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Recent questions in CBSE XII
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CBSE XII
CBSE XII
Math
Physics
Chemistry
Biology
If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?
cbse
class12
bookproblem
ch13
misc
p583
q8
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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.
cbse
class12
bookproblem
ch13
misc
p583
q7
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
cbse
class12
bookproblem
ch13
misc
p583
q6
sec-b
easy
modelpaper
2012
q21
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability for the following: (i) all will bear 'X' mark. (ii) not more than 2 will bear 'Y' mark. (iii) at least one ball will bear 'Y' mark. (iv) the number of balls with 'X' mark and 'Y' mark will be equal.
cbse
class12
bookproblem
ch13
misc
p583
q5
medium
sec-c
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
cbse
class12
bookproblem
ch13
misc
p582
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
cbse
class12
bookproblem
ch13
misc
p582
q3
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A couple has two children, (i) Find the probability that both children are males, if it is known that at least one of the children is male. (ii) Find the probability that both children are females, if it is known that the elder child is a female.
cbse
class12
bookproblem
ch13
misc
p582
q2
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A and B are two events such that P (A) $\neq$ 0. Find P(B|A), if (i) A is a subset of B (ii) A $\cap$ B = $\phi$
cbse
class12
bookproblem
ch13
misc
p582
q1
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers is?
cbse
class12
bookproblem
ch13
sec5
p578
q15
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
cbse
class12
bookproblem
ch13
sec5
p578
q14
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
cbse
class12
bookproblem
ch13
sec5
p578
q13
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
cbse
class12
bookproblem
ch13
sec5
p578
q12
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability of getting 5 exactly twice in 7 throws of a die.
cbse
class12
bookproblem
ch13
sec5
p578
q11
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $ \frac{1}{100}$. What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?
cbse
class12
bookproblem
ch13
sec5
p577
q10
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?
cbse
class12
bookproblem
ch13
sec5
p577
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose X has a binomial distribution \(B\: ( 6, \frac{1}{2})\) . Show that X = 3 is the most likely outcome. Hint : P(X = 3) is the maximum among all \(P(x_i),\: x_i = 0,1,2,3,4,5,6\)
cbse
class12
bookproblem
ch13
sec5
p577
q8
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers TRUE; if it falls tails, he answers FALSE. Find the probability that he answers at least 12 questions correctly.
cbse
class12
bookproblem
ch13
sec5
p577
q7
sec-a
difficult
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
cbse
class12
bookproblem
ch13
sec5
p577
q6
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs \[ \text{ (i) none (ii) not more than one (iii) more than one (iv) at least one} \] will fuse after 150 days of use.
cbse
class12
bookproblem
ch13
sec5
p577
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
cbse
class12
bookproblem
ch13
sec5
p577
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
cbse
class12
bookproblem
ch13
sec5
p577
q3
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
cbse
class12
bookproblem
ch13
sec5
p577
q2
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die is thrown 6 times. If getting an odd number is a success, what is the probability?
cbse
class12
bookproblem
ch13
sec5
p576
q1
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is ?
cbse
class12
bookproblem
ch13
sec4
p571
q17
sec-a
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
cbse
class12
bookproblem
ch13
sec4
p571
q16
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0, if he opposed, and X = 1, if he is in favour. Find E(X) and Var (X).
cbse
class12
bookproblem
ch13
sec4
p571
q15
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q14
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q13
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
2
answers
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
cbse
class12
bookproblem
ch13
sec4
p571
q12
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q11
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the mean number of heads in three tosses of a fair coin.
cbse
class12
bookproblem
ch13
sec4
p571
q10
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The random variable X has a probability distribution P(X) of the following form, where k is some number : \[ P(X) = \left\{ \begin{array}{l l} k & \quad \text{if $x$ = 0}\\ 2k & \quad \text{if $x$ = 1} \\ 3k & \quad \text{if $x$ = 2} \\ 0 & \quad \text{otherwise} \end{array} \right. \] (a) Determine the value of k. (b) Find $P (X \lt 2), P (X \leq 2), P(X \geq 2).$
cbse
class12
bookproblem
ch13
sec4
p571
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Given the following probability distribution, $\begin{matrix} \text{X} & 0 &1 &2 &3&4&5&6&7\\ \text{P(X)}&0&k&2k&2k&3k&k^2&2k^2&7k^2+k \end{matrix}$ \[\]determine $\;(i) k\quad (ii) P(X \lt 3)\quad (iii) P(X \gt 6)\quad (iv) P(0 \lt X \lt 3)$
cbse
class12
bookproblem
ch13
sec4
p570
q8
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.
cbse
class12
bookproblem
ch13
sec4
p570
q7
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
cbse
class12
bookproblem
ch13
sec4
p570
q6
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as \[ \text {(i) number greater than 4 (ii) six appears on at least one die} \]
cbse
class12
bookproblem
ch13
sec4
p570
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?
cbse
class12
bookproblem
ch13
sec4
p570
q3
sec-a
concepts
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable ?
cbse
class12
bookproblem
ch13
sec4
p570
q2
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
State which of the following is a probability distributions of a random variable. Give reasons for your answer.
cbse
class12
bookproblem
ch13
sec4
p569
q1
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
If A and B are two events such that \(A ⊂ B\) and \(P(B) ≠ 0\), then which of the following is correct?
cbse
class12
bookproblem
ch13
sec3
p557
q14
concepts
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Probability that A speaks truth is $\large \frac{4}{5} $ . A coin is tossed. A reports that a head appears. The probability that actually there was head is?
cbse
class12
bookproblem
ch13
sec3
p557
q13
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond
cbse
class12
bookproblem
ch13
sec3
p557
q12
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Show that semi-vertical angle of right circular cone of given surface area and maximum volume is \( \sin^{-1} \left(\frac{1}{3}\right)\)
cbse
class12
bookproblem
ch6
sec5
q26
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
cbse
class12
bookproblem
ch13
sec3
p557
q11
sec-c
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?
cbse
class12
bookproblem
ch13
sec3
p557
q10
sec-c
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
cbse
class12
bookproblem
ch13
sec3
p556
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?
cbse
class12
bookproblem
ch13
sec3
p556
q8
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is \(\tan^{-1} \sqrt {2}\).
cbse
class12
bookproblem
ch6
sec5
q25
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver? (Note, in 2014, this was modified to ask for the probability that he is a car driver also).
cbse
class12
bookproblem
ch13
sec3
p556
q7
sec-b
easy
math
modelpaper-2014
q26-a
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?
cbse
class12
bookproblem
ch13
sec3
p556
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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