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Questions asked by meena.p
Questions
14353
questions
1
answer selected
Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} =\begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix} $ find the possible values of x and y, find the values if x = y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q48
p10
math
sec-a
asked
Jan 24, 2013
0
answers
If the points (2,0), (0,5) and (x,y) are collinear give a relation between x and y.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q47
p10
math
sec-a
asked
Jan 24, 2013
0
answers
If P and Q are invertible matrices of same order, then show that PQ is also invertible.
cbse
class12
kvquestionbank2012
ch3
q46
p10
math
sec-b
asked
Jan 24, 2013
0
answers
Find x, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} =0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q45
p10
math
sec-a
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix} \;find\;A^2\;Hence\;find\;A^6.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q44
p10
math
sec-b
asked
Jan 24, 2013
0
answers
If $A=\begin{bmatrix} \cos \theta & \sin \theta & \\ -\sin \theta & \cos \theta \end{bmatrix} $ then show that $A^n=\begin{bmatrix} \cos 2\theta & \sin 2\theta & \\ -\sin 2\theta & \cos 2\theta \end{bmatrix} $
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q43
p10
math
sec-b
asked
Jan 24, 2013
0
answers
If a, b, c are in A.P. then find the value of: $\begin{vmatrix} 2y+4 & 5y+7 & 8y+a \\ 3y+5 & 6y+8 & 9y+b \\ 4y+6 & 7y+9 & 10y+c \end{vmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q42
p10
math
sec-b
asked
Jan 24, 2013
0
answers
If x, y and z all positive, are $p^{th},q^{th}and\;r^{th}$ terms of a G.P. Prove that $\begin{vmatrix} logx & p & 1 \\ logy & q & 1 \\ logz & r & 1 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q41
p9
math
sec-b
asked
Jan 24, 2013
0
answers
Find the quadratic function defined by the equation $ f(x)=ax^2+bx+c\;if\;f(0)=6,f(2)=11,f(-3)=6,$ using determinants.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q40
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A+B+C=\large\pi,\;\normalsize show\;that\;\begin{vmatrix} \sin (A+B+C) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0 \end{vmatrix}=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q39
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If x, y, z are positive and unequal show that the value of determinant $ \begin{vmatrix} x & y & z \\ y & z & x \\ z & x & y \end{vmatrix}$ is negative.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q38
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 3 & -4 \\ -1 & 2 \end{bmatrix}$ find Matrix B such that AB= 1
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q37
p9
math
sec-a
asked
Jan 24, 2013
0
answers
If $A=\begin{bmatrix} \cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{bmatrix}$ then prove by Mathematical Induction that :$A^n=\begin{bmatrix} \cos n\theta & i\sin n\theta \\ i\sin n\theta & \cos n\theta \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q36
p9
math
sec-c
asked
Jan 24, 2013
0
answers
If $ p(\alpha)=\begin{bmatrix} \cos \alpha & i\sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}\;show\;that\;p(\alpha) \times p(\beta)=p(\alpha+\beta)$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q35
p9
math
sec-b
asked
Jan 24, 2013
0
answers
Find the values of a and b such that $ A^2+aI=bA\;where\; A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q34
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$ verify $(AdjA)^{-1}=adj(A^{-1})$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q33
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If two matrices $ A^{-1}\;and\;B$ are given how to find $(AB)^{-1}$verify with an example.\[(Find\; B^{-1} then\; find\; B^{-1} \times A^{-1})\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q32
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If $P(a)=\begin{bmatrix} \cos a & -\sin a & 0 \\ \sin a & \cos a & 0 \\ 0 & 0 & 1 \end{bmatrix}$then show that $[P(x)]^{-1}=[P(-x)]$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q31
p9
math
sec-b
asked
Jan 24, 2013
0
answers
Find the matrix x if $ \begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix} \times \begin{bmatrix} 0 & 2 \\ 1 & 3 \end{bmatrix}=\begin{bmatrix} 1 & 6 \\ 3 & -2 \end{bmatrix}$\[X=-\frac{1}{4}\begin{bmatrix} -53 & 18 \\ 25 & -10 \end{bmatrix}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q30
p9
math
sec-a
asked
Jan 24, 2013
0
answers
If $A=\begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix} $satisfies the equation : $ x^2+6x+17=0\;find\;A^{-1}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q29
p9
math
sec-b
asked
Jan 24, 2013
0
answers
If $\begin{vmatrix} x & b & c \\ a & y & c \\ a & b & z \end{vmatrix}=0$ then find the value of $ \large\frac{x}{x-a}+\frac{y}{y-b}+\frac{z}{z-c}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q28
p8
math
sec-a
asked
Jan 24, 2013
0
answers
Given $ A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ such that $ |A|=-10.\;Find\;a_{11}c_{11}+a_{12}c_{12}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q27
p8
math
sec-a
asked
Jan 24, 2013
0
answers
If A is a non-singular matrix of order 3 and |A| = - 4 Find |adj A|
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q26
p8
math
sec-a
asked
Jan 24, 2013
0
answers
For what value of 'K' the matrix $ \begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix}$has no inverse.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q25
p8
math
sec-a
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix},$ show that $ A^2-5A+7I=0,$ use the result to find $A^4$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q24
p8
math
sec-b
asked
Jan 24, 2013
0
answers
