Class 11 Math - Binomial Theorem - MERIT YARD
Class 11 Math - Binomial Theorem - MERIT YARD
1 / 40What is the total number of terms in the expansion of:
\( (x+y)^n \)?
A) \( n \)
B) \( n - 1 \)
C) \( 2n \)
D) \( n + 1 \)
2 / 40What is the total number of terms in the expansion of:
\( (x+y)^5 \)?
A) \( 6 \)
B) \( 5 \)
C) \( 4 \)
D) \( 7 \)
3 / 40The sum of the indices (powers) of \( x \) and \( y \) in any single term of the expansion \( (x+y)^n \) is always:
A) \( n - 1 \)
B) \( n \)
C) \( n + 1 \)
D) \( 0 \)
4 / 40The coefficients in the binomial expansion follow the famous pattern of:
A) Fibonacci Sequence
B) Euler's Circle
C) Pascal's Triangle
D) Newton's Square
5 / 40What is the first term in the expansion of:
\( (a+b)^n \)?
A) \( ^nC_n a^n \)
B) \( ^nC_1 a^{n-1} \)
C) \( ^nC_0 b^n \)
D) \( ^nC_0 a^n \)
6 / 40What is the last term in the expansion of:
\( (a+b)^n \)?
A) \( ^nC_n b^n \)
B) \( ^nC_0 a^n \)
C) \( ^nC_n a^n \)
D) \( ^nC_1 b^{n-1} \)
7 / 40What is the correct formula for the general term \( T_{r+1} \) in \( (a+b)^n \)?
A) \( ^nC_r a^r b^{n-r} \)
B) \( ^nC_r a^{n-r} b^r \)
C) \( ^nC_{r+1} a^{n-r} b^r \)
D) \( ^nC_{r-1} a^{n-r} b^r \)
8 / 40For finding the 5th term in an expansion using \( T_{r+1} \), what is the value of \( r \)?
A) \( 5 \)
B) \( 6 \)
C) \( 4 \)
D) \( 3 \)
9 / 40What is the exact value of the binomial coefficient
\( ^nC_0 \)?
A) \( 0 \)
B) \( n \)
C) \( n! \)
D) \( 1 \)
10 / 40What is the exact value of the binomial coefficient
\( ^nC_n \)?
A) \( 1 \)
B) \( n \)
C) \( 0 \)
D) \( n! \)
11 / 40What is the exact value of
\( ^nC_1 \)?
A) \( 1 \)
B) \( n \)
C) \( 0 \)
D) \( n! \)
12 / 40If \( n \) is an even number, how many middle terms are there in \( (x+y)^n \)?
A) \( 2 \)
B) \( 0 \)
C) \( 1 \)
D) \( n/2 \)
13 / 40If \( n \) is an odd number, how many middle terms are there in \( (x+y)^n \)?
A) \( 1 \)
B) \( 3 \)
C) \( 0 \)
D) \( 2 \)
14 / 40For the expansion of \( (x+y)^4 \), which term is strictly the middle term?
A) \( 3^{\text{rd}} \text{ term} \)
B) \( 2^{\text{nd}} \text{ term} \)
C) \( 4^{\text{th}} \text{ term} \)
D) \( 5^{\text{th}} \text{ term} \)
15 / 40For the expansion of \( (x+y)^5 \), how many middle terms exist?
A) \( 1 \)
B) \( 2 \)
C) \( 3 \)
D) \( 0 \)
16 / 40Find the total sum of all binomial coefficients:
\( ^nC_0 + ^nC_1 + \dots + ^nC_n \)
A) \( n^2 \)
B) \( 2n \)
C) \( 2^n \)
D) \( 0 \)
17 / 40Find the sum of the odd binomial coefficients:
\( ^nC_1 + ^nC_3 + \dots \)
A) \( 2^n \)
B) \( 0 \)
C) \( n \)
D) \( 2^{n-1} \)
18 / 40What is the coefficient of \( x^2 \) in the simple expansion of \( (x+1)^2 \)?
A) \( 1 \)
B) \( 2 \)
C) \( 0 \)
D) \( 3 \)
19 / 40What is the coefficient of \( x \) in the simple expansion of \( (x+1)^2 \)?
A) \( 1 \)
B) \( 2 \)
C) \( 3 \)
D) \( 0 \)
20 / 40What is the exact value of
\( ^4C_2 \)?
