Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

If P(A) = `1/2`,  P(B) = 0, then P(A|B) is ______.

A die is tossed thrice. Find the probability of getting an odd number at least once.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

1. both balls are red.
2. first ball is black and second is red.
3. one of them is black and other is red.

A and B are two events such that P (A) ≠ 0. Find P (B|A), if  A is a subset of B.

A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.

If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

Suppose we have four boxes. A, B, C and D containing coloured marbles as given below:

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Find the direction cosines of a line which makes equal angles with the coordinate axes.

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.

Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).

If l₁, m₁, n₁ and l₂, m₂, n₂ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m₁n₂ − m₂n₁, n₁l₂ − n₂l₁, l₁m₂ ­− l₂m₁.

If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.

Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`

Classify the following measures as scalar and vector.

10 kg

Classify the following as scalar and vector quantity.

Time period