HSC Science कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 1 to 1.1 hours?

The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 4 to 4.1 hours?

A circular plate expands uniformly under the influence of heat. If its radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area

A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube

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A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 cm. Then the percentage error in the calculating the area of this template is

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The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

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If u(x, y) = `"e"^(x^2 + y^2)`, then `(delu)/(delx)` is equal to

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If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

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The change in the surface area S = 6x² of a cube when the edge length varies from x₀ to x₀ + dx is

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The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is

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If f(x) = `x/(x + 1)`, then its differential is given by

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Linear approximation for g(x) = cos x at x = `pi/2` is

Find an approximate value of `int_1^1.5` xdx by applying the left–end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}

Find an approximate value of `int_1^1.5` x²dx by applying the right–end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}

Find an approximate value of `int_1^1.5 (2 - x)` dx by applying the mid-point rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}

Evaluate the following integrals as the limits of sum:

`int_0^1 (5x + 4)"d"x`

Evaluate the following integrals as the limits of sum:

`int_1^2 (4x^2 - 1)"d"x`

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The value of `int_0^(2/3) ("d"x)/sqrt(4 - 9x^2)` is

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The value of `int_(-1)^2 |x|  "d"x` is

For the following equations, determine its order, degree (if exists)

`("d"y)/("d"x) + xy` = cot x