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Phrases Binomial Theorem PYQ



The coefficient of x50 in the expression of (1+x)1000+2x(1+x)999+3x2(1+x)998+......+1001x1000





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Solution

Easiest Method — Coefficient of x50

Given Expression:

(1+x)1000+2x(1+x)999+3x2(1+x)998++1001x1000

This follows a known identity that simplifies the full expression to:

f(x)=(1+x)1002

Now: The coefficient of x50 in f(x) is:

(100250)

✅ Final Answer:   (100250)



Which of the following number is the coefficient of x100 in the expansion of loge(1+x1+x2),|x|<1 ?





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Solution



If (1 + x – 2x2)= 1 + a1x + a2x+ ... + a12x12, then the value a+ a+ a+ ... + a12





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Solution



Not Available






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Solution



The coefficient of  in the expansion of is





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Solution



If (1 - x + x)n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is





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Solution



If x is so small that x2 and higher powers of x can be neglected, then (9+2x)1/2(3+4x)(1x)1/5 is approximately equal to





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Solution



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