HSC Science (Computer Science) 11th Standard - Maharashtra State Board Important Questions

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.

Answer briefly.

Give two uses of radio waves.

Answer the following question.

Under what conditions are total internal reflection possible? Explain it with a suitable example.

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.

Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

If A = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.

If A = `[(7,1), (2,5)]` and B = `[(1,2), (3,-1)]` then verify that |AB| = |A|  |B|.

If A = `[(3, 1),(-1, 2)]`, prove that A² – 5A + 7I = 0, where I is unit matrix of order 2

An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.

Suppose that 80% of all families own a television set. If 5 families are interviewed at  random, find the probability that
a. three families own a television set.
b. at least two families own a television set.

Define the following term:

Free fall

The distance between two bodies is doubled. How is the magnitude of the gravitational force between them affected?

Define emissive power and coefficient of emmision of a body.

The dimensions of emissive power are ______.

A pinhole is made in a hollow sphere of radius 5 cm whose inner wall is at temperature 727^oC. Find the power radiated per unit area. [Stefan’s constant σ = 5.7 x 10^-8 J/m² s K4 , emissivity (e) = 0.2]

Compute the temperature at which the r.m.s. speed of nitrogen molecules is 832 m/s. [Universal gas constant, R = 8320 J/k mole K, molecular weight of nitrogen = 28.]

The light from the Sun is found to have a maximum intensity near the wavelength of 470 nm. Assuming the surface of the Sun as a black body, the temperature of the Sun is _____________.

[Wien's constant b = 2 .898 x l0^{- 3}mK]

A metal ball cools from 64 ^°C to 50 ^°C in 10 minutes and to 42 ^°C in next 10 minutes. The ratio of rates of fall of temperature during the two intervals is _______.

The susceptibility of magnesium at 300 K is 2.4 x 10^-5. At what temperature will the susceptibility increase to 3.6 x 10^-5?

1000 tiny mercury droplets coalesce to form a bigger drop. In this process, temperature of the drop _______ .

(A) increases

(B) may increase or decrease

(C) decreases

(D) does not change