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Recent questions tagged sec2
Questions
Check the injectivity and surjectivity of the following functions: $f : R\to R $ given by $ f(x)\; = x^2 $
cbse
class12
bookproblem
ch1
sec2
q2
q2-3
p10
sec-b
math
asked
Mar 5, 2013
by
meena.p
1
answer
Check the injectivity and surjectivity of the following functions: \(f : Z\to Z \;given\; by\; f(x)\; = x^2 \)
cbse
class12
bookproblem
ch1
sec2
q2
q2-2
p10
easy
sec-b
math
asked
Mar 5, 2013
by
meena.p
1
answer
A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5 $\%$ interest per year, and the second bond pays 7 $\%$ interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: b) Rs. 2000
cbse
class12
bookproblem
ch3
sec2
p82
medium
q19-2
shortanswer
sec-b
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
Show that: $ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-2
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Show that: $(i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p81
easy
q14
q14-1
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find $X$ and $Y$ if $(ii) \quad 2X + 3Y = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix} \text{ and } 3X + 2Y = \begin{bmatrix} 2 & -2 \\ -1 & 5 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p81
medium
q7-2
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Find $X$ and $Y$ if: $(i) \quad X + Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix} \text{ and } X - Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p81
easy
q7-1
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(vi)\;\begin{bmatrix}3 & -1 &3\\-1 & 0 &2\end{bmatrix}\begin{bmatrix}2 & -3\\1 & 0\\3 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-6
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-5
shortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products:$ (iv)\;\begin{bmatrix}2 & 3 &4\\3 & 4 &4\\4 & 5 & 6\end{bmatrix}\begin{bmatrix}1 & -3 & 5\\0 & 2 &4\\3 & 0 & 5\end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-4
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-3
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(ii)\;\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3 & 4\end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-2
sec-b
shortanswer
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the indicated products: $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}\begin{bmatrix}a &-b\\b & a\end{bmatrix}$
cbse
class12
bookproblem
ch3
sec2
p80
easy
q3-1
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $ (iv)\;\begin{bmatrix}\cos^2x & \sin^2x\\ \sin^2x & \cos^2x\end{bmatrix}+\begin{bmatrix}\sin^2x & \cos^2x\\ \cos^2x & \sin^2x\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-4
shortanswer
sec-b
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $ (iii)\;\begin{bmatrix}-1 & 4 & -6\\8 & 5 &16\\2 & 8 &5\end{bmatrix}+\begin{bmatrix}12 & 7 & 6\\8 & 0 & 5\\3 & 2 & 4\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-3
shortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Compute the following $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}+\begin{bmatrix}a & b\\b & a\end{bmatrix}$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q2-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ (v)\;BA\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-5
veryshort
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ AB\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-4
veryshort
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ 3A-C$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-3
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$ Find: $(ii) (A-B)\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-2
veryshortanswer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $\;A+B\qquad$
class12
cbse
bookproblem
ch3
sec2
p80
easy
q1-1
veryshort-answer
sec-a
math
asked
Feb 27, 2013
by
balaji.thirumalai
1
answer
Prove, using properties of determinants: $\begin{vmatrix} x+y+2z & x & y \\ z & y+z+2x & y \\ z & x & z+x+2y \end{vmatrix} = 2(x+y+z)^3 $
cbse
class12
modelpaper
2012
sec-b
q11
ch4
bookproblem
sec2
q11-2
p120
math
asked
Feb 6, 2013
by
thanvigandhi_1
0
answers
Prove, using properties of determinants: $ \begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} = (a+b+c)^3 $
cbse
class12
modelpaper
2012
sec-b
q19
ch4
bookproblem
sec2
q11-1
p120
math
asked
Feb 6, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove that $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ca & cb & -c^2 \end{vmatrix} = 4a^2b^2c^2 $
cbse
class12
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q7
p120
medium
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Prove that \( \begin{bmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{bmatrix} = (5x+4)(4-x)^2. \)
cbse
class12
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q10-1
p120
medium
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove the following : $\begin{bmatrix} 1+a^2-b^2 & 2ab & -2b \\ 2ab & 1-a^2+b^2 & 2a \\ 2b & -2a & 1-a^2=b^2 \end{bmatrix} = (1 + a^2 + b^2)^3. $
cbse
class12
modelpaper
2012
sec-b
q12
ch4
bookproblem
sec2
q13
p121
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, show that $\begin{bmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{bmatrix} = (a + b + c )^3 $
cbse
class12
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q11-1
p120
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Using properties of determinants, prove that : $ \begin{bmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1 \end{bmatrix} = (1+a^2+b^2+c^2) $
cbse
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q14
p121
asked
Dec 26, 2012
by
thanvigandhi_1
0
answers
Find the angle between the following pair of lines: $ \frac{\large x-2}{\large 2} = \frac{\large y-1}{\large 5} = \frac{\large z + 3}{\large -3} \: and\: \frac{\large x+2}{\large -1} = \frac{\large y-4}{\large 8} = \frac{\large z - 5}{\large 4} $
cbse
class12
bookproblem
ch11
sec2
q11
p478
easy
sec-b
q11-1
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( 1 - t ) \hat i + ( t - 2 )\hat j + ( 3 - 2t )\hat k$ and $ \overrightarrow r = ( s + 1 )\hat i + ( 2s - 1 )\hat j - (2s + 1)\hat k $
cbse
class12
bookproblem
ch11
sec2
q17
p478
p382
easy
sec-b
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( \hat i + 2\hat j + 3\hat k) + \lambda ( \hat i - 3\hat j + 2\hat k )$ and $ \overrightarrow r = 4 \hat i + 5\hat j + 6\hat k + \mu (2\hat i + 3\hat j + \hat k )$
cbse
class12
bookproblem
ch11
sec2
q16
p478
medium
sec-c
modelpaper
2012
q22
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the shortest distance between the lines: $ \frac{ \large x + 1 }{ \large 7} = \frac{ \large y + 1}{ \large -6} = \frac{ \large z + 1}{ \large 1}$ and $ \frac{ \large x - 3 }{ \large 1} = \frac{ \large y - 5}{ \large -2} = \frac{ \large z - 7}{ \large 1}$
cbse
class12
bookproblem
ch11
sec2
q15
p478
medium
sec-b
modelpaper
2012
q20
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the shortest distance between the lines $ \overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $ \overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$
cbse
class12
bookproblem
ch11
sec2
q14
p478
medium
sec-b
modelpaper
2012
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Show that the lines $ \frac{ \large x - 5 }{ \large 7} = \frac{ \large y + 2}{ \large -5} = \frac{ \large z}{ \large 1}$ and $ \frac{ \large x }{ \large 1} = \frac{ \large y}{ \large 2} = \frac{ \large z}{ \large 3}$ are perpendicular to each other.
