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Questions asked by balaji.thirumalai
Questions
4474
questions
1
answer selected
Find the probability distribution of the number of sixes in throwing three dice once.
tnstate
class12
bookproblem
ch10
sec2
exercise10-1
p203
q1
modelpaper
mar-2006
asked
Nov 27, 2012
1
answer
Show that the set $ G = \{2^n / n \in Z\} $ is an abelian group under multiplication.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q12
asked
Nov 27, 2012
1
answer
Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q11
modelpaper
mar-2008
asked
Nov 27, 2012
1
answer
Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q10
asked
Nov 27, 2012
1
answer
Show that the set {[1], [3], [4], [5], [9]} forms an abelian group under multiplication modulo 11.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q9
modelpaper
mar-2007
jun-2009
asked
Nov 27, 2012
1
answer
Show that the set G of all rational numbers except − 1 forms an abelian group with respect to the operation $*$ given by $a * b = a + b + ab$ for all $a, b \in G$.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q8
modelpaper
jun-2007
mar-2009
asked
Nov 27, 2012
1
answer
Show that the set M of complex numbers z with the condition | z | = 1 forms a group with respect to the operation of multiplication of complex numbers.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q7
asked
Nov 27, 2012
1
answer
Show that { $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega & 0 \\ 0 & \omega^2\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega^2 & 0 \\ 0 & \omega\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega^2\\ \omega & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega\\ \omega^2 & 0\end{smallmatrix} \bigr) $} where $\omega^3 = 1, \omega \neq 1$ form a group with respect to matrix multiplication.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q6
asked
Nov 27, 2012
1
answer
Show that the set G of all positive rationals forms a group under the composition $*$ defined by $a * b = (\large\frac{ab}{3})$ for all $a, b \in G.$
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q5
modelpaper
mar-2006
jun-2006
oct-2007
asked
Nov 27, 2012
1
answer
Prove that the matrices $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr) $ form a group under matrix multiplication
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q4
asked
Nov 27, 2012
1
answer
Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q3
asked
Nov 27, 2012
1
answer
Show that the set N of natural members is a semi-group under the operation $x * y $= max {x, y}. Is it a monoid?
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q2
asked
Nov 27, 2012
1
answer
Let $S$ be a non-empty set and o be a binary operation on $S$ defined by $xoy = x ; x, y \in S$. Determine whether o is commutative and associative.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q1
asked
Nov 27, 2012
1
answer
Show that $(p \wedge q)\rightarrow (p \vee q)$ is a tautology.
bookproblem
ch9
sec1
exercise9-3
p168
q7
tnstate
class12
asked
Nov 27, 2012
1
answer
Show that $p \rightarrow q$ and $q \rightarrow p$ are not equivalent.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q6
modelpaper
mar-2009
asked
Nov 27, 2012
1
answer
Show that $\sim(p\wedge q) \equiv (\sim p)\vee (\sim q)$
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q5
asked
Nov 27, 2012
1
answer
Show that p ↔ q ≡ ((∼ p) ∨ q) ∧ ((∼ q) ∨ p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q4
modelpaper
mar-2007
jun-2007
oct-2008
mar-2010
asked
Nov 27, 2012
1
answer
Show that p ↔ q ≡ (p → q) ∧ (q → p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p168
q3
modelpaper
oct-2006
jun-2009
asked
Nov 27, 2012
1
answer
Show that p → q ≡ (∼ p) ∨ q
tnstate
class12
bookproblem
ch9
sec2
exercise9-3
p168
q2
asked
Nov 27, 2012
1
answer
Use the truth table to establish which of the following statements are tautologies and which are contradictions.
