The coefficient of x^2 in the expansion of (2x^2 + 1/x)^10, x ≠ 0, is :

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Maths Q7 – JEE-MAIN 2026

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Home Maths Binomial TheoremQuestion #40

The coefficient of

x^{2}

in the expansion of

(2 x^{2} + \frac{1}{x})^{10}

x \neq 0

, is :

Clue 1 of 3: Binomial Theorem

Recall the general term formula for a binomial expansion $(a + b)^{n}$ .

🧠 Full Solution Path

Step 1: Identify the General Term✦ Active

The general term $T_{r + 1}$ in the binomial expansion of $(a + b)^{n}$ is given by $T_{r + 1} = (\binom{n}{r}) a^{n - r} b^{r}$ . For the given expression $(2 x^{2} + \frac{1}{x})^{10}$ , we have $a = 2 x^{2}$ , $b = x^{- 1}$ , and $n = 10$ . Substituting these values, the general term is:

T_{r + 1} = (\binom{10}{r}) (2 x^{2})^{10 - r} (x^{- 1})^{r}

Step 2: Determine the Value of r○ Expand

Simplify the general term to find the power of $x$ :

T_{r + 1} = (\binom{10}{r}) 2^{10 - r} (x^{2})^{10 - r} x^{- r} = (\binom{10}{r}) 2^{10 - r} x^{2 (10 - r)} x^{- r} = (\binom{10}{r}) 2^{10 - r} x^{20 - 2 r - r} = (\binom{10}{r}) 2^{10 - r} x^{20 - 3 r}

We need the coefficient of $x^{2}$ , so we equate the power of $x$ to $2$ :

20 - 3 r = 2 ⟹ 3 r = 18 ⟹ r = 6

💡 Teacher's Secret Hint

Ensure careful handling of exponents when combining terms with $x$ .

Step 3: Calculate the Coefficient○ Expand

Substitute $r = 6$ into the coefficient part of the general term:

Coefficient = (\binom{10}{6}) 2^{10 - 6} = (\binom{10}{6}) 2^{4}

Calculate the binomial coefficient and the power of 2:

(\binom{10}{6}) = (\binom{10}{4}) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 10 \times 3 \times 7 = 210

2^{4} = 16

Multiply these values to get the final coefficient:

Coefficient = 210 \times 16 = 3360

💡 Teacher's Secret Hint

Remember that $(\binom{n}{k}) = (\binom{n}{n - k})$ can simplify calculations.

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Maths Question 7 – JEE-MAIN 2026

Clue 1 of 3: Binomial Theorem

🧠 Full Solution Path