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Recent questions in Determinants
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CBSE XII
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Math
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Determinants
\[ \text{For the matrix A = } \begin{bmatrix} 2&-1&1 \\ -1& 2&- 1 \\ 1 &-1& 2 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 9A - 4I = O. \text{ Hence, find } A^{-1}\]
cbse
class12
bookproblem
ch4
sec5
q16
p132
difficult
sec-c
math
asked
Feb 26, 2013
by
sreemathi.v
1
answer
Find area of the triangle with vertices at the point given in each of the following (-2, -3), (3, 2), (-1, -8)
cbse
class12
bookproblem
ch4
sec3
q1
p122
qp3
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find area of the triangle with vertices at the point given in each of the following (2, 7), (1, 1), (10, 8)
cbse
class12
bookproblem
ch4
sec3
q1
p122
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find equation of line joining (3, 1) and (9, 3) using determinants.
cbse
class12
bookproblem
ch4
sec3
q4
p123
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find values of $k$ if area of triangle is $4\; sq. units$ and vertices are $(-2, 0), (0, 4), (0, k)$
cbse
class12
bookproblem
ch4
sec3
q3
p123
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Using properties of determinants, solve the following for x : $ \begin{vmatrix} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x \end{vmatrix} = 0 $
cbse
class12
modelpaper
2012
sec-c
q20
ch4
easy
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
True or False: The maximum value of $\begin{vmatrix}1 & 1 & 1\\1 &(1-\sin x) & 1\\1 & 1 & 1-cos x\end{vmatrix}\;is\;\Large \frac{1}{2}$.
cbse
class12
ch4
sec-a
q58
p85
true-or-false
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: Let $\begin{vmatrix}a & p & x\\b & q & y\\c & r & z\end{vmatrix}$ = 16, then $\Delta_1=\begin{vmatrix}p+x & a+x & a+p\\q+y & b+y & b+q\\r+z & c+z & c+r\end{vmatrix}$ = 32
cbse
class12
ch4
sec-a
q57
p85
true-or-false
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: If the determinant $\small\begin{vmatrix}x+a & p+u & l+ f\\y+b & q+v & m +g\\z+c & r+w & n + h\end{vmatrix}$ splits into exactly $k$ determinants of order $3$, each element of which contains online term,then the value of $k$ is $8$.
cbse
class12
ch4
q56
p84
true-or-false
exemplar
sec-a
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: The determinant $ \begin{vmatrix}\sin A & \cos A & \sin A+\cos B\\\sin B & \cos A & \sin B+\cos B\\\sin C & \cos A & \sin C+\cos B\end{vmatrix}$ is equal to zero
cbse
class12
ch4
sec-a
q55
p84
true-or-false
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: $\mid adj A\mid={\mid A\mid}^2$,where A is a square matrix of order two.
cbse
class12
ch4
sec-a
q54
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: $\begin{vmatrix}x+1 & x+2 & x+a\\x+2 & x+3 & x+b\\x+3 & x+4 & x+c\end{vmatrix}=0,$where a,b,c are in A.P.
cbse
class12
ch4
sec-a
q53
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: If the value of a third order determinant is 12,then the value of the determinant formed by replacing each element by its co-factor will be 144.
cbse
class12
ch4
sec-a
q52
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: If A and B are matrices of order 3 and $\mid A\mid=5,\mid B \mid=3,then\mid 3AB\mid=27\times 5\times 3=405$
cbse
class12
ch4
sec-a
q51
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: $|\;A^{-1}\;|\neq |\;A\;|^{-1}$,where A is non-singular matrix.
cbse
class12
ch4
sec-a
q50
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: $(aA)^{-1}= \Large{ \frac{1}{a}}\normalsize A^{-1}$, where $a$ is a any real number and $A$ is a square matrix.
cbse
class12
ch4
sec-a
q49
p84
true-or-false
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
True or False: $(A^3)^{-1}=(A^{-1})^3$,where A is a square matrix and $|\;A\;|\neq 0$
cbse
class12
ch4
sec-a
q48
p84
true-or-false
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
If $f(x)$ = $\small\begin{vmatrix}(1+x)^{17} & (1+x)^{19} & (1+x)^{23}\\(1+x)^{23} & (1+x)^{29} & (1+x)^{34}\\(1+x)^{41} & (1+x)^{43} & (1+x)^{47}\end{vmatrix}$ = $A+Bx+Cx^2+.....$, then $A$ =
cbse
class12
ch4
sec-a
q47
p84
fitb
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
$\begin{vmatrix}0 & xyz & x-z\\y-x & 0 & y-z\\z-x & z-y & 0\end{vmatrix}$ =
cbse
class12
ch4
sec-a
q46
p83
fitb
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
if $x=-9$ is a root of $\begin{vmatrix}x & 3 & 7\\2 & x & 2\\7 & 6 & x\end{vmatrix}=0$, then other roots are
cbse
class12
ch4
sec-a
q45
p83
fitb
exemplar
difficult
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ________________.
