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Recent questions tagged cbse
Questions
Find $x$ and $y$, if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q9
p81
easy
shortanswer
sec-a
math
asked
Nov 26, 2012
by
pady_1
1
answer
Solve the equation for $x, y, z$ and $t$ if $ 2\begin{bmatrix}x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q10
p81
easy
shortanswer
sec-a
math
asked
Nov 26, 2012
by
pady_1
1
answer
Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?
cbse
class12
bookproblem
ch1
misc
q15
p30
sec-b
math
asked
Nov 26, 2012
by
vaishali.a
1
answer
Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $\: f (x) = x^3, x \in [– 2, 2] $
cbse
class12
bookproblem
ch6
sec5
q5
q5-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Prove that the following functions do not have maxima or minima: $ (i)\: f (x) = e^x $
cbse
class12
bookproblem
ch6
sec5
q4
q4-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: $ (i)\: f (x) = x^2 $
cbse
class12
bookproblem
ch6
sec5
q3
q3-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values, if any, of the following functions given by $ f (x) = |x + 2| - 1$
cbse
class12
bookproblem
ch6
sec5
q2
q2-1
p232
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values, if any, of the following functions given by?$\;f(x)=(2x-1)^2+3$
cbse
class12
bookproblem
ch6
sec5
q1
q1-1
p231
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is
cbse
class12
bookproblem
ch6
sec4
q9
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is
cbse
class12
bookproblem
ch6
sec4
q8
p216
sec-b
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.
cbse
class12
bookproblem
ch6
sec4
q7
p216
sec-a
easy
modelpaper
q15
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.
cbse
class12
bookproblem
ch6
sec4
q6
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.
cbse
class12
bookproblem
ch6
sec4
q5
p216
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate change in the volume V of a cube of side $x$ metres caused by increasing the side by $1\%$.
cbse
class12
bookproblem
ch6
sec4
q4
p216
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate value of \(f (5.001)\), where $f (x) = x^3 – 7x^2 + 15.$
cbse
class12
bookproblem
ch6
sec4
q3
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Find the approximate value of $ f (2.01)$, where $f (x) = 4x^2 + 5x + 2$.
cbse
class12
bookproblem
ch6
sec4
q2
p216
sec-a
medium
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$
cbse
class12
bookproblem
ch6
sec4
q1
q1-1
p216
sec-b
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point
cbse
class12
bookproblem
ch6
sec3
q27
p213
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the slope of the normal to the curve $ y = 2x^2 + 3 \sin\: x$ at $x = 0$ is
cbse
class12
bookproblem
ch6
sec3
q26
p213
sec-a
easy
math
asked
Nov 26, 2012
by
thanvigandhi_1
1
answer
If $ x\begin{bmatrix} 2 \\ 3 \end{bmatrix} + y\begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix} $, find the values of $x$ and $y$.
cbse
class12
bookproblem
ch3
sec2
q11
p81
easy
veryshort-answer
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
Given $3\begin{bmatrix} x & y \\ z & w \end{bmatrix}$ = $\begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix}$ + $\begin{bmatrix} 4 & x + y \\ z + w & 3 \end{bmatrix}$, find the values of $x, y, z$ and $w$.
