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Binomial Theorem — BITSAT Mathematics PYQs

34 previous year questions from Binomial Theorem with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

Binomial Theorem — BITSAT Mathematics PYQs

The coefficient of x^2 term in the binomial expansion of ( 1 3 x^ 1 2 +x^ -1 4 )¹⁰ is

The coefficient of x^n in the expansion of e^ 7 x +e^x e^ 3 x is

The coefficient of the highest power of x in the expansion of (x+ x^2-1 )^8+ (x- x^2-1 )^8

If the 17^ th and the 18^ th terms in the expansion of (2+a)⁵⁰ are equal, then the coefficient of x³⁵ in the expansion of (a+x)⁻² is

If x¹⁸ occurs in the rth term in the expansion of (x^4+ 1 x^3 )¹⁵ , then what is the value of r ?

The middle term in the expansion of ( 10 x + x 10 )¹⁰ is

The number of terms in the expansion of (1+5 2 x)^9+(1-5 2 x)^9 , is

If the sum of the coefficients in the expansion of (x+y)^n is 1024 , then the value of the greatest coefficient in the expansion is

The coefficient of the term independent of x in the expansion of ( x 3 + 3 2 x² )¹⁰ is

Coefficient of x¹³ in the expansion of (1-x)⁵ (1+x+x²+x³ )⁴ is

If a, b, c are three natural numbers in AP and a + b + c =21 then the possible number of values of the ordered triplet ( a , b , c ) is

Let 2 x 2 + 3 x + 4 10 = &#8721; r = 0 20 a r x r , then the value of a₈ a₁₂ , is

If 1 + x + x 2 20 = &#8721; r = 0 40 a r &#183; x r , then &#8721; r = 0 39 - 1 r &#183; a r &#183; a r + 1 equal to

If the coefficient of x 3 and x 4 in the expansion of 1 + a x + b x 2 1 - 2 x 18 in powers of x are both zero, then a , b is equal to

In the expansion of 1 + x + x 3 + x 4 10 , the coefficient of x 4 is

The coefficient of x - n in 1 + x n 1 + 1 x n is

The greatest term in the expansion of 3 1 + 1 3 20 is

The coefficient of x 5 in the expansion of 1 + x 21 + 1 + x 22 + &#8230; + 1 + x 30 is

The number of values of satisfying the equation ³⁹ C _ 3 r -1 - ³⁹ C _ r ² = ³⁹ C _ r ²-1 - ³⁹ C _ 3 r is

If _ r=0 ^ n r+2 r+1 ^ n C_ r = 2⁸-1 6 , then n=

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x+a)^ n are A and B respectively, then the value of (x²- . .a² )^ n is

If the third term in the expansion of [ x + x ^ ₁₀ x ]⁵ is 10⁶, then x may be

If e^ x +e^ 5 x e^ 3 x =a₀+a₁ x+a₂ x²+a₃ x³+ then the value of 2 a₁+2³ a₃+2⁵ a₅+ is

The coefficient of x ⁴ in the expansion of (1+x+x²+x³ )¹¹, is

If T ₀, ~T ₁, ~T ₂ T _ n represent the terms in the expansion of (x+a)^ n , then ( T ₀- T ₂+ T ₄- . )²+ ( T ₁- T ₃+ T ₅- . . )²=

The coefficient of the middle term in the expansion of (2+3 x )⁴ is:

If C ₀, C ₁, C ₂, . C _ n denote the binomial coefficientsin the expansion of (1+ x )^ n , then the value of C ₀+ ( C ₀+ C ₁ )+ ( C ₀+ C ₁+ C ₂ )+ + (C₀+C₁+ . .+C_ n-1 )

The coefficient of x²⁰ in the expansion of (1+x² )⁴⁰ (x²+2+ 1 x² )⁻⁵ is

For (n N , x^ n+1 +(x+1)^ 2 n-1 ) is divisible by

The term independent of (x ) in the expansion of ( (9 x - 1 3 x )¹⁸, x > 0 ), is a times the corresponding binomial coefficient. Then a is

In the binomial ( (2^ 1 / 3 +3^ -1 / 3 )^ n ), if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is (1 / 6 ), then (n ) equal to

With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each en

The general solution of (8 ^2 x 2 =1+ x ) is

The letters of the word TOUGH are written in all possible orders and these words are written out as in a dictionary, then the rank of the word TOUGH is

Let 2 x 2 + 3 x + 4 10 = ∑ r = 0 20 a r x r , then the value of a₈ a₁₂ , is

If 1 + x + x 2 20 = ∑ r = 0 40 a r · x r , then ∑ r = 0 39 - 1 r · a r · a r + 1 equal to

The coefficient of x 5 in the expansion of 1 + x 21 + 1 + x 22 + … + 1 + x 30 is