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Recent questions tagged additionalproblem
Questions
let A be the set of all students of class XII in a school and R be the relation, having the same *** on A, and then prove that R is an equivalence relation. Do you think, co-education may be helpful in child development and why?
cbse
class12
valuebasedproblems2012
additionalproblem
ch1
q4
math
sec-b
asked
Jan 24, 2013
by
shanthinig
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
by
meena.p
0
answers
Prove that $f: R → R $ is a bijection given by $f(x) = x^3+3$. Find $f ^{-1} (x)$. Does the truthfulness and honesty may have any relation?
cbse
class12
additionalproblem
ch1
q1
math
sec-b
asked
Jan 24, 2013
by
shanthinig
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
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
by
meena.p
1
answer
Solve for x:$\tan^{-1}(x+1)+\tan^{-1}x+\tan^{-1}(x-1)=\tan^{-1}3.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q23
p6
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove that $ \tan^{-1}\large\frac{yz}{xr}+ \tan^{-1}\frac{zx}{yr}+ \tan^{-1}\frac{xy}{zr}=\frac{\pi}{2}\;where\;x^2+y^2+z^2=r^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q22
p6
difficult
sec-c
math
asked
Jan 24, 2013
by
meena.p
1
answer
If $ \tan^{-1}a+\tan^{-1}b+\tan^{-1}c=\pi,\;prove\;that\;a+b+c=abc.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q21
p6
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove: $\cos^{-1}x-\cos^{-1}y=\cos^{-1}\bigg[xy+\sqrt{1-x^2}.\sqrt{1-y^2}\bigg]$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q20
p6
easy
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Solve for x $ \sin^{-1}\frac{2\alpha}{1+\alpha^2}+ \sin^{-1}\frac{2\beta}{1+\beta^2}=2\tan^{-1}x.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q19
p6
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove that :$\cot^{-1}\bigg[\frac{ab+1}{a-b}\bigg]+\cot^{-1}\bigg[\frac{bc+1}{b-c}\bigg]+\cot^{-1}\bigg[\frac{ca+1}{c-a}\bigg]=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q18
p6
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
If $ x= cosec \lfloor\tan^{-1}\{\cos(\cot^{-1}(\sec(\sin^{-1}a)))\}\rfloor\; $ and $ y=\sec\lfloor\cot^{-1}\{\sin(\tan^{-1}(cosec(\cos^{-1}a)))\}\rfloor\;$ where $\;a\;\in [0,1]$ Find the relationship between $x$ and $y$ in terms of $a$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q17
p6
difficult
sec-c
math
asked
Jan 24, 2013
by
meena.p
1
answer
In any Triangle ABC, if $ A=\tan^{-1}2\;and\;B=\tan^{-1}3,$prove that $C=\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q16
p5
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove that $\sin2[\cot^{-1}\{\cos(\tan^{-1}x)\}]=2\frac{\sqrt{x^2+1}}{x^2+2}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q15
p5
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Prove that $f: \text{R} \rightarrow \text{R}$ is a bijection given by $f(x) = x^3 + 3$. Find $f^{-1}(x)$. Does the truthfulness and honesty may have any relation?
cbse
class12
additionalproblem
valuebasedproblems2012
ch1
q1
math
sec-b
asked
Jan 24, 2013
by
pady_1
0
answers
If $ \sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$ prove that $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q14
p5
difficult
sec-c
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $ \cos^{-1}\frac{x}{a}+\cos^{-1}\frac{y}{b}=\alpha,$prove that $\frac{x^2}{a^2}-\frac{2xy}{ab}\cos \alpha+\frac{y^2}{b^2}=\sin^2\alpha.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q13
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $x,y,z \in [-1,1]\;$ such that $\;\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\frac{3\pi}{2},$ find the value of $x^{2006}+y^{2007}+z^{2008}-\Large \frac{9}{x^{2006}+y^{2007}+z^{2008}}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q12
p5
difficult
sec-a
math
asked
Jan 23, 2013
by
meena.p
1
answer
Prove that $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q11
p5
medium
sec-c
math
asked
Jan 23, 2013
by
meena.p
1
answer
Prove that $\cos\bigg\{2\cot^{-1}\sqrt{\large\frac{1-x}{1+x}}\bigg\}+x=0$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q10
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $x>0$ and $\sin^{-1}\bigg(\large{\frac{5}{x}}\bigg)+\sin^{-1}\bigg(\frac{12}{x}\bigg)=\large\frac{\pi}{2},$ than find the value of $x$.
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q9
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
If $\cos^{-1}x=\tan^{-1}x,\;show\;that\;\sin(\cos^{-1}x)=x^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q8
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
Find the value of x if $cosec^{-1}x=2\cot^{-1}7+\cot^{-1}\frac{3}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q7
p5
medium
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
Find the principal value of $\sin^{-1}\bigg(\frac{-\sqrt {3}}{2}\bigg)+\cos^{-1}\bigg(\frac{-\sqrt {3}}{2}\bigg)$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q6
p5
easy
sec-a
math
asked
Jan 23, 2013
by
meena.p
1
answer
Considering the principal solutions, find the number of solutions of $ \tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q5
p5
easy
sec-b
math
asked
Jan 23, 2013
by
meena.p
1
answer
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