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Recent questions tagged sec2
Questions
By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]
cbse
class12
bookproblem
ch4
sec2
q12
p121
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that $ (i) \begin{vmatrix} a-b-c&2a&2a \\ 2b&b-c-a&2b \\ 2c&2c&c-a-b \end{vmatrix} = (a+b+c)^3 $
cbse
class12
bookproblem
ch4
sec2
q11
q11-1
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $
cbse
class12
bookproblem
ch4
sec2
q10
q10-1
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that \[\begin{vmatrix} x&x^2&yz \\ y&y^2&zx \\ z&z^2&xy \end{vmatrix} = (x-y)(y-z)(z-x)(xy+yz+zx) \]
cbse
class12
bookproblem
ch4
sec2
q9
p120
difficult
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that $ (i) \quad \begin{vmatrix} 1&a&a^2 \\ 1&b&b^2 \\ 1&c&c^2 \end{vmatrix} = (a-b)(b-c)(c-a) $
cbse
class12
bookproblem
ch4
sec2
q8
q8-1
p120
easy
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]
cbse
class12
bookproblem
ch4
sec2
q7
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 0&a&-b \\ -a&0&-c \\ b&c&0 \end{vmatrix} = 0 \]
cbse
class12
bookproblem
ch4
sec2
q6
p120
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} b+c&q+r&y+z \\ c+a&r+p&z+x \\ a+b&p+q&x+y \end{vmatrix} = 2 \begin{vmatrix} a&p&x \\ b&q&y \\ c&r&z \end{vmatrix} \]
cbse
class12
bookproblem
ch4
sec2
q5
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 1&bc&a(b+c) \\ 1&ca&b(c+a) \\ 1&ab&c(a+b) \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q4
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 2&7&65 \\ 3&8&75 \\ 5&9&86 \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q3
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a-b&b-c&c-a \\b-c&c-a&a-b \\c-a&a-b&b-c \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q2
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} x&a&x+a \\y&b&y+b \\ z&c&z+c \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q1
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
A discrete random variable X has the following probability distributions (see table below). (i) Find the value of a
tnstate
class12
bookproblem
ch10
sec2
exercise10-1
p203
q4
q4-1
modelpaper
mar-2007
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two bad oranges are accidentally mixed with ten good ones. Three oranges are drawn at random without replacement from this lot. Obtain the probability distribution for the number of bad oranges. and find the expected value of the distribution.
tnstate
class12
bookproblem
ch10
sec2
exercise10-1
p203
q3
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two cards are drawn successively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of queens.
tnstate
class12
bookproblem
ch10
sec2
exercise10-1
p203
q2
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
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
by
balaji.thirumalai
1
answer
Show that p → q ≡ (∼ p) ∨ q
tnstate
class12
bookproblem
ch9
sec2
exercise9-3
p168
q2
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two events A and B will be independent, if which of the following is true?
cbse
class12
bookproblem
ch13
sec2
p548
q18
easy
concepts
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Choose the correct answer: The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
cbse
class12
bookproblem
ch13
sec2
p548
q17
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a hostel, 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and English news papers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English news papers. (b) If she reads Hindi news paper, find the probability that she reads English news paper. (c) If she reads English news paper, find the probability that she reads Hindi news paper.
cbse
class12
bookproblem
ch13
sec2
p548
q16
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independant if: E : the card drawn is a spade F : the card drawn is an ace
cbse
class12
bookproblem
ch13
sec2
p547
q15
q15-1
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Probability of solving specific problem independently by A and B are $\large \frac{1}{2} $ and $\large \frac{1}{3} $ respectively. If both try to solve the problem independently, find the probability that $ \text {(i) the problem is solved (ii) exactly one of them solves the problem.} $
cbse
class12
bookproblem
ch13
sec2
p547
q14
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.
cbse
class12
bookproblem
ch13
sec2
p546
q13
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die is tossed thrice. Find the probability of getting an odd number at least once.
cbse
class12
bookproblem
ch13
sec2
p546
q12
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)
cbse
class12
bookproblem
ch13
sec2
p546
q11
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Events A and B are such that $P (A) = \frac{1}{2} , P(B) = \frac{7}{12}$ and P(not A or not B) = $ \frac{1}{4} $ . State whether A and B are independent?
cbse
class12
bookproblem
ch13
sec2
p546
q10
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
If A and B are two events such that $P (A) = \large \frac{1}{4} , P (B) = \large\frac{1}{2} $ and $P(A \cap B) = \large \frac{1}{8} $ , find $P$ (not A and not B).
cbse
class12
bookproblem
ch13
sec2
p546
q9
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find (i) P(A $\cap$ B) (ii) P(A $\cup$ B) (iii) P ($\large\frac{A}{B}$) (iv) P ($\large\frac{B}{A}$)
cbse
class12
bookproblem
ch13
sec2
p546
q8
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Given that the events A and B are such that $P(A) = \large \frac{1}{2} , P (A \cap B) = \large \frac{3}{5} $ and $P(B) = p$. Find p if they are (i) mutually exclusive (ii) independent.
cbse
class12
bookproblem
ch13
sec2
p546
q7
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Let E and F be events with $P (E) = \frac{3}{5} , P (F)= \frac{3}{10} $ and $P (E \cap F) = \frac{1}{5} $ . Are E and F independent?
cbse
class12
bookproblem
ch13
sec2
q6
p546
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event of the number being even, and B be the event of the number being red. Are A and B independent?
cbse
class12
bookproblem
ch13
sec2
q5
p546
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A fair coin and an unbiased die are tossed. Let A be the event - head appears on the coin and B be the event 3 on the die. Check whether A and B are independent events or not.
cbse
class12
bookproblem
ch13
sec2
q4
p546
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
cbse
class12
bookproblem
ch13
sec2
q3
546
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
cbse
class12
bookproblem
ch13
sec2
q2
546
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
If $P(A) = \frac{3}{5} $ and $P(B) = \frac{1}{5} $ , find $P (A \cap B) $ if A and B are independent events.
cbse
class12
bookproblem
ch13
sec2
q1
546
easy
sec-a
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
If $ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix} , B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \text{ and } C = \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -3 & 2 \end{bmatrix} $, then compute $( A + B )$ and $( B - C )$. Also verify that $A + ( B - C ) = ( A + B ) - C. $
cbse
class12
bookproblem
ch3
sec2
q4
p81
easy
long-answer
sec-c
math
asked
Nov 26, 2012
by
pady_1
1
answer
If $ A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix} \text{ and } B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix} \text{ then compute } 3A - 5B $
cbse
class12
bookproblem
ch3
sec2
q5
p81
medium
sec-b
math
asked
Nov 26, 2012
by
pady_1
1
answer
Simplify $\cos\theta\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ + $\sin\theta\begin{bmatrix} \sin\theta & -\cos\theta \\ \cos\theta & \sin\theta \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q6
p81
easy
shortanswer
sec-a
math
asked
Nov 26, 2012
by
pady_1
1
answer
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