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Recent questions tagged sec-b
Questions
Express the matrix $\begin{bmatrix}2 & 3 & 1\\1 & -1 & 2\\4 & 1 & 2\end{bmatrix}\;$as the sum of symmetric and skew symmetric matrices P&Q.
cbse
class12
ch3
q52
p59
exemplar
easy
sec-b
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If A,B are square matrices of same order and B is a skew-symmetric matrix,show that A'BA is skew symmetric.
cbse
class12
ch3
q48
p58
short-answer
exemplar
easy
sec-b
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If A is square matrix such that $A^2=A,$show that $(I+A)^3=7A+I.$
cbse
class12
ch3
q47
p58
short-answer
sec-b
easy
exemplar
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $P(x)=\begin{bmatrix}\cos x & \sin x\\-\sin x & \cos x\end{bmatrix}$,then show that\[P(x).P(y)=P(x+y)=P(y).P(x).\]
cbse
class12
ch3
q46
p58
short-answer
easy
sec-b
exemplar
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the value of $\alpha$ if $A=\begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$ and $\;A^{-1}=A'$
cbse
class12
ch3
q44
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If the matrix $\begin{bmatrix}0 & a & 3\\2 & b & -1\\c & 1 & 0\end{bmatrix}\;$is a skew symmetric matrix,find the values of a,b and c.
cbse
class12
ch3
q45
p58
short-answer
exemplar
sec-b
medium
qod
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\4 & 1\end{bmatrix},find\;A^2+2A+7I.$
cbse
class12
ch3
q43
p58
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the matrix A such that$\begin{bmatrix}2 & -1\\1 & 0\\-3 & 4\end{bmatrix}\;A=\begin{bmatrix}-1 & -8 & -10\\1& -2 & -5\\9 & 22 &15\end{bmatrix}.$
cbse
class12
ch3
q42
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find the values of a,b,c and d,if $3\begin{bmatrix}a & b\\c & d\end{bmatrix}=\begin{bmatrix}a & 6\\-1 & 2d\end{bmatrix}+\begin{bmatrix}4 & a+b\\c+d & 3\end{bmatrix}$
cbse
class12
ch3
q41
p58
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let R be the set of real numbers, f : R\( \rightarrow \)R be the function defined by f (x) = 4x + 3, x ∈ R. Show that f is invertible. Find the inverse of f.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
Prove that \[ tan^{-1} \bigg( \frac{\sqrt {1+x}-\sqrt {1-x}}{\sqrt {1+x}+\sqrt {1-x}} \bigg) = \frac{\pi}{4} - \frac{1}{2} cos^{-1}x , \frac{-1}{\sqrt 2} \leq x \: \leq 1 \]
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
If x, y, z are different numbers and \[ A = \begin{bmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{bmatrix} = 0 \] , then show that 1 + x y z = 0
cbse
class12
modelpaper
2012
sec-b
q23
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
Is the function f defined by \[ f (x) = \left\{ \begin{array}{l l} x+5, & \quad {if\: x\: \leq 1}\\ x-5 & \quad \text{ if $x$ > 1} \end{array} \right.\] a continuous function? Justify your answer.
cbse
class12
modelpaper
2012
sec-b
q24
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
Find inverse,by elementary row operations(if possible),of the following matrices$\quad\begin{bmatrix}1 & 3\\-5 & 7\end{bmatrix}$
cbse
class12
ch3
q37
q37-1
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Prove by Mathematical Induction that $(A')^n=(A^n)'$,where $n\in N$ for any square matrix A.
cbse
class12
ch3
q36
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}0 & x\\x & 0\end{bmatrix},B=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\;and\;x^2=-1,then\;show\;that\;(A+B)^2=A^2+B^2.$
cbse
class12
ch3
q34
p57
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(i)\;(A-B)^T=A^T-B^T.\]
cbse
class12
ch3
q32i
p57
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(h)\;(A-B)C=AC-BC.\]
cbse
class12
ch3
q32h
p57
short-answer
exemplar
easy
sec-b
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;$and$\;a=4,b=-2$.Show that$\;(g)\;(AB)^T=B^TA^T.$
cbse
class12
ch3
q32g
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that$:\[(d)\;a(C-A)=aC-aA.\]
cbse
class12
ch3
q32d
p57
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;,\;a=4,b=-2\;$.Show that:$\;(c)\;(a+b)B=aB+bB$
cbse
class12
ch3
q32c
p57
short-answer
exemplar
sec-b
easy
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If \(x = a (cos\: t + t\: sin \: t), y = a (sin\: t – t \: cos \: t)\). Find \( \frac{d^2y}{dx^2} \)
cbse
class12
modelpaper
2012
sec-b
q25
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
Find \[ \int \mathrm \: ( sin^{-1} x)^2\: dx \]
cbse
class12
modelpaper
2012
sec-b
q26
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
Evaluate \[ \int_{-2}^2 \mathrm \: | 1 - x^2 |dx \]
cbse
class12
modelpaper
2012
sec-b
q27
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
Find the solution of the differential equation \( (x^2 + y^2) dx = 2xy \: dy\)
cbse
class12
modelpaper
2012
sec-b
q28
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that:$\[(b)\;A(BC)=(AB)C\]
cbse
class12
ch3
q32b
p56
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;and\;a=4,b=-2.Show\;that:$\[(a)\;A+(B+C)=(A+B)+C\]
cbse
class12
ch3
q32a
p56
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Show that $A'A$ and $AA'$ are both symmetric matrices for any matrix A
