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Recent questions tagged exemplar
Questions
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
If $a_1,a_2,a_3,....,a_r$ are in G.P., then prove that the determinant $\begin{vmatrix} a_{r-1} & a_{r-5} & a_{r-9} \\ a_{r-7} & a_{r-11} & a_{r-15} \\ a_{r-13} & a_{r-17} & a_{r-21} \end{vmatrix} is\; independent\; of\; r$
cbse
class12
ch4
sec-b
q14
p78
short-answer
exemplar
difficult
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Find the value of $\theta$ satisfying $\begin{bmatrix} 1 & 1 & \sin3\theta \\ -4 & 3 & \cos2\theta \\ 7 & -7 & -2 \end{bmatrix}\;=\;0$
cbse
class12
ch4
sec-b
q12
p78
short-answer
exemplar
difficult
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, Prove that$\begin{vmatrix} y+z & z & y \\ z & z+x & x \\ y & x & x+y \end{vmatrix}\;=\;4xyz$
cbse
class12
ch4
sec-b
q8
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, prove that: $\begin{vmatrix} y^2z^2 & yz &y+ z \\ z^2x^2 & zx & z+x \\ x^2y^2 & xy & x+y \end{vmatrix}\;=\;0$
cbse
class12
ch4
sec-b
q7
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix}$
cbse
class12
ch4
sec-b
q6
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} x+4 & x & x \\ x & x+4 & x \\ x & x & x+4 \end{vmatrix}$
cbse
class12
ch4
sec-b
q5
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} 3x & -x+y & -x+z \\ x-y & 3y & z-y \\ x-z & y-z & 3z \end{vmatrix}$
cbse
class12
ch4
sec-b
q4
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} 0 & xy^2 & xz^2 \\ x^2y & 0 & yz^2 \\ x^2z & zy^2 & 0 \end{vmatrix}$
cbse
class12
ch4
sec-b
q3
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} a+x & y & z \\ x & a+y & z \\ x & y & a+z \end{vmatrix}$
cbse
class12
ch4
sec-b
q2
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} x^2 - x+1 & x-1 \\ x +1 & x+1 \end{vmatrix}$
cbse
class12
ch4
sec-b
q1
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: $(AB)^{-1}=A^{-1}B^{-1},$ where A and B are invertible matrices satisfying commutative property with respect to multiplication.
cbse
class12
ch3
q101
p64
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A is skew symmetric matrix, then $A^2$ is a symmetric matrix.
cbse
class12
ch3
q100
p64
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If $A =\begin{bmatrix} 2 & 3 & 1 \\ 1 &4 & 2 \end{bmatrix}\; and\; B=\begin{bmatrix}2 & 3 \\ 4& 5 \\ 2 & 1 \end{bmatrix},$ then AB and BA are defined and equal.
cbse
class12
ch3
q99
p64
true-or-false
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: AA' is always a symmetric matrix for any matrix A.
cbse
class12
ch3
q98
p64
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A,B and C are square matrices of same order, then AB = AC always implies that B=C.
cbse
class12
ch3
q97
p64
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If (AB)' = B'A', where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.
cbse
class12
ch3
q96
p64
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A and B are any two matrices of the same order, then (AB)' = A'B'.
cbse
class12
ch3
q95
p64
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If each of the three matrices of the same order are symmetric matrix.
cbse
class12
ch3
q94
p63
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A and B are two square matrices of the same order , then AB = BA.
cbse
class12
ch3
q93
p63
true-or-false
exemplar
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: Transpose of a column matrix is a column matrix.
cbse
class12
ch3
q92
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If a matrix AB = 0, then A=0 or B=0 or both A and B are null matrices.
cbse
class12
ch3
q91
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A and B are two matrices of the same order, then A-B = B-A.
cbse
class12
ch3
q90
p63
true-or-false
exemplar
concepts
toolbox
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: If A and B are two square matrices of the same order , then A+B = B+A.
cbse
class12
ch3
q89
p63
true-or-false
exemplar
toolbox
concepts
sec-a
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
True or False: A square matrix where every element is unity is called an identify matrix.
cbse
class12
ch3
q88
p63
true-or-false
exemplar
concepts
toolbox
math
sec-a
asked
Dec 24, 2012
by
sreemathi.v
1
answer
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