PUC Science 2nd PUC Class 12 - Karnataka Board PUC Important Questions

If `int(2x^(1/2))/(x^2)  dx = k  .  2^(1/x) + C`, then k is equal to ______.

Solve the differential equation:

(1 + y²) dx = (tan⁻¹ y − x) dy

If the vectors \[\vec{a}\]  and \[\vec{b}\] are such that \[\left| \vec{a} \right| = 3, \left| \vec{b} \right| = \frac{2}{3}\] and \[\vec{a} \times \vec{b}\] is a unit vector, then write the angle between \[\vec{a}\] and \[\vec{b}\] 

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

Define self-inductance of a coil.

Why does endosperm development precede embryo development in angiosperm seeds?

Our government has intentionally imposed strict conditions for M.T.P. in our country. Justify giving a reason.

Public all over India is very much concerned about the deteriorating air quality in large parts of North India. Alarmed by this situation the Resident’s Welfare Association of your locality organized an awareness programme entitled “Bury not burn”. They invited you, being a biology student to participate.

1. How would you justify your arguments that promote burying and discourage burning? (Give two reasons.)
2. With the help of flow charts, one for each practice depicts the chain of events that follow.

Mention the evolutionary significance of the Shrews

Mention the evolutionary significance of the Lobefins

Mention the evolutionary significance of the Homo habilis

p² + 2pq + q² = 1. Explain this algebraic equation on the basis of Hardy Weinberg's principle.

Suggest a method to ensure an anamnestic response in humans.

Write the steps you would suggest to be undertaken to obtain a foreign-gene-product.

What is an age-pyramid?

'in-situ' Conservation can help endangered/threatened species. Justify the statement.

Name and describe any three causes of bio-diversity losses.

What is ferromagnetism?

What type of magnetism is shown by a substance if magnetic moments of domains are arranged in same direction?

An element crystallizes in a f.c.c. lattice with a cell edge of 250 pm. Calculate the density if 300 g of this element contains 2 × 10²⁴ atoms.