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

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The population P in any year t is such that the rate of increase in the population is proportional to the population. Then

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P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then

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If the solution of the differential equation `("d"y)/("d"x) = ("a"x + 3)/(2y + f)` represents a circle, then the value of a is

Find the principal value of `sec^-1 (2/sqrt(3))`

Find the principal value of `cot^-1 (sqrt(3))`

Find the principal value of `"cosec"^-1 (- sqrt(2))`

Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`

Find the value of  `sin^-1 (- 1) + cos^-1 (1/2) + cot^-1 (2)`

Find the value of  `cot^-1(1) + sin^-1 (- sqrt(3)/2) - sec^-1 (- sqrt(2))`

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The value of sin^–1(cos x), 0 ≤ x ≤ π is

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If x = `1/5`, the value of `cos(cos^-1x + 2sin^-1x)` is

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If `sin^-1x + "cosec"^-1  5/4 = pi/2`, then the value of x is

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The coordinates of the point where the line `vec"r" = (6hat"i" - hat"j" - 3hat"k") + "t"(- hat"i" + 4hat"k")` meets the plane `vec"r"*(hat"i" + hat"j" - hat"k")` = 3 are

Find the asymptotes of the following curves:

f(x) = `x^2/(x^2 - 1)`

Find the asymptotes of the following curves:

f(x) = `(x^2 - 6x - 1)/(x + 3)`

Find the asymptotes of the following curves:

f(x) = `(x^2 + 6x - 4)/(3x - 6)`

Find by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = 2x², y = 0 and x = 1

Find, by integration, the volume of the solid generated by revolving about the x axis, the region enclosed by y = e^-2x, y = 0, x = 0 and x = 1

Find, by integration, the volume of the solid generated by revolving about the y axis, the region enclosed by x² = 1 + y and y = 3

The region enclosed between the graphs of y = x and y = x² is denoted by R. Find the volume generated when R is rotated through 360° about x-axis