cbse
class12
bookproblem
ch11
sec2
q13
p478
easy
sec-b
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the values of p so that the lines $ \frac{ \large 1 - x }{ \large 3} = \frac{ \large 7y - 14}{ \large 2p} = \frac{ \large z - 3}{ \large 2}\: and \: \frac{ \large 7 - 7x }{ \large 3 \: p} = \frac{ \large y - 5}{ \large 1} = \frac{ \large 6 - z}{ \large 5}$ are at right angles.
cbse
class12
bookproblem
ch11
sec2
q12
p478
medium
sec-b
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the angle between the pairs of lines: $ \overrightarrow r = 2\hat i - 5 \hat j + \hat k + \lambda (3\hat i + 2\hat j + 6\hat k)\: and \: \overrightarrow r = 7\hat i - 6 \hat k+ \mu (\hat i + 2\hat j + 2\hat k) $
cbse
class12
bookproblem
ch11
sec2
q10-1
p478
easy
sec-b
q10
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Prove the following: \[ 2 \: tan^{-1} \frac{1}{2} + tan ^{-1} \frac{1}{7} = tan^{-1} \frac{31}{17} \]
cbse
class12
bookproblem
ch2
sec2
q4
p47
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following function in the simplest form: \[ tan^{-1} \frac{\sqrt {1 + x^2} - 1}{x}, x \neq 0\]
cbse
class12
bookproblem
ch2
sec2
q5
p47
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following function in the simplest form: \[ tan^{-1} \frac{1}{\sqrt{x^2 - 1}}, | x | > 1 \]
cbse
class12
bookproblem
ch2
sec2
q6
p47
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following function in the simplest form: \[ tan^{-1} \bigg( \sqrt {\frac{1-cos \: x}{1 + cos \: x}} \bigg), x < \pi\]
cbse
class12
bookproblem
ch2
sec2
q7
p47
easy
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following function in the simplest form: \[ tan^{-1} \bigg( \frac{cos\: x - sin\: x}{cos\: x + sin\: x} \bigg) , 0 < x < \pi \]
cbse
class12
bookproblem
ch2
sec2
q8
p47
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following in the simplest form: $ \tan^{-1} \large \frac{x}{\sqrt {a^2 - x^2}},$$ | x | < a $
cbse
class12
bookproblem
ch2
sec2
q9
p48
easy
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Write the following function in the simplest form:\[ tan^{-1} \bigg( \frac{3a^2x-x^3}{a^3-3ax^2} \bigg), a > 0 ; \frac{-a}{\sqrt 3} \leq x \leq \frac{a}{\sqrt 3} \]
cbse
class12
bookproblem
ch2
sec2
q10
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the value of $ \tan^{-1} \bigg[ 2\cos \bigg(2\sin^{-1}\frac{1}{2}\bigg) \bigg] $
cbse
class12
bookproblem
ch2
sec2
q11
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the value of \[ \cot \;( \tan^{-1}a + \cot^{-1}a) \]
cbse
class12
bookproblem
ch2
sec2
q12
p48
easy
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the value of \[ tan\frac{1}{2} \bigg[ sin^{-1} \frac{2x}{1+x^2} + cos^{-1} \frac{1-y^2}{1+y^2} \bigg], | x | < 1, y > 0 \: and \: xy < 1\]
cbse
class12
bookproblem
ch2
sec2
q13
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the value of $x$ if \( sin \bigg ( sin^{-1} \frac{1}{5} + cos^{-1} \: x \bigg) = 1\).
cbse
class12
bookproblem
ch2
sec2
q14
p48
easy
veryshort
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
If $ \tan^{-1} \frac{\large x-1}{\large x-2} + \tan^{-1} \frac{\large x+1}{\large x+2} = \frac{\large \pi}{\large 4} $ then find the value of $x$
cbse
class12
bookproblem
ch2
sec2
q15
p48
medium
sec-b
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the values of \[ sin^{-1} \bigg( sin \frac{2\pi}{3} \bigg) \]
cbse
class12
bookproblem
ch2
sec2
q16
p48
easy
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the value of the expression in \[ tan^{-1} \bigg( tan \frac{3\pi}{4} \bigg) \]
cbse
class12
bookproblem
ch2
sec2
q17
p48
easy
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
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