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Recent questions in TN XII Math
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TN XII Math
TN XII Math
Applications of Matrices and Determinants
Vector Algebra
Complex Numbers
Analytical Geometry
Differential Calculus Applications - I
Differential Calculus Applications - II
Integral Calculus and its applications
Differential Equations
Discrete Mathematics
Probability Distribution
Objective type Questions and Answers
A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p36
q10
oct-2007
modelpaper
sec-c
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method: $\large \frac{1}{x}+\frac{2}{y}-\frac{1}{z}=1\;;\frac{2}{x}+\frac{4}{y}+\frac{1}{z}=5\;;\frac{3}{x}-\frac{2}{y}-\frac{2}{z}=0$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p36
q9
jun-2008
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q8
sec-c
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q7
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $3x+y-z=2\;,2x-y+2z=6\;,2x+y-2z=-2 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q6
sec-b
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $ 2x+y-z=4\;,x+y-2z=0\;,3x+2y-3z=4 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q5
sec-c
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $x+y+z=4\;,x-y+z=2\;,2x+y-z=1 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q4
sec-c
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q3
oct-2006
oct-2009
modelpaper
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method: $2x+3y=5\;,4x+6y=12 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q2
sec-a
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $3x+2y=5\;,x+3y=4$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q1
sec-b
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q6
mar-2006
modelpaper
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q5
oct-2008
modelpaper
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 0 & 1 & 2 &1 \\2 & -3 & 0 &-1 \\1 & 1 & -1 & 0 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q4
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 3 & 1 & 2 &0 \\1 & 0 & -1 &0 \\2 & 1 & 3 &0 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q3
jun-2008
sec-b
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q2
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the rank of the following matrix :$\begin{bmatrix} 1 & 1 & -1 \\3 & -2 & 3 \\2 & -3 & 4 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-3
p19
q1
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation$\;x-3y-8z+10=0\;,3x+y=4\;,2x+5y+6z=13$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q5
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation $2x-y+z=7\;,3x+y-5z=13\;,x+y+z=5$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q4
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation $\;x+y+z=9\;,\;2x+5y+7z=52\;,2x+y-z=0$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q3
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation $\;7x\;+\;3y\;=\;-1\;,\;2x\;+\;y\;=\;0$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q2
sec-b
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation:$\;2x\;-\;y\;=7\;,\;3x\;-2y\;=11$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q1
jun-2007
modelpaper
sec-b
easy
asked
Mar 29, 2013
by
poojasapani_1
1
answer
For $A=\begin{bmatrix} -1 & 2 & -2 \\4 & -3 & 4 \\4 & -4 & 5 \end{bmatrix}$ show that $A=A^{-1}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q10
mar-2006
modelpaper
asked
Mar 29, 2013
by
poojasapani_1
1
answer
If $A=\Large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q9
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q8
mar-2008
modelpaper
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Show that the adjoint of $A=\begin{bmatrix} -1 & -2 & -2 \\2 & 1 & -2 \\2 & -2 & 1 \end{bmatrix}$ is$\; 3A^T.$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q7
asked
Mar 28, 2013
by
poojasapani_1
1
answer
If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that\((AB)^{T}=B^{T}A^{T}\)
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q5
q5-2
sec-b
easy
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of the matrix $A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify that $A^3=A^{-1}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q6
asked
Mar 28, 2013
by
poojasapani_1
1
answer
If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that \((AB)^{-1}=B^{-1}A^{-1}\)
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p10
q5
q5-1
jun-2006
modelpaper
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of following matrix : $\begin{bmatrix} 2 & 2 & 1 \\1 & 3 & 1 \\1 & 2 & 2 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q4
q4-5
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of following matrix : $\begin{bmatrix} 8 & -1 &- 3 \\-5 & 1 & 2 \\10 & -1 & -4 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q4
q4-4
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of the following matrix : $\begin{bmatrix} 1 & 2 & -2 \\-1 & 3 & 0 \\0 & -2 & 1 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q4
q4-3
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of following matrix: $\begin{bmatrix} 1 & 3 & 7 \\4 & 2 & 3 \\1 & 2 & 1 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec1
exercise1-1
p9
q4
q4-2
sec-b
medium
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the inverse of following matrix :$\begin{bmatrix} 1 & 0 & 3 \\2 & 1 & -1 \\1 & -1 & 1 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q4
q4-1
mar-2007
modelpaper
sec-b
difficult
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the adjoint of matrix A=$\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify the result $A\;(adj A)=(adj A)\;A=$|$A$|$.I$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q3
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the adjoint of the matrix A =$\begin{bmatrix} 1 & 2 \\3 & -5 \end{bmatrix}$ and verify the result $ A\;(adj\; A)=(adj\;A)\;A=$|$A$|$.I$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q2
mar-2007
mar-2009
modelpaper
sec-b
medium
asked
Mar 28, 2013
by
poojasapani_1
1
answer
Find the adjoint of the following matrics;$\begin{bmatrix} 2& 5 & 3 \\3 & 1 & 2 \\1 & 2 & 1 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q1-3
sec-b
easy
asked
Mar 27, 2013
by
poojasapani_1
1
answer
Find the adjoint of the following matrices:$\begin{bmatrix} 1 & 2 & 3 \\0 & 5 & 0 \\2 & 4 & 3 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q1
q-1-2
sec-b
easy
asked
Mar 27, 2013
by
poojasapani_1
1
answer
Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q1
q1-1
oct-2007
modelpaper
sec-a
easy
asked
Mar 27, 2013
by
poojasapani_1
1
answer
Verify that the following is a probability distribution functions: $ f(n) = \left\{ \begin{array}{l l} n/2 & \quad \text{if $n$ is even}\\ -(n+1)/2 & \quad \text{if $n$ is odd}\\ \end{array} \right. $
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
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
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