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Recent questions tagged sec2
Questions
Find $X$ and $Y$ if $$ \begin{array}{l \qquad l} (i) \quad X + Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix} \text{ and } X - Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix} \\ (ii) \quad 2X + 3Y = \begin{bmatrix} 2 & 3 \\ 4 & 0 \end{bmatrix} \text{ and } 3X + 2Y = \begin{bmatrix} 2 & -2 \\ -1 & 5 \end{bmatrix} \end{array} $$
cbse
class12
bookproblem
ch3
sec2
q7
p81
math
sec-a
asked
Nov 26, 2012
by
pady_1
1
answer
Find $X$ , if $Y = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} $ and $ 2X + Y = \begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec2
q8
p81
easy
shortanswer
sec-a
math
asked
Nov 26, 2012
by
pady_1
1
answer
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
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
The interval in which $y = x^2 e ^{- x}$ is increasing is
cbse
class12
bookproblem
ch6
sec2
q19
p206
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function given by \(f (x) = x^3 – 3x^2 + 3x - 100\) is increasing in \(R.\)
cbse
class12
bookproblem
ch6
sec2
q18
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by $f (x) = \log \cos\: x$ is strictly decreasing on $ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly increasing on, $\left( \large {\frac{\pi}{2},} \normalsize \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q17
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function $f$ given by $f (x) = \log \sin x$ is strictly increasing on$ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly decreasing on $\left( \large {\frac{\pi}{2}}, \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q16
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by \( f(x) = x + \frac{1}{\large x}\) is strictly increasing on $I$.
cbse
class12
bookproblem
ch6
sec2
q15
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the least value of a such that the function $f$ given by $f (x) = x^2 + ax + 1$ is strictly increasing on $(1, 2).$
cbse
class12
bookproblem
ch6
sec2
q14
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
On which of the following intervals is the function $f $ given by $f (x) = x^{100} + sin x –1$ strictly decreasing ?
cbse
class12
bookproblem
ch6
sec2
q13
p206
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Which of the following functions are strictly decreasing on $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q12
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by \(f (x) = x^2 – x + 1\) is neither strictly increasing nor strictly decreasing on \((– 1, 1).\)
cbse
class12
bookproblem
ch6
sec2
q11
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the logarithmic function is strictly increasing on $(0, \infty).$
cbse
class12
bookproblem
ch6
sec2
q10
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$
cbse
class12
bookproblem
ch6
sec2
q9
p205
sec-b
easy
modelpaper
2012
q15
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.
cbse
class12
bookproblem
ch6
sec2
q8
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that $ y = log(1+x)-\large {\frac{2x}{2+x}}, \normalsize x > – \normalsize 1$, is an increasing function of $x$ throughout its domain.
cbse
class12
bookproblem
ch6
sec2
q7
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$
cbse
class12
bookproblem
ch6
sec2
q6
q6-a
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?
cbse
class12
bookproblem
ch6
sec2
q5
p205
sec-b
easy
modelpaper
2012
q16
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) $ strictly increasing
cbse
class12
bookproblem
ch6
sec2
q4
q4-b
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$
cbse
class12
bookproblem
ch6
sec2
q3c
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$
cbse
class12
bookproblem
ch6
sec2
q3
q3b
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = \sin \;x\) is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q3
q3a
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.
cbse
class12
bookproblem
ch6
sec2
q2
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = 3x + 17\) is strictly increasing on \(R\).
cbse
class12
bookproblem
ch6
sec2
q1
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The corner points of the feasible region determined by the following system of linear inequalities: 2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. The condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is (A) p = q (B) p = 2q (C) p = 3q (D) q = 3p?
cbse
class12
bookproblem
ch12
sec2
q11
p520
sec-a
easy
math
asked
Nov 16, 2012
by
fingeazy
1
answer
There are two types of fertilisers \(F_{1} \) and \(F_{2} \). \(F_{1} \) consists of 10% nitrogen and 6% phosphoric acid and \(F_{2} \) consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If \(F_{1} \) costs Rs 6/kg and \(F_{2} \) costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
cbse
class12
bookproblem
ch12
sec2
q10
p520
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $F_{1} $ and $F_{2} $ are available. Food $F_1$ costs Rs 4 per unit food and $F_2$ costs Rs 6 per unit. One unit of food $F_{1} $ contains 3 units of vitamin A and 4 units of minerals. One unit of food $F_{2} $ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
cbse
class12
bookproblem
ch12
sec2
q9
p520
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A merchant plans to sell two types of personal computers, a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant would stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
cbse
class12
bookproblem
ch12
sec2
q8
p520
sec-c
easy
modelpaper
2012
q29
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?
cbse
class12
bookproblem
ch12
sec2
q7
p520
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
cbse
class12
bookproblem
ch12
sec2
q6
p520
sec-c
medium
math
modelpaper-2012
modelpaper-2014
65-2-3
q23
asked
Nov 16, 2012
by
fingeazy
1
answer
A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.
cbse
class12
bookproblem
ch12
sec2
q5
p519
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
cbse
class12
bookproblem
ch12
sec2
q4
p519
sec-c
easy
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftmans time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftmans time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsmans time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
cbse
class12
bookproblem
ch12
sec2
q3
p519
medium
sec-c
math
asked
Nov 16, 2012
by
fingeazy
1
answer
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
cbse
class12
bookproblem
ch12
sec2
q2
p519
sec-c
easy
math
asked
Nov 16, 2012
by
fingeazy
1
answer
Reshma wishes to mix two types of Food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while Food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture
cbse
class12
bookproblem
ch12
sec2
q1
p519
sec-c
medium
math
asked
Nov 16, 2012
by
fingeazy
1
answer
Let $f : R \to R$ be defined as $f (x) = 3x$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec2
q12
p11
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f: R \to R $, be defined as $f(x) = x^4$. Choose the correct answer.
cbse
class12
bookproblem
ch1
sec2
q11
p11
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
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