cbse
class12
ch3
q29
p56
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(i)\quad(2A+B)'=2A'+B'$
cbse
class12
ch3
q28
q28-1
p56
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 0 & -1\\2 & 1 & 3\\0 & 1 & 1\end{bmatrix},then\;verify\;that\;A^2+A=A(A+I),where\;I\;is\;3\times 3\;unit\;matrix.$
cbse
class12
ch3
q26
p56
short-answer
exemplar
medium
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}2 & 1\end{bmatrix}\;B=\begin{bmatrix}5 & 3 & 4\\8 & 7 & 6\end{bmatrix}\;andC=\begin{bmatrix}-1 & 2 & 1\\1 & 0 & 2\end{bmatrix},verify\;that\;A(B+C)=(AB+AC)$
cbse
class12
ch3
q25
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $\begin{bmatrix}2 & 1 & 3\end{bmatrix}\begin{bmatrix}-1 & 0 & -1\\-1 & 1 & 0\\0 & 1 & 1\end{bmatrix}\begin{bmatrix}1\\0\\-1\end{bmatrix}=A,find\;A.$
cbse
class12
ch3
q24
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $P=\begin{bmatrix}x & 0 &0\\0 & y & 0\\0 & 0 & z\end{bmatrix}\;$ and $\;Q=\begin{bmatrix}a & 0 & 0\\0 & b & 0\\0 & 0 & c\end{bmatrix}$ prove that $PQ=\begin{bmatrix}xa & 0 & 0\\0 & yb & 0\\0 & 0 & zc\end{bmatrix}=QP$
cbse
class12
ch3
q23
p55
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(i)\;(AB)C=A(BC)$
cbse
class12
ch3
q22
q22-1
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Which of the following is an example of matrices A,B and C such that AB=AC,where A is non-zero matrix,but $B\neq C.$
cbse
class12
ch3
q21
p55
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If A=[3 , 5],B=[7, 3],then find a non-zero matrix C such that AC=BC.
cbse
class12
ch3
q20
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If X and Y are $2\times 2$matrices,then solve the following matrix equation for X and Y\[2X+3Y=\begin{bmatrix}2 & 3\\4 & 0\end{bmatrix},3X+2Y=\begin{bmatrix}-2 & 2\\1 & -5\end{bmatrix}.\]
cbse
class12
ch3
q19
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Solve for x and y:\[x\begin{bmatrix}2\\1\end{bmatrix}+y\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0\]
cbse
class12
ch3
q18
p54
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Given $A=\begin{bmatrix}2 & 4 & 0\\3 & 9 & 6\end{bmatrix}\;and\;B=\begin{bmatrix}1& 4\\2 & 8\\1 & 3\end{bmatrix}.\;Is \;(AB)'=B'A'?$
cbse
class12
ch3
q17
p54
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}3 & -4\\1 & 1\\2 & 0\end{bmatrix}\;and\;B=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix} \;$ then verify that $(BA)^2\neq B^2A^2$
cbse
class12
ch3
q14
p54
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Find A,if $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}4 & 8 & 4\\1 & 2 &1\\3 & 6 & 3\end{bmatrix}$
cbse
class12
ch3
q13
p54
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Find the matrix A satisfying the matrix equation $\begin{bmatrix}2 & 1\\3 & 2\end{bmatrix}A\begin{bmatrix}3 & 2\\5 & 3\end{bmatrix}=\begin{bmatrix}1 & 0\\0 & 12\end{bmatrix}$
cbse
class12
ch3
q12
p54
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Find the value of $x$ if $\begin{bmatrix}1 & x &1\end{bmatrix}\begin{bmatrix}1 & 3 & 2\\2 & 5 & 1\\15 & 3 & 2\end{bmatrix}\begin{bmatrix}1\\2\\x\end{bmatrix}=0$.
cbse
class12
ch3
q10
p53
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}0 & 1\\1& 1\end{bmatrix}\;and\;B=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},\;show\;that\;(A+B)(A-B)\neq A^2-B^2$
cbse
class12
ch3
q9
p53
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Find non-zero values of $x$ satisfying the matrix equation $x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\(10) & 6x\end{bmatrix}$
cbse
class12
ch3
q8
p53
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If the magnitude of the vectors, \( \overline {a} , \overline{b} , \overline{c} \) are 3, 4, 5 respectively and \( \overline{a} \) and \( \overline{b} + \overline{c}, \overline{b} \) and \( ( \overline{c} + \overline{a} ), \overline{c}\: and\: ( \overline{a} + \overline{b} )\) are mutually perpendicular, then find the magnitude of \(( \overline{a} + \overline{b} + \overline{c} ) \)
cbse
class12
modelpaper
2012
sec-b
q29
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
Find the equation of the straight line passing through (1, 2, 3) and perpendicular to the plane \( x + 2y – 5z + 9 = 0\)
cbse
modelpaper
2012
sec-b
q30
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
A man and his wife appear for an interview for two posts. The probability of husband’s selection is \( \frac{1}{7} \) and that of the wife’s selection is \( \frac{1}{5} \) . Find the probability that only one of them will be selected.
cbse
class12
modelpaper
2012
sec-b
q31
math
asked
Dec 22, 2012
by
thanvigandhi_1
1
answer
Find values of a and b if A=B,where A=$\begin{bmatrix}a + 4 & 3b\\8 & - 6\end{bmatrix},B=\begin{bmatrix}2a + 2 & b^2 + 2\\8 & b^2 - 5b\end{bmatrix}$
cbse
class12
ch3
q5
p53
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
If $y=2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ for all x,then _________< y < ___________.
cbse
class12
ch2
q46
p40
fitb
exemplar
easy
sec-a
sec-b
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
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