HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the asymptotes of the following curves:

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

Choose the correct alternative:

One of the closest points on the curve x² – y² = 4 to the point (6, 0) is

Find the area of the region bounded by 3x – 2y + 6 = 0, x = – 3, x = 1 and x-axis

Find the area of the region bounded by 2x – y + 1 = 0, y = – 1, y = 3 and y-axis

Find the area of the region bounded by the curve 2 + x – x² + y = 0, x axis, x = – 3 and x = 3

Find the area of the region bounded by the line y = 2x + 5 and the parabola y = x² – 2x

Find the area of the region bounded between the curves y = sin x and y = cos x and the lines x = 0 and x = π

Find the area of the region bounded by y = tan x, y = cot x and the lines x = 0, x = `pi/2`, y = 0

Find the area of the region bounded by the parabola y² = x and the line y = x – 2

Father of a family wishes to divide his square field bounded by x = 0, x = 4, y = 4 and y = 0 along the curve y² = 4x and x² = 4y into three equal parts for his wife, daughter and son. Is it possible to divide? If so, find the area to be divided among them

The curve y = (x – 2)² + 1 has a minimum point at P. A point Q on the curve is such that the slope of PQ is 2. Find the area bounded by the curve and the chord PQ

Find the area of the region common to the circle x² + y² = 16 and the parabola y² = 6x

Choose the correct alternative:

The area between y² = 4x and its latus rectum is

Choose the correct alternative:

If `int_0^"a" 1/(4 + x^2)  "dx=pi/8` then a is

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours?

Find the population of a city at any time t, given that the rate of increase of population is proportional to the population at that instant and that in a period of 40 years the population increased from 3,00,000 to 4,00,000

The equation of electromotive force for an electric circuit containing resistance and self-inductance is E = `"Ri"  + "L" "di"/"dt"`, where E is the electromotive force is given to the circuit, R the resistance and L, the coefficient of induction. Find the current i at time t when E = 0

The engine of a motor boat moving at 10 m/s is shut off. Given that the retardation at any subsequent time (after shutting off the engine) equal to the velocity at that time. Find the velocity after 2 seconds of switching off the engine

Suppose a person deposits ₹ 10,000 in a bank account at the rate of 5% per annum compounded continuously. How much money will be in his bank account 18 months later?

Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample, 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. What percentage of the original radioactive nuclei will remain after 1000 years?