cbse
class12
ch4
sec-a
q44
p83
fitb
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
If A is a matrix of order $3\times 3$,then number of minors in determinant of A are____________.
cbse
class12
ch4
sec-a
q43
p83
fitb
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
If A is a matrix of order $3\times 3$,then $(A^2)^{-1}$=_____________.
cbse
class12
ch4
sec-a
q42
p83
fitb
exemplar
easy
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
If $\cos 2\theta=0$, then ${\begin{vmatrix}0 & \cos\theta & \sin\theta\\\cos\theta & \sin\theta & 0\\\sin\theta & 0 & \cos\theta\end{vmatrix}}^2$ =
cbse
class12
ch4
sec-a
q41
p83
fitb
exemplar
medium
math
asked
Dec 28, 2012
by
sreemathi.v
1
answer
If $x,y, z\in R,$ then the value of determinant $\small\begin{vmatrix}(2^x + 2^{-x})^2 & (2^x - 2^{-x})^2 & 1\\ (3^x + 3^{-x})^2 & (3^x - 3^{-x})^2 & 1\\(4^x + 4^{-x})^2 & (4^x - 4^{-x})^2 & 1\end{vmatrix}$ is
cbse
class12
ch4
sec-a
q40
p83
fitb
exemplar
difficult
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If A is invertible matrix of order $3\times 3$,then $| A^{-1} |$___________.
cbse
class12
ch4
sec-a
q39
p83
fitb
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If A is a matrix of order $3\times 3$,then | 3A |=_______________.
cbse
class12
ch4
sec-a
q38
p83
fitb
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
There are two values of $a$ which makes the determinant $\Delta=\begin{vmatrix}1 & -2 & 5\\2 & a & 1\\0 & 4 & 2a\end{vmatrix}= 86,$ then sum of these number is
cbse
class12
ch4
sec-a
q37
p83
objective
exemplar
medium
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
The value of the determinant $\begin{vmatrix}x & x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$ is
cbse
class12
ch4
sec-a
q36
p82
objective
exemplar
medium
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If $x,y,z$ are all different from zero and $\begin{vmatrix}1+x & 1 & 1\\1 & 1+y & 1\\1 & 1 & 1+z\end{vmatrix}$ = 0, then value of $x^{-1}+y^{-1}+z^{-1}$ is
cbse
class12
ch4
sec-a
q35
p82
objective
exemplar
medium
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If A and B are invertible matrices,then which of the following is not correct?\[\begin{array}{1 1}(A)\quad adjA=|A|.A^{-1} & (B)\quad det(A)^{-1}=[det(A)]^{-1}\\(C)\quad (AB)^{-1}=B^{-1}A^{-1} & (D)\quad (A+B)^{-1}=B^{-1}+A^{-1}\end{array}\]
cbse
class12
ch4
sec-a
q34
p82
objective
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If $A=\begin{vmatrix}2 & \lambda & 3\\0 & 2 & 5\\1 & 1 & 3\end{vmatrix},$ then$\;A^{-1}\;$exists if $\lambda = ?$
cbse
class12
ch4
sec-a
q33
p82
objective
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
If $f(x)=\begin{vmatrix}0 & x-a & x-b\\x-a & 0 & x-c\\x-b & x-c & 0\end{vmatrix},then$\[\begin{array}{1 1}(A)\quad f(a)=0 & (B)\quad f(b)=0\\(C)\quad f(0)=0 & (D)\quad f(1)=0\end{array}\]
cbse
class12
ch4
sec-a
q32
p82
objective
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
The maximum value of $\begin{vmatrix}1 & 1 & 1\\1 & 1-sin\theta & 1\\1-\cos\theta & 1 & 1\end{vmatrix}\;(is\;\theta\; is\; real\;number)$
cbse
class12
ch4
sec-a
q31
p81
objective
exemplar
easy
math
asked
Dec 27, 2012
by
sreemathi.v
1
answer
Let $f(t)=\begin{vmatrix}\cos t & t & 1\\2\sin t & t & 2t\\\sin t & t & t\end{vmatrix}$, then $\displaystyle \lim_{t \to 0}\Large \frac{f(t)}{t^2}$ is equal to
cbse
class12
ch4
sec-a
q30
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If A,B and C are angles of a triangle ,then the determinant$\begin{vmatrix}1 & \cos C & \cos B\\\cos C & 1 & \cos A\\\cos B & \cos A & 1\end{vmatrix}$ is equal to
