HSC Arts कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

At 10.00 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant, the temperature of the coffee was 180°F and 10 minutes later it was 160°F. Assume that the constant temperature of the kitchen was 70°F. What was the temperature of the coffee at 10.15 AM? `|log  9/100 = - 0.6061|`

At 10.00 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant, the temperature of the coffee was 180°F and 10 minutes later it was 160°F. Assume that the constant temperature of the kitchen was 70°F. The woman likes to drink coffee when its temperature is between130°F and 140°F. between what times should she have drunk the coffee? `|log  6/11 =  - 0.2006|`

A pot of boiling water at 100°C is removed from a stove at time t = 0 and left to cool in the kitchen. After 5 minutes, the water temperature has decreased to 80° C and another 5 minutes later it has dropped to 65°C. Determine the temperature of the kitchen

A tank initially contains 50 litres of pure water. Starting at time t = 0 a brine containing 2 grams of dissolved salt per litre flows into the tank at the rate of 3 litres per minute. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. Find the amount of salt present in the tank at any time t > 0

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The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/lambda` is

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The Integrating factor of the differential equation `("d"y)/("d"x) + "P"(x)y = "Q"(x)` is x, then p(x)

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The solution of the differential equation `("d"y)/("d"x) = 2xy` is

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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