Bank Guides Notes Mocks Board Questions / Maharashtra State Board Class 11 / Mathematics Binomial Theorem 125 Maharashtra State Board Class 11 Mathematics practice questions with answers and worked solutions.
Difficulty: 13 easy · 82 moderate · 30 hard. Most-asked subtopics: General Term in the Expansion (53), Binomial Theorem for a Positive Integral Index (30), Binomial Theorem for a Negative or Fractional Index (29). Updated 16 August 2026. Balbharati textbook · 4.2 SolvedEx.1 Moderate Add #1 · Binomial Theorem for a Positive Integral Index
Expand ( x 2 + 3 y ) 5 (x^2 + 3y)^5 ( x 2 + 3 y ) 5 Balbharati textbook · 4.2 SolvedEx.2 Moderate Add #2 · Binomial Theorem for a Positive Integral Index
Expand ( 2 x − y 2 ) 5 \left(2x - \frac{y}{2}\right)^5 ( 2 x − 2 y ) 5 Balbharati textbook · 4.2 SolvedEx.3 Moderate Add #3 · Binomial Theorem for a Positive Integral Index
Expand ( 5 + 3 ) 4 \left(\sqrt{5} + \sqrt{3}\right)^4 ( 5 + 3 ) 4 Balbharati textbook · 4.2 SolvedEx.4 Hard Add #4 · Binomial Theorem for a Positive Integral Index
Evaluate ( 2 + 1 ) 5 − ( 2 − 1 ) 5 \left(\sqrt{2}+1\right)^5 - \left(\sqrt{2}-1\right)^5 ( 2 + 1 ) 5 − ( 2 − 1 ) 5 Balbharati textbook · 4.2 SolvedEx.5 Moderate Add #5 · Binomial Theorem for a Positive Integral Index
Using binomial theorem, find the value of ( 99 ) 4 (99)^4 ( 99 ) 4 . Done a few? Here’s your next move
Balbharati textbook · 4.2 SolvedEx.6 Moderate Add #6 · Binomial Theorem for a Positive Integral Index
Find the value of ( 2.02 ) 5 (2.02)^5 ( 2.02 ) 5 correct upto 4 decimal places. Balbharati textbook · 4.2 SolvedEx.7 Hard Add #7 · Binomial Theorem for a Positive Integral Index
Without expanding, find the value of
( 2 x − 1 ) 5 + 5 ( 2 x − 1 ) 4 ( 1 − x ) + 10 ( 2 x − 1 ) 3 ( 1 − x ) 2 + 10 ( 2 x − 1 ) 2 ( 1 − x ) 3 + 5 ( 2 x − 1 ) ( 1 − x ) 4 + ( 1 − x ) 5 (2x-1)^5 + 5(2x-1)^4(1-x) + 10(2x-1)^3(1-x)^2 + 10(2x-1)^2(1-x)^3 + 5(2x-1)(1-x)^4 + (1-x)^5 ( 2 x − 1 ) 5 + 5 ( 2 x − 1 ) 4 ( 1 − x ) + 10 ( 2 x − 1 ) 3 ( 1 − x ) 2 + 10 ( 2 x − 1 ) 2 ( 1 − x ) 3 + 5 ( 2 x − 1 ) ( 1 − x ) 4 + ( 1 − x ) 5 Expand.
Balbharati textbook · Ex 4.2 Q1(i) Moderate Add #8 · Binomial Theorem for a Positive Integral Index
( 3 + 2 ) 4 \left(\sqrt{3} + \sqrt{2}\right)^4 ( 3 + 2 ) 4 Balbharati textbook · Ex 4.2 Q1(ii) Moderate Add #9 · Binomial Theorem for a Positive Integral Index
( 5 − 2 ) 5 \left(\sqrt{5} - \sqrt{2}\right)^5 ( 5 − 2 ) 5 Expand.