tnstate
class12
bookproblem
ch9
sec1
exercise9-3
p167
q1
q1-1
asked
Nov 27, 2012
1
answer
Construct the truth tables for the following statement: (p ∧ q) ∨ r
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q10
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (p ∨ q) ∨ r
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q9
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q8
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ [∼ (p ∧ q)]
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q7
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: ∼ (p ∨ (∼ q))
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q6
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (p ∧ q) ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q5
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (p ∨ q) ∨ (∼ p)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q4
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: ∼ (p ∨ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q3
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement: (∼ p) ∧ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q2
asked
Nov 27, 2012
0
answers
Construct the truth tables for the following statement :p ∨ (∼ q)
tnstate
class12
bookproblem
ch9
sec1
exercise9-2
p164
q1
asked
Nov 27, 2012
0
answers
Write negation of the each of the following statements :
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q25
asked
Nov 27, 2012
0
answers
If p stands for the statement “Sita likes reading” and q for the statement “Sita likes playing’ what does ∼p ∧ ∼ q stand for?
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q24
asked
Nov 27, 2012
1
answer
Translate each of the following compound statements into symbolic form:
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q23
asked
Nov 27, 2012
0
answers
Let p be “Kamala is going to school” and q be “There are twenty students in the class “. Give a simple verbal sentence which describes each of the following statements : (i) p ∨ q (ii) p ∧ q (iii) ∼ p (iv) ∼ q (v) ∼p ∨ q
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q22
asked
Nov 27, 2012
1
answer
Form the conjunction and the disjunction of (i) p : Anand reads newspaper, q : Anand plays cricket. (ii) p : I like tea. q : I like ice-cream.
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q21
asked
Nov 27, 2012
0
answers
Find out which of the following sentences are statements and which are not? Justify your answer
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p160
q1-10
asked
Nov 27, 2012
0
answers
Write down the truth value (T or F) of the following statements
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p160
q11-20
asked
Nov 27, 2012
1
answer
If A and B are any two events such that \(P(A) + P(B) - P(A \text{and} B) = P(A)\), then choose the correct answer:
cbse
class12
bookproblem
ch13
misc
p584
q19
sec-a
easy
math
asked
Nov 27, 2012
1
answer
If P(A|B) > P(A), then which of the following is correct ?
cbse
class12
bookproblem
ch13
misc
p584
q18
sec-a
easy
math
asked
Nov 27, 2012
1
answer
If A and B are two events such that P(A) $\neq$ 0 and P(B | A) = 1 . Then choose the correct answer.
cbse
class12
bookproblem
ch13
misc
p584
q17
sec-a
easy
math
asked
Nov 27, 2012
1
answer
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
cbse
class12
bookproblem
ch13
misc
p584
q16
sec-b
easy
math
asked
Nov 27, 2012
1
answer
An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: $ \text {P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15}$. Evaluate the following probabilities \[ \text {(i) P(A fails | B has failed) (ii) P(A fails alone)} \]
cbse
class12
bookproblem
ch13
misc
p584
q15
sec-a
easy
math
asked
Nov 27, 2012
1
answer
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability \(\frac{1}{2}\)).
cbse
class12
bookproblem
ch13
misc
p584
q14
sec-a
easy
math
asked
Nov 27, 2012
1
answer
Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
cbse
class12
bookproblem
ch13
misc
p584
q13
sec-c
medium
modelpaper
2012
q26
math
asked
Nov 27, 2012
1
answer
Suppose we have four boxes A,B,C and D containing coloured marbles as given in the box 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? \[\]$\begin{matrix} \text{Box} & &\text{Marble Colour} & \\ &\text{Red} &\text{White} & \text{Black}\\ A & 1 & 6 & 3\\ B & 6 & 2 &2 \\ C & 8 & 1 & 1\\ D & 0 & 6 & 4 \end{matrix}$
cbse
class12
bookproblem
ch13
misc
p583
q12
sec-b
difficult
math
asked
Nov 27, 2012
1
answer
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.
cbse
class12
bookproblem
ch13
misc
p583
q11
sec-b
easy
math
asked
Nov 27, 2012
2
answers
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
cbse
class12
bookproblem
ch13
misc
p583
q10
easy
sec-b
math
asked
Nov 27, 2012
1
answer
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
cbse
class12
bookproblem
ch13
misc
p583
q9
easy
sec-b
math
asked
Nov 27, 2012
1
answer
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
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
1
answer
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