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

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

Find, by integration, the volume of the container which is in the shape of a right circular conical frustum as shown in the Fig 9.46

A watermelon has an ellipsoid shape which can be obtained by revolving an ellipse with major-axis 20 cm and minor-axis 10 cm about its major-axis. Find its volume using integration

Choose the correct alternative:

The volume of solid of revolution of the region bounded by y² = x(a – x) about the x-axis is

Find the equation of the plane passing through the line of intersection of the planes `vec"r"*(2hat"i" - 7hat"j" + 4hat"k")` = 3 and 3x – 5y + 4z + 11 = 0, and the point (– 2, 1, 3)

Find the equation of the plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x – y + z = 3 and at a distance `2/sqrt(3)` from the point (3, 1, –1)

Find the angle between the line `vec"r" = (2hat"i" - hat"j" + hat"k") + "t"(hat"i" + 2hat"j" - 2hat"k")` and the plane `vec"r"*(6hat"i" + 3hat"j" + 2hat"k")` = 8

Find the angle between the planes `vec"r"*(hat"i" + hat"j" - 2hat"k")` = 3 and 2x – 2y + z = 2

Find the equation of the plane which passes through the point (3, 4, –1) and is parallel to the plane 2x – 3y + 5z + 7 = 0. Also, find the distance between the two planes

Find the length of the perpendicular from the point (1, – 2, 3) to the plane x – y + z = 5

Find the point of intersection of the line with the plane (x – 1) = `y/2` = z + 1 with the plane 2x – y – 2z = 2. Also, the angle between the line and the plane

Find the co-ordinates of the foot of the perpendicular and length of the perpendicular from the point (4, 3, 2) to the plane x + 2y + 3z = 2.

Choose the correct alternative:

If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = hat"i" + hat"j", vec"c" = hat"i"` and `(vec"a" xx vec"b")vec"c" - lambdavec"a" + muvec"b"` then the value of λ + µ is

Sketch the graphs of the following functions

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