) $\sum_{r=0}^n{ }^n C _r x^{n-r} y^r$
2. $(2+\sqrt{5})^5+(2-\sqrt{5})^5$(b) 9
3. $999^3$(c) 1364
4. Number of terms in the expansion of $(a+b x)^{17} -(a-b x)^{17}$(d) 19
5. $(x+y)^{ n }$(e) 997002999
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