cbse
class12
ch4
sec-a
q29
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
The number of distinct real roots of $\begin{vmatrix}\sin x & \cos x & \cos x\\\cos x & \sin x & \cos x\\\cos x & \cos x &\sin x\end{vmatrix}=0\;$ in the interval $\large \frac{-\pi}{4}$$ \leq x \leq\large \frac {\pi}{4}$ is
cbse
class12
ch4
sec-a
q28
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
The determinant $\begin{vmatrix}b^2 - ab & b - c & bc - ac\\ab - a^2 & a - b & b^2 - ab\\bc - ac & c - a & ab -a^2\end{vmatrix}$ equals
cbse
class12
ch4
sec-a
q27
p80
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
The area of a triangle with vertices(-3,0),(3,0) and (0,k) is 9 sq. units.The value of k will be\[ \begin{array}{1 1}(A)\quad 9 & (B)\quad 3\\(C)\quad-9 & (D)\quad 6\end{array}\]
cbse
class12
ch4
sec-a
q26
p80
objective
exemplar
easy
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find the value of the determinant $\begin{vmatrix}a-b & b+c & a\\b-c & c+a & b\\c-a & a+b & c\end{vmatrix}$
cbse
class12
ch4
sec-a
q25
p80
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If $\begin{vmatrix}2x & 5\\8 & x\end{vmatrix}=\begin{vmatrix}6 & -2\\7 & 3\end{vmatrix}$,then value of x is \[\begin{array}{1 1}(A)\quad3 & (B)\quad\pm 3\\(C)\quad \pm 6 & (D)\quad 6\end{array}\]
cbse
class12
ch4
sec-a
q24
p80
objective
exemplar
easy
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If x+y+z=0,prove that $\begin{vmatrix}xa & yb & zc\\yc & za & xb\\zb & xc & ya\end{vmatrix}=xyz\begin{vmatrix}a & b & c\\c & a & b\\b & c & a\end{vmatrix}$.
cbse
class12
ch4
sec-b
q23
p80
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Prove that $\begin{vmatrix}bc - a^2 & ca - b^2 & ab - c^2\\ca - b^2 & ab - c^2 & bc - a^2\\ab -c^2 & bc - a^2 & ca - b^2\end{vmatrix}$ is divisible by a+b+c and find the quotient.
cbse
class12
ch4
sec-b
q22
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If $a+b+c\neq 0\;and\;\begin{vmatrix}a & b & c\\b & c & a\\c & a & b\end{vmatrix}=0,then\;prove\;that\;a=b=c.$
cbse
class12
ch4
sec-b
q21
p79
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Given $A=\begin{bmatrix}2 & 2 & 4\\4 & 2 & 4\\2 & 1 & 5\end{bmatrix},B=\begin{bmatrix}1 & 1 & 0\\2 & 3 & 4\\0 & 1 & 2\end{bmatrix}$,find BA and use this to solve the system of equations y+2z=7,x-y=3,2x+3y+4z=17
cbse
class12
ch4
sec-c
q20
p79
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Using matrix method ,solve the system of equations 3x+2y-2z=3,x+2y+3z=6,2x-y+z=2.
cbse
class12
ch4
sec-c
q19
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2 & 0\\-2 & -1 & -2\\0 & -1 & 1\end{bmatrix},find\;A^{-1}.$\[Using\;A^{-1}, solve\; the\; system\; of\; linear\; equations\; x-2y=10,2x-y-z=8,-2y+Z=7.\]
cbse
class12
ch4
sec-c
q18
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find $A^{-1}$ if $A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}$ and show that $ A^{-1}=\Large \frac{A^2-3I}{2}$
cbse
class12
ch4
sec-c
q17
p79
short-answer
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
show that the $\Delta$ABC is an isosceles triangle if the determinant\[\Delta=\begin{bmatrix}1 & 1& 1\\1+\cos A & 1+\cos B & 1+\cos C\\\cos^2A+\cos A & \cos^2B+\cos B & \cos^2C+\cos C\end{bmatrix}=0\]
cbse
class12
ch4
sec-c
q16
p78
short-answer
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Show that the point(a+5,a-4),(a-2,a+3) and (a,a) do not lie on a straight line for any value of a.
cbse
class12
ch4
sec-b
q15
p78
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
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