HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

If `bar c = 3bara - 2barb` and `[bara   barb + barc   bara + barb + barc] = 0` then prove that `[bara  barb  barc] = 0`

If `overlinec = 3overlinea - 2overlineb` and `[overlinea         overlineb + overlinec         overlinea + overlineb + overlinec]` = 0 then prove that `[overlinea  overlineb  overlinec]` = 0

Show that the volume of the parallelopiped whose coterminus edges are `bara barb barc` is `[(bara, barb, barc)].`

If `barc = 3bara - 2barb and [bara     barb+barc       bara+barb+barc] = 0` then prove that `[bara  barb  barc] = 0`

If `bar"c" = 3bar"a"-2bar"b"` and `[bar"a"     bar"b" +bar"c"      bar"a" +bar"b" +bar"c"]` = 0 then prove that `[bar"a"  bar"b"  bar"c"]` = 0

If `barc = 3bara - 2barb and [bara   barb + barc   bara + barb + barc] = 0` then prove that `[bara  barb  barc]=0`

If `barc = 3bara - 2barb and [bara       barb+barc        bara + barb + barc] = 0` then prove that `[bara  barb  barc] = 0`

If `barc=3bara-2barb` and `[bara       barb+barc       bara+barb+barc ]=0` then prove that `[bara  barb  barc]=0` 

If `barc = 3bara - 2barb`, then prove that `[bara  barb  barc]` = 0.

If, `barc = 3bara -2barb, "then prove that" [bara  barb  barc] = 0` 

If, `barc = 3bara - 2barb`, then prove that `[bara  barb  barc] = 0`

With the help of a neat labelled diagram, describe the Geiger- Marsden experiment

Thorium ₉₀Th²³² is disintegrated into lead ₈₂Pb²⁰⁰. Find the number of α and β particles emitted in disintegration.

A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.

Answer in brief:

Why are curved roads banked?

Do we need a banked road for a two-wheeler? Explain.

On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?

While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?

Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate:

1. The number of revolutions completed by the ant in these 10 seconds.
2. Time is taken by it for first complete revolution and the last complete revolution.

The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π²m/s²)