Balbharati textbook · Ex 4.2 Q2(i) Moderate Add #10 · Binomial Theorem for a Positive Integral Index
( 2 x 2 + 3 ) 4 (2x^2 + 3)^4 ( 2 x 2 + 3 ) 4 Balbharati textbook · Ex 4.2 Q2(ii) Moderate Add #11 · Binomial Theorem for a Positive Integral Index
( 2 x − 1 x ) 6 \left(2x - \frac{1}{x}\right)^6 ( 2 x − x 1 ) 6 Find the value of
Balbharati textbook · Ex 4.2 Q3(i) Hard Add #12 · Binomial Theorem for a Positive Integral Index
( 3 + 1 ) 4 − ( 3 − 1 ) 4 \left(\sqrt{3}+1\right)^4 - \left(\sqrt{3}-1\right)^4 ( 3 + 1 ) 4 − ( 3 − 1 ) 4 Balbharati textbook · Ex 4.2 Q3(ii) Hard Add #13 · Binomial Theorem for a Positive Integral Index
( 2 + 5 ) 5 + ( 2 − 5 ) 5 \left(2+\sqrt{5}\right)^5 + \left(2-\sqrt{5}\right)^5 ( 2 + 5 ) 5 + ( 2 − 5 ) 5 Prove that
Balbharati textbook · Ex 4.2 Q4(i) Hard Add #14 · Binomial Theorem for a Positive Integral Index
( 3 + 2 ) 6 + ( 3 − 2 ) 6 = 970 \left(\sqrt{3}+\sqrt{2}\right)^6 + \left(\sqrt{3}-\sqrt{2}\right)^6 = 970 ( 3 + 2 ) 6 + ( 3 − 2 ) 6 = 970 Balbharati textbook · Ex 4.2 Q4(ii) Hard Add #15 · Binomial Theorem for a Positive Integral Index
( 5 + 1 ) 5 − ( 5 − 1 ) 5 = 352 \left(\sqrt{5}+1\right)^5 - \left(\sqrt{5}-1\right)^5 = 352 ( 5 + 1 ) 5 − ( 5 − 1 ) 5 = 352 Using binomial theorem, find the value of
Balbharati textbook · Ex 4.2 Q5(i) Moderate Add #16 · Binomial Theorem for a Positive Integral Index
Balbharati textbook · Ex 4.2 Q5(ii) Moderate Add #17 · Binomial Theorem for a Positive Integral Index
Using binomial theorem, find the value of
Balbharati textbook · Ex 4.2 Q6(i) Moderate Add #18 · Binomial Theorem for a Positive Integral Index
Balbharati textbook · Ex 4.2 Q6(ii) Moderate Add #19 · Binomial Theorem for a Positive Integral Index
Without expanding, find the value of
Balbharati textbook · Ex 4.2 Q7(i) Hard Add #20 · Binomial Theorem for a Positive Integral Index
( x + 1 ) 4 − 4 ( x + 1 ) 3 ( x − 1 ) + 6 ( x + 1 ) 2 ( x − 1 ) 2 − 4 ( x + 1 ) ( x − 1 ) 3 + ( x − 1 ) 4 (x+1)^4 - 4(x+1)^3(x-1) + 6(x+1)^2(x-1)^2 - 4(x+1)(x-1)^3 + (x-1)^4 ( x + 1 ) 4 − 4 ( x + 1 ) 3 ( x − 1 ) + 6 ( x + 1 ) 2 ( x − 1 ) 2 − 4 ( x + 1 ) ( x − 1 ) 3 + ( x − 1 ) 4 Balbharati textbook · Ex 4.2 Q7(ii) Hard Add #21 · Binomial Theorem for a Positive Integral Index
( 2 x − 1 ) 4 + 4 ( 2 x − 1 ) 3 ( 3 − 2 x ) + 6 ( 2 x − 1 ) 2 ( 3 − 2 x ) 2 + 4 ( 2 x − 1 ) 1 ( 3 − 2 x ) 3 + ( 3 − 2 x ) 4 (2x-1)^4 + 4(2x-1)^3(3-2x) + 6(2x-1)^2(3-2x)^2 + 4(2x-1)^1(3-2x)^3 + (3-2x)^4 ( 2 x − 1 ) 4 + 4 ( 2 x − 1 ) 3 ( 3 − 2 x ) + 6 ( 2 x − 1 ) 2 ( 3 − 2 x ) 2 + 4 ( 2 x − 1 ) 1 ( 3 − 2 x ) 3 + ( 3 − 2 x ) 4 Balbharati textbook · Ex 4.2 Q8 Moderate Add #22 · Binomial Theorem for a Positive Integral Index
