HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

If p − q is small compared to either p or q, then show `root("n")("p"/"q")` ∼ `(("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q")`. Hence find `root(8)(15/16)`

Find the coefficient of x⁴ in the expansion `(3 - 4x + x^2)/"e"^(2x)`

Find the value of `sum_("n" = 1)^oo 1/(2"n" - 1) (1/(9^("n" - 1)) + 1/(9^(2"n"- 1)))`

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The coefficient of x⁶ in (2 + 2x)¹⁰ is

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The coefficient of x⁸y¹² in the expansion of (2x + 3y)²⁰ is

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If a is the arithmetic mean and g is the geometric mean of two numbers, then

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If (1 + x²)² (1 + x)ⁿ = a₀ + a₁x + a₂x² + …. + x^{n + 4} and if a₀, a₁, a₂ are in AP, then n is

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If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n − 2S_n−1 + S_n−2 is

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The sum up to n terms of the series `1/(sqrt(1)  +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is 

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The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` is

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The sum of an infinite GP is 18. If the first term is 6, the common ratio is

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The coefficient of x⁵ in the series e^-2x is

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The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is

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The value of `1 - 1/2(2/3) + 1/3(2/3)^2  1/4(2/3)^3 + ...` is

If f'(x) = 4x – 5 and f(2) = 1, find f(x)

If f'(x) = 9x² – 6x and f(0) = – 3 find f(x)

If f” (x) = 12x – 6 and f(1) = 30, f’(1) = 5, find f(x)

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find how long will it take for the ball to strike the ground?

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find the speed with which will it strike the ground?

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find how high the ball will rise?