HSC Science इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

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)`

Sketch the graphs of the following functions:

y = `xsqrt(4 - x)`

Sketch the graphs of the following functions:

y = `(x^2 + 1)/(x^2 - 4)`

Sketch the graphs of the following functions:

y = `1/(1 + "e"^-x)`

What is electromagnetic induction?

An electron moves on a straight-line path XY as shown in the figure. The coil abcd is adjacent to the path of the electron. What will be the direction of the current, if any, induced in the coil?

A thin semi-circular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure.

The potential difference developed across the ring when its speed v , is

State Lenz’s law.

State Fleming’s right-hand rule.

What for an inductor is used? Give some examples.

Establish the fact that the relative motion between the coil and the magnet induces an emf in the coil of a closed circuit.