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NIMCET Previous Year Questions (PYQs)
NIMCET Binomial Theorem 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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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: \( \boxed{\binom{1002}{50}} \)
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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Solution
If (1 + x – 2x2)6 = 1 + a1x + a2x2 + ... + a12x12,
then the value a2 + a4 + a6 + ... + a12
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Solution
in the expansion of 
is
If (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is
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Solution
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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Solution
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