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Visual Solutions

11 step-by-step animated solutions for Binomial Theorem. Each solution breaks the problem into visual clips with key insights.

PYQ 2024 · Jan 27 Shift 1Easy4 steps
If AA denotes the sum of all the coefficients in the expansion of (1−3x+10x2)n(1 - 3x + 10x^2)^n and BB denotes the sum of all the coefficients in the expansion of (1+x2)n(1 + x^2)^n, then:
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PYQ 2024 · Jan 29 Shift 2Easy4 steps
Remainder when 64323264^{32^{32}} is divided by 9 is equal to _____.
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PYQ 2024 · Jan (1 Feb) Shift 2Standard4 steps
Let mm and nn be the coefficients of seventh and thirteenth terms respectively in the expansion of (13x13+12x23)18\left(\frac{1}{3}x^{\frac{1}{3}} + \frac{1}{2x^{\frac{2}{3}}}\right)^{18}. Then (nm)13\left(\frac{n}{m}\right)^{\frac{1}{3}} is:
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PYQ 2024 · Jan 30 Shift 1Standard4 steps
Number of integral terms in the expansion of {712+1116}824\left\{7^{\frac{1}{2}} + 11^{\frac{1}{6}}\right\}^{824} is equal to _____.
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PYQ 2024 · Apr 4 Shift 2Standard4 steps
If the coefficients of x4,x5x^4, x^5 and x6x^6 in the expansion of (1+x)n(1 + x)^n are in the arithmetic progression, then the maximum value of nn is:
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PYQ 2024 · Apr 8 Shift 2Standard4 steps
If the term independent of xx in the expansion of (a x2+12x3)10\left(\sqrt{a}\,x^2 + \frac{1}{2x^3}\right)^{10} is 105, then a2a^2 is equal to:
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PYQ 2024 · Apr 4 Shift 1Standard4 steps
The sum of all rational terms in the expansion of (215+513)15\left(2^{\frac{1}{5}} + 5^{\frac{1}{3}}\right)^{15} is equal to:
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PYQ 2024 · Jan 29 Shift 1Tricky4 steps
If 11C12+11C23+…+11C910=nm\frac{^{11}C_1}{2} + \frac{^{11}C_2}{3} + \ldots + \frac{^{11}C_9}{10} = \frac{n}{m} with gcd⁡(n,m)=1\gcd(n, m) = 1, then n+mn + m is equal to _____.
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PYQ 2024 · Apr 9 Shift 1Tricky4 steps
The remainder when 4282024428^{2024} is divided by 21 is _____.
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PYQ 2024 · Jan 31 Shift 1Tricky4 steps
In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5(1+x)(1-x^2)\left(1 + \frac{3}{x} + \frac{3}{x^2} + \frac{1}{x^3}\right)^5, x≠0x \neq 0, the sum of the coefficient of x3x^3 and x−13x^{-13} is equal to _____.
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PYQ 2023 · Jan 24 Shift 2Standard4 steps
The coefficient of x18x^{18} in the expansion of (x4−1x3)15\left(x^4 - \frac{1}{x^3}\right)^{15} is:
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