A) \( 4 \)
B) \( 8 \)
C) \( 6 \)
D) \( 12 \)
21 / 40What is the exact value of
\( ^3C_2 \)?
A) \( 1 \)
B) \( 2 \)
C) \( 6 \)
D) \( 3 \)
22 / 40A term "independent of \( x \)" means the power of \( x \) in that specific term is:
A) \( 0 \)
B) \( 1 \)
C) \( -1 \)
D) \( n \)
23 / 40How many terms are in the expansion of:
\( (2x - 3y)^{10} \)?
A) \( 10 \)
B) \( 11 \)
C) \( 9 \)
D) \( 20 \)
24 / 40The general term in the expansion of \( (a-b)^n \) always contains which sign factor?
A) \( (-1)^{n} \)
B) \( (-1)^{r+1} \)
C) \( (-1)^r \)
D) Always positive
25 / 40What is the correct expansion of
\( (x+y)^2 \)?
A) \( x^2 - 2xy + y^2 \)
B) \( x^2 + y^2 \)
C) \( x^2 + 2x + y^2 \)
D) \( x^2 + 2xy + y^2 \)
26 / 40What is the total number of terms in the expansion of:
\( (x+y)^{15} \)?
A) \( 16 \)
B) \( 15 \)
C) \( 14 \)
D) \( 30 \)
27 / 40Evaluate the value of:
\( ^5C_0 \)
A) \( 0 \)
B) \( 1 \)
C) \( 5 \)
D) \( 120 \)
28 / 40Which formula correctly represents the binomial coefficient \( ^nC_r \)?
A) \( \frac{n!}{r!} \)
B) \( \frac{n!}{(n-r)!} \)
C) \( \frac{n!}{r!(n-r)!} \)
D) \( n! - r! \)
29 / 40If \( n = 6 \), the exact position of the middle term is:
A) \( 3^{\text{rd}} \text{ term} \)
B) \( 2^{\text{nd}} \text{ term} \)
C) \( 5^{\text{th}} \text{ term} \)
D) \( 4^{\text{th}} \text{ term} \)
30 / 40The index \( n \) in the standard basic binomial theorem \( (a+b)^n \) must be a:
A) Positive integer
B) Negative integer
C) Fraction
D) Irrational number
31 / 40In successive terms of the expansion \( (a+b)^n \), the power of \( a \):
A) Increases by 1
B) Decreases by 1
C) Remains constant
D) Becomes zero
32 / 40In successive terms of the expansion \( (a+b)^n \), the power of \( b \):
A) Decreases by 1
B) Remains constant
C) Increases by 1
D) Becomes zero
33 / 40How many total terms are present in the expansion of:
\( ((x+y)^2)^3 \)?
A) \( 6 \)
B) \( 5 \)
C) \( 8 \)
D) \( 7 \)
34 / 40What is the exact value of
\( ^5C_5 \)?
A) \( 1 \)
B) \( 5 \)
C) \( 0 \)
D) \( 120 \)
35 / 40If the total number of terms in an expansion is 9, what is the value of index \( n \)?
A) \( 9 \)
B) \( 8 \)
C) \( 10 \)
D) \( 7 \)
36 / 40What is the constant term (independent of x) in:
\( \left(x + \frac{1}{x}\right)^2 \)?
A) \( 1 \)
B) \( 0 \)
C) \( 2 \)
D) \( 4 \)
37 / 40What is the 2nd term in the simple expansion of:
\( (x+y)^2 \)?
A) \( x^2 \)
B) \( y^2 \)
C) \( xy \)
D) \( 2xy \)
38 / 40The sum of all the even binomial coefficients \( (^nC_0 + ^nC_2 + \dots) \) is:
A) \( 2^{n-1} \)
B) \( 2^n \)
C) \( n \)
D) \( 0 \)
39 / 40In Pascal's Triangle, the first and last number of every single row is always:
A) \( 0 \)
B) \( 1 \)
C) \( 2 \)
D) The row number
40 / 40What is the coefficient of \( x^3 \) in the expansion of:
\( (x+1)^3 \)?
A) \( 3 \)
B) \( 0 \)
C) \( 1 \)
D) \( 2 \)
Test Analysis

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Time Taken ⏱️ 00m 00s

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