HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the coefficients of x⁶ in the expansion of `(3x^2 - 1/(3x))^9`.

Find the coefficients of x⁶⁰ in the expansion of `(1/x^2 + x^4)^18`

Answer the following:

Find the constant term in the expansion of `((4x^2)/3 + 3/(2x))^9`

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Find the constant term in the expansion of `(2x^2 - 1/x)^12`

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If the coefficient of x² and x³ in the expansion of (3 + kx)⁹ are equal, find k

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If the constant term in the expansion of `(x^3 + "k"/x^8)^11` is 1320, find k

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Show that there is no term containing x⁶ in the expansion of `(x^2 - 3/x)^11`

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Show that there is no constant term in the expansion of `(2x - x^2/4)^9`

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State, first four terms in the expansion of `(1 - (2x)/3)^(-1/2)`

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State, first four terms in the expansion of `(1 - x)^(-1/4)`

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State, first three terms in the expansion of `(5 + 4x) ^(-1/2)`

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Find the term independent of x in the in expansion of `(1 - x^2) (x + 2/x)^6`

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(a + bx) (1 − x)⁶ = 3 − 20x + cx² + ..... then find a, b, c

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The 3^rd term of (1 + x)ⁿ is 36x². Find 5^th term

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Suppose (1 + kx)ⁿ = 1 − 12x + 60x² − .... find k and n.

If (x − 1, y + 4) = (1, 2) find the values of x and y

If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y

If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B

If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P

Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)