Find the value of ( 1.02 ) 6 (1.02)^6 ( 1.02 ) 6 , correct upto four places of decimals. Balbharati textbook · Ex 4.2 Q9 Moderate Add #23 · Binomial Theorem for a Positive Integral Index
Find the value of ( 1.01 ) 5 (1.01)^5 ( 1.01 ) 5 , correct upto three places of decimals. Balbharati textbook · Ex 4.2 Q10 Moderate Add #24 · Binomial Theorem for a Positive Integral Index
Find the value of ( 0.9 ) 6 (0.9)^6 ( 0.9 ) 6 , correct upto four places of decimals. Balbharati textbook · 4.3 SolvedEx.1 Moderate Add #25 · General Term in the Expansion
Find the fifth term in the expansion of ( 2 x 2 + 3 2 x ) 8 \left(2x^{2}+\frac{3}{2x}\right)^{8} ( 2 x 2 + 2 x 3 ) 8 . Balbharati textbook · 4.3 SolvedEx.2 Moderate Add #26 · General Term in the Expansion
Find the middle term(s) in the expansion of ( x 2 + 2 x ) 8 \left(x^{2}+\frac{2}{x}\right)^{8} ( x 2 + x 2 ) 8 . Balbharati textbook · 4.3 SolvedEx.3 Hard Add #27 · General Term in the Expansion
Find the middle terms in the expansion of ( 2 x − 1 4 x ) 9 \left(2x-\frac{1}{4x}\right)^{9} ( 2 x − 4 x 1 ) 9 . Balbharati textbook · 4.3 SolvedEx.4 Moderate Add #28 · General Term in the Expansion
Find the coefficient of x 7 x^{7} x 7 in the expansion of ( x 2 + 1 x ) 11 \left(x^{2}+\frac{1}{x}\right)^{11} ( x 2 + x 1 ) 11 . Balbharati textbook · 4.3 SolvedEx.5 Hard Add #29 · General Term in the Expansion
Find the coefficient of x − 2 x^{-2} x − 2 in the expansion of ( 2 x − 1 3 x 2 ) 10 \left(2x-\frac{1}{\sqrt{3}x^{2}}\right)^{10} ( 2 x − 3 x 2 1 ) 10 . Balbharati textbook · 4.3 SolvedEx.6 Hard Add #30 · General Term in the Expansion
Find the term independent of x x x , in the expansion of ( x − 2 x 2 ) 10 \left(\sqrt{x}-\frac{2}{x^{2}}\right)^{10} ( x − x 2 2 ) 10 . In the following expansions, find the indicated term.
Balbharati textbook · Ex 4.3 Q1(i) Moderate Add #31 · General Term in the Expansion
( 2 x 2 + 3 2 x ) 8 \left(2x^{2}+\frac{3}{2x}\right)^{8} ( 2 x 2 + 2 x 3 ) 8 , 3 rd 3^{\text{rd}} 3 rd term Balbharati textbook · Ex 4.3 Q1(ii) Moderate Add #32 · General Term in the Expansion
( x 2 − 4 x 3 ) 11 \left(x^{2}-\frac{4}{x^{3}}\right)^{11} ( x 2 − x 3 4 ) 11 , 5 th 5^{\text{th}} 5 th term Balbharati textbook · Ex 4.3 Q1(iii) Moderate Add #33 · General Term in the Expansion
( 4 x 5 − 5 2 x ) 9 \left(\frac{4x}{5}-\frac{5}{2x}\right)^{9} ( 5 4 x − 2 x 5 ) 9 , 7 th 7^{\text{th}} 7 th term Balbharati textbook · Ex 4.3 Q1(iv) Moderate Add #34 · General Term in the Expansion
( 1 3 + a 2 ) 12 \left(\frac{1}{3}+a^{2}\right)^{12} ( 3 1 + a 2 ) 12 , 9 th 9^{\text{th}} 9 th term Balbharati textbook · Ex 4.3 Q1(v) Moderate Add #35 · General Term in the Expansion
( 3 a + 4 a ) 13 \left(3a+\frac{4}{a}\right)^{13} ( 3 a + a 4 ) 13 , 10 th 10^{\text{th}} 1 0 th term In the following expansions, find the indicated coefficients.
