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MCA NIMCET Previous Year Questions (PYQs)
MCA NIMCET Binomial Theorem PYQ
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2023 PYQ
The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001x^{1000}}$
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2023 PYQ
Solution
Easiest Method — Coefficient of \( x^{50} \)
Given Expression:
\[ (1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + \cdots + 1001x^{1000} \]
This follows a known identity that simplifies the full expression to:
\[ f(x) = (1 + x)^{1002} \]
Now: The coefficient of \( x^{50} \) in \( f(x) \) is:
\[ \boxed{\binom{1002}{50}} \]
✅ Final Answer: \( \boxed{\binom{1002}{50}} \)
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2023 PYQ
Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\Bigg{)},\, |x|{\lt}1$ ?
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2023 PYQ
Solution
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2019 PYQ
If (1 + x – 2x2)6 = 1 + a1x + a2x2 + ... + a12x12,
then the value a2 + a4 + a6 + ... + a12
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2019 PYQ
Solution
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2019 PYQ
Not Available
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2019 PYQ
Solution
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2018 PYQ
The coefficient of 
in the expansion of 
is
in the expansion of isGo to Discussion
MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2018 PYQ
Solution
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2017 PYQ
If (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2017 PYQ
Solution
MCA NIMCET PYQ
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ
If $x$ is so small that $x^{2}$ and higher powers of $x$ can be neglected, then $\frac{(9+2x)^{1/2}(3+4x)}{(1-x)^{1/5}}$ is approximately equal to
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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ
Solution
MCA NIMCET
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