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Maths MCQ

Methods of Induction and Binomial Theorem · Maharashtra Board STD 11 (MSBSHSE - Semi English Medium). 10 questions.

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10 questions · auto-graded multiple-choice test.

MCQ 11 Mark
If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+a x)^9$ are the same, then the value of a is
  • A
    $-\frac{7}{9}$
  • B
    $-\frac{9}{7}$
  • C
    $\frac{7}{9}$
  • ✓
    $\frac{9}{7}$
Answer
Correct option: D.
$\frac{9}{7}$
$\frac{9}{7}$
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MCQ 21 Mark
The coefficient of the 8th term in the expansion of $(1+x)^{10}$ is:
  • A
    7
  • ✓
    120
  • C
    ${ }^{10} C _8$
  • D
    210
Answer
Correct option: B.
120
120
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MCQ 31 Mark
In the expansion of $(3 x+2)^4$, the coefficient of the middle term is
  • A
    36
  • B
    54
  • C
    81
  • ✓
    216
Answer
Correct option: D.
216
216
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MCQ 41 Mark
The value of ${ }^{11} C_2+{ }^{11} C_4+{ }^{11} C_6+{ }^{11} C_8$ is equal to
  • A
    $2^{10}-1$
  • B
    $2^{10}-11$
  • C
    $2^{10}+12$
  • ✓
    $2^{10}-12$
Answer
Correct option: D.
$2^{10}-12$
$2^{10}-12$
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MCQ 51 Mark
The value of ${ }^{14} C_1+{ }^{14} C_3+{ }^{14} C_5+\ldots .+{ }^{14} C_{11}$ is
  • A
    $2^{14}-1$
  • B
    $2^{14}-14$
  • C
    $2^{12}$
  • ✓
    $2^{13}-14$
Answer
Correct option: D.
$2^{13}-14$
$2^{13}-14$
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MCQ 71 Mark
The term not containing $x$ in expansion of $(1-x)^2\left(x+\frac{1}{x}\right)^{10}$ is
  • ✓
    ${ }^{11} C_5$
  • B
    ${ }^{10} C_5$
  • C
    ${ }^{10} C _4$
  • D
    ${ }^{10} C _7$
Answer
Correct option: A.
${ }^{11} C_5$
${ }^{11} C_5$
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MCQ 81 Mark
In the expansion of $\left(x^2-2 x\right)^{10}$, the coefficient of $x^{16}$ is
  • A
    -1680
  • B
    1680
  • ✓
    3360
  • D
    6720
Answer
Correct option: C.
3360
3360
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MCQ 91 Mark
The middle term in the expansion of $(1+x)^{2 n}$ will be:
  • A
    $(n-1)^{t h}$
  • B
    nth
  • ✓
    $(n+1)^{\text {th }}$
  • D
    $(n+2)^{\text {th }}$
Answer
Correct option: C.
$(n+1)^{\text {th }}$
$(n+1)^{\text {th }}$
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MCQ 101 Mark
The total number of terms in the expression of $(x+y)^{100}+(x-y)^{100}$ after simplification is:
  • A
    50
  • ✓
    51
  • C
    100
  • D
    202
Answer
Correct option: B.
51
51
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