Balbharati textbook · Ex 4.3 Q2(i) Moderate Add #36 · General Term in the Expansion
x 3 x^{3} x 3 in ( x 2 + 3 2 x ) 9 \left(x^{2}+\frac{3\sqrt{2}}{x}\right)^{9} ( x 2 + x 3 2 ) 9 Balbharati textbook · Ex 4.3 Q2(ii) Moderate Add #37 · General Term in the Expansion
x 8 x^{8} x 8 in ( 2 x 5 − 5 x 3 ) 8 \left(2x^{5}-\frac{5}{x^{3}}\right)^{8} ( 2 x 5 − x 3 5 ) 8 Balbharati textbook · Ex 4.3 Q2(iii) Moderate Add #38 · General Term in the Expansion
x 9 x^{9} x 9 in ( 1 x + x 2 ) 18 \left(\frac{1}{x}+x^{2}\right)^{18} ( x 1 + x 2 ) 18 Balbharati textbook · Ex 4.3 Q2(iv) Moderate Add #39 · General Term in the Expansion
x − 3 x^{-3} x − 3 in ( x − 1 2 x ) 5 \left(x-\frac{1}{2x}\right)^{5} ( x − 2 x 1 ) 5 Balbharati textbook · Ex 4.3 Q2(v) Moderate Add #40 · General Term in the Expansion
x − 20 x^{-20} x − 20 in ( x 3 − 1 2 x 2 ) 15 \left(x^{3}-\frac{1}{2x^{2}}\right)^{15} ( x 3 − 2 x 2 1 ) 15 Find the constant term (term independent of x x x ) in the expansion of Balbharati textbook · Ex 4.3 Q3(i) Moderate Add #41 · General Term in the Expansion
( 2 x + 1 3 x 2 ) 9 \left(2x+\frac{1}{3x^{2}}\right)^{9} ( 2 x + 3 x 2 1 ) 9 Balbharati textbook · Ex 4.3 Q3(ii) Moderate Add #42 · General Term in the Expansion
( x − 2 x 2 ) 15 \left(x-\frac{2}{x^{2}}\right)^{15} ( x − x 2 2 ) 15 Balbharati textbook · Ex 4.3 Q3(iii) Moderate Add #43 · General Term in the Expansion
( x − 3 x 2 ) 10 \left(\sqrt{x}-\frac{3}{x^{2}}\right)^{10} ( x − x 2 3 ) 10 Balbharati textbook · Ex 4.3 Q3(iv) Moderate Add #44 · General Term in the Expansion
( x 2 − 1 x ) 8 \left(x^{2}-\frac{1}{x}\right)^{8} ( x 2 − x 1 ) 8 Balbharati textbook · Ex 4.3 Q3(v) Moderate Add #45 · General Term in the Expansion
( 2 x 2 − 5 x ) 9 \left(2x^{2}-\frac{5}{x}\right)^{9} ( 2 x 2 − x 5 ) 9 Find the middle terms in the expansion of
Balbharati textbook · Ex 4.3 Q4(i) Moderate Add #46 · General Term in the Expansion
( x y + y x ) 12 \left(\frac{x}{y}+\frac{y}{x}\right)^{12} ( y x + x y ) 12 Balbharati textbook · Ex 4.3 Q4(ii) Moderate Add #47 · General Term in the Expansion
( x 2 + 1 x ) 7 \left(x^{2}+\frac{1}{x}\right)^{7} ( x 2 + x 1 ) 7 Balbharati textbook · Ex 4.3 Q4(iii) Moderate Add #48 · General Term in the Expansion
( x 2 − 2 x ) 8 \left(x^{2}-\frac{2}{x}\right)^{8} ( x 2 − x 2 ) 8 Balbharati textbook · Ex 4.3 Q4(iv) Moderate Add #49 · General Term in the Expansion
( x a − a x ) 10 \left(\frac{x}{a}-\frac{a}{x}\right)^{10} ( a x − x a ) 10 Balbharati textbook · Ex 4.3 Q4(v) Moderate Add #50 · General Term in the Expansion
( x 4 − 1 x 3 ) 11 \left(x^{4}-\frac{1}{x^{3}}\right)^{11} ( x 4 − x 3 1 ) 11 Showing the first 50 of 125.
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