cbse
class12
bookproblem
ch3
sec2
q12
p81
easy
shortanswer
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $
cbse
class12
bookproblem
ch3
sec2
q13
p82
easy
long-answer
sec-c
math
asked
Nov 25, 2012
by
pady_1
1
answer
Show that $$ \begin{array}{l} (i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \\[0.5em] (ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \end{array} $$
cbse
class12
bookproblem
ch3
sec2
q14
p82
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find $ A^2 -5A + 6I $ , if $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q15
p82
easy
shortanswer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
if $ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} ,$ prove that $ A^3 - 6A^2 + 7A + 2I = 0 $
cbse
class12
bookproblem
ch3
sec2
q16
p82
medium
long-answer
sec-c
math
asked
Nov 25, 2012
by
pady_1
1
answer
If $ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} $ and $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $ find $k$ so that $A^2 = kA - 2I$
cbse
class12
bookproblem
ch3
sec2
q17
p82
easy
shortanswer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
If $ A = \begin{bmatrix} 0 & -tan \frac{\alpha}{2} \\ tan\frac{\alpha}{2} & 0 \end{bmatrix} $ and $I$ is the identity matrix of order $2$, show that $ I + A = ( I - A ) \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q18
p82
medium
sec-b
math
asked
Nov 25, 2012
by
pady_1
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: $$ \text{(a) Rs 1800} \qquad \qquad \text{(b) Rs 2000} $$
cbse
class12
bookproblem
ch3
sec2
q19
p82
easy
long-answer
math
sec-b
asked
Nov 25, 2012
by
pady_1
1
answer
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
cbse
class12
bookproblem
ch3
sec2
q20
p83
medium
long-answer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Assume $X, Y, Z, W$ and $P$ are matrices of order $2\times n, 3\times k, 2\times p, n\times 3$ and $p\times k$, respectively. The restriction on $n, p, k$ so that $PY + WY$ will be defined are:
cbse
class12
bookproblem
ch3
sec2
q21
p83
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
Assume $X, Y, Z, W$ and $P$ are matrices of order $2\times n$, $3\times k$, $2\times p$, $n\times 3$ and $p\times k$, respectively. If $n = p$ then the order of the matrix $7X - 5Z$ is:
cbse
class12
bookproblem
ch3
sec2
q22
p83
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find the transpose of each of the following matrices : $$ \text{ (i) } \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix} \qquad \qquad (ii) \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} \qquad \qquad (iii)\begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix} $$
cbse
class12
bookproblem
ch3
sec3
q1
p88
math
sec-a
asked
Nov 25, 2012
by
pady_1
1
answer
if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$
cbse
class12
bookproblem
ch3
sec3
q2
p88
easy
sec-b
q2-1
math
asked
Nov 25, 2012
by
pady_1
1
answer
If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $
cbse
class12
bookproblem
ch3
sec3
q3-1
p88
easy
shortanswer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then find $(A + 2B)'$
cbse
class12
bookproblem
ch3
sec3
q4
p88
easy
shortanswer
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$
cbse
class12
bookproblem
ch3
sec3
q5
p88
easy
q5-1
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
$ (i) A = \begin{bmatrix} cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{bmatrix}$ then verify that $A'A = I$
cbse
class12
bookproblem
ch3
sec3
q6
p89
easy
sec-b
q6-1
math
asked
Nov 25, 2012
by
pady_1
1
answer
$ (i)$ Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.
cbse
class12
bookproblem
ch3
sec3
q7
p89
medium
sec-b
q7-1
math
asked
Nov 25, 2012
by
pady_1
1
answer
For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.
cbse
class12
bookproblem
ch3
sec3
q8
p89
easy
sec-b
q8-1
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q9
p89
medium
shortanswer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ \quad \begin{bmatrix} 3 & 5 \\ 1 & -1 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-1
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find the equation of the tangent to the curve $y = \sqrt {3x - 2}$ which is parallel to the line $4x - 2y + 5 = 0 $.
cbse
class12
bookproblem
ch6
sec3
q25
p213
sec-c
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equations of the tangent and normal to the hyperbola $\large {\frac{x^2}{a^2}} -\large { \frac{y^2}{b^2}} =\normalsize 1$ at the $ (x_0, \: y_0)$.
cbse
class12
bookproblem
ch6
sec3
q24
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Prove that the curves \(x = y^2\) and \(xy = k\) cut at right angles* if \(8k^2 = 1.\)
cbse
class12
bookproblem
ch6
sec3
q23
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equations of the tangent and normal to the parabola $y^2 = 4ax$ at the point $(at^2, 2at)$.
cbse
class12
bookproblem
ch6
sec3
q22
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equation of the normals to the curve $y = x^3 + 2x + 6$ which are parallel to the line $x + 14y + 4 = 0$.
cbse
class12
bookproblem
ch6
sec3
q21
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equation of the normal at the point \((am^2,am^3)\) for the curve \(ay^2 = x^3.\)
cbse
class12
bookproblem
ch6
sec3
q20
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the points on the curve \(x^2 + y^2 - 2x - 3 = 0\) at which the tangents are parallel to the \(x\) - axis.
cbse
class12
bookproblem
ch6
sec3
q19
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
For the curve $y = 4x^3 – 2x^5$, find all the points at which the tangent passes through the origin.
cbse
class12
bookproblem
ch6
sec3
q18
p212
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the points on the curve $y = x^3$ at which the slope of the tangent is equal to the $y$ - coordinate of the point.
cbse
class12
bookproblem
ch6
sec3
q17
p212
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
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