Let A and B be 3 x 3 matrices such that $ A^T=-A\;and\;B^T=B.$Then the matrix $\lambda(AB+3BA)$ is skew symmetric matrix for $\lambda$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q23
p8
math
sec-b
asked
Jan 24, 2013
0
answers
Assume X, Y, Z, W and P are matrices of order (2 x n), (3xk), (n x 3) and (p x k) respectively, then the restriction on n, k and p so that py + my will be defined are : (k=3, p=n)
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q22
p8
math
sec-b
asked
Jan 24, 2013
0
answers
Find the values of a, b, c if the matrix $\begin{bmatrix} 0 & 2b & c \\ a & b & -c \\ a & -b & c \end{bmatrix}$ satisfy the equation $ A^1A=I_3$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q21
p8
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 1& 1 & 1 \\ 1& 1 & 1 \\ 1& 1 & 1 \end{bmatrix}$ then prove that $ A^n=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}\;n\in N$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q20
p8
math
sec-b
asked
Jan 24, 2013
0
answers
If A and B are two matrices such that AB = B and BA = A then $A^2+B^2$=_______?_______\
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q19
p8
math
sec-a
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix},\;then\;A^5=?$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q18
p8
math
sec-a
asked
Jan 24, 2013
1
answer
If P and Q are equal matrices of same order such that PQ = QP, then prove by induction that $ PQ^n=Q^nP.$ Further, show that $(PQ)^n=P^n\times Q^n.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q17
p8
math
sec-b
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$ find x and y such that $ A^2+xl=yA.\;Find\;A^{-1}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q16
p8
math
sec-b
asked
Jan 24, 2013
1
answer
Give that x = -9 is a root of $ \begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{vmatrix}=0$ find the other roots. Hint: Evaluate, find other roots.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q15
p8
math
sec-a
asked
Jan 24, 2013
0
answers
If $ \begin{bmatrix} \cos^2A & \cos A\sin A \\ \cos A\sin A & \sin^2A \end{bmatrix},Y=\begin{bmatrix} \cos^2B & \cos B\sin B \\ \cos B\sin B & \sin^2B \end{bmatrix}$then show that XY is a zero matrix, provided (A-B) is an odd multiple of $\large\pi/2$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q14
p8
math
sec-b
asked
Jan 24, 2013
0
answers
Prove that $\begin{bmatrix} (a+1) & (a+2) & (a+2) & 1 \\ (a+2) & (a+3) & (a+3) & 1 \\(a+3) & (a+4) & (a+4) & 1 \end{bmatrix}=-2$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q13
p7
math
sec-b
asked
Jan 24, 2013
0
answers
If $f(x)=3x^2-9x+7,$ then for a square matrix A, write f(A)
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q12
p7
math
sec-a
asked
Jan 24, 2013
0
answers
Find the matrix X such that :$ \begin{bmatrix} 2 & -1 \\ 0 & 1 \\ -2 & 4 \end{bmatrix}X=\begin{bmatrix} -1 & -8 & -10 \\ 3 & 4 & 0 \\10 & 20 & 10 \end{bmatrix}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q11
p7
math
sec-a
asked
Jan 24, 2013
0
answers
The total number of elements in a matrix represents a prime number. How many possible orders a matrix can have.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q10
p7
math
sec-a
asked
Jan 24, 2013
0
answers
Prove the determinant $\begin{vmatrix} x & -\sin\alpha & \cos\alpha \\ \sin\alpha & -x & 1 \\ \cos\alpha & 1 & x \end{vmatrix}$ is independent as $\alpha$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q9
p7
math
sec-b
asked
Jan 24, 2013
0
answers
Prove that $ \begin{vmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ca & bc & (a+b)^2 \end{vmatrix}=2abc(a+b+c)^2$ (Use properties to prove the above)
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q8
p7
math
sec-b
asked
Jan 24, 2013
0
answers
Express $\begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ as sum of the symmetric and skew symmetric matrices.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q7
p7
math
sec-a
asked
Jan 24, 2013
0
answers
Using properties of Determinants prove that : $ \begin{vmatrix} a^2 & bc & ac+c^2 \\ a^2+ab & b^2 & ac \\ab & b^2+ac & c^2 \end{vmatrix}=4a^2b^2c^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q6
p7
math
sec-b
asked
Jan 24, 2013
0
answers
Prove that $\begin{vmatrix} x-3 & x-4 & x-a \\ x-2 & x-3 & x-b \\ x-1 & x-2 & x-c \end{vmatrix}=0,$ where a,b,c are in A.P
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q5
p7
math
sec-b
asked
Jan 24, 2013
0
answers
Inverse of a square matrix is unique. Give an example to prove it?
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q4
p7
math
sec-a
asked
Jan 24, 2013
0
answers
If $ A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}\;and\;A+A^T=1.$Find the possible values of $\theta=\large\pi/3.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q3
p7
math
sec-a
asked
Jan 24, 2013
0
answers
If $ \begin{bmatrix} p & q \\ r & -p \end{bmatrix}$ is such that $A^2=1$ then find the value of $1-p^2+qr$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q2
p7
math
sec-b
asked
Jan 24, 2013
0
answers
If a+b+c=0 anb $ \begin{vmatrix} a-x & a & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix}$ then prove that either x=0 or $x= \pm\sqrt{\frac{3}{2}(a^2+b^2+c^2)}$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q1
p7
math
sec-c
asked
Jan 24, 2013
0
answers
If $ \cos^{-1}\Large\frac{x}{2}+\normalsize\cos^{-1}\large\frac{y}{3}=\theta ,\;\normalsize prove\;that\;9x^2-12xy\cos\theta +4y^2=36\sin^2\theta $
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q25
p6
medium
sec-b
math
asked
Jan 24, 2013
1
answer
Solve: $\sin\lfloor2\cos^{-1}\{\cot(2\tan^{-1}x)\}\rfloor=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q24
p6
difficult
sec-b
math
asked
Jan 24, 2013
1
answer
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