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Recent questions tagged cbse
Questions
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
A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
cbse
class12
bookproblem
ch12
misc
q10
p528
sec-c
difficult
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$ \[\] If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?
cbse
class12
bookproblem
ch12
misc
q9
p528
sec-c
difficult
math
asked
Nov 16, 2012
by
fingeazy
1
answer
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$
cbse
class12
bookproblem
ch12
misc
q8
p527
sec-c
difficult
math
asked
Nov 16, 2012
by
fingeazy
1
answer
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. Assuming that the transportation cost of 10 litres of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost? The distances (in km) between the depots and the petrol pumps is given in the following table: \[\] $\begin{matrix} & \underline{\text{Distance in Km}} & \\ \underline{\text{From} \setminus\text{To}}& \text{A}&& \text{B}\\ \text{D}& 7 &&3 \\ \text{E}& 6 &&4 \\ \text{F} & 3 && 2 \end{matrix}$
cbse
class12
bookproblem
ch12
misc
q7
p527
sec-c
difficult
math
asked
Nov 15, 2012
by
fingeazy
1
answer
Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively.
cbse
class12
bookproblem
ch12
misc
q6
p527
sec-c
difficult
math
asked
Nov 15, 2012
by
fingeazy
1
answer
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
cbse
class12
bookproblem
ch12
misc
q5
p526
sec-c
difficult
math
asked
Nov 15, 2012
by
fingeazy
1
answer
Find \( \large\frac {dy}{dx} \) in the following: $ y = cos^{-1} \left(\large\frac{2x}{1 + x^2}\right), -1 < x < 1 $
cbse
class12
bookproblem
ch5
sec3
q13
p169
exercise5-3
sec-b
easy
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following:$ y = sin^{-1} \left(\frac{1 - x^2}{1 + x^2}\right), 0 < x < 1 $
cbse
class12
bookproblem
ch5
sec3
q12
p169
exercise5-3
sec-a
easy
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Find \( \frac {dy}{dx} \) in the following: $y = cos^{-1} \left(\frac{1 - x^2}{1 + x^2}\right), 0 < x < 1 $
cbse
class12
bookproblem
ch5
sec3
q11
p169
exercise5-3
sec-a
medium
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx}$ in the following: $y = tan^{-1} \left(\frac{3x - x^3}{1 - 3x^2}\right), - \; { \frac{1}{\sqrt3} } < x < \;{\frac{1}{\sqrt3} }\\ $
cbse
class12
bookproblem
ch5
sec3
q10
p169
exercise5-3
sec-a
easy
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ y = sin^{-1} \left(\frac{2x}{1 + x^2}\right) $
cbse
class12
bookproblem
ch5
sec3
q9
p169
easy
sec-a
exercise5-3
math
asked
Nov 15, 2012
by
thanvigandhi_1
1
answer
Consider\(f:\{1,2,3\} \to\{a,b,c\}\) given by \(f(1)=a, \,f(2)=b\) and \(f(3)=c\). Find \(f^{-1} \) and show that \((f^{-1})^{-1} = f\).
cbse
class12
bookproblem
ch1
sec3
q11
p19
easy
sec-a
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Let \(f : X \to Y\) be an invertible function. Show that \(f\) has unique inverse.
cbse
class12
bookproblem
ch1
sec3
q10
p19
easy
sec-a
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Consider \(f:R_+ \to [\;\text{–5}, \infty )\)given by \(f(x)=9x^2 +6x\)-\(5\).Show that \(f\) is invertible with \( f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) \)
cbse
class12
bookproblem
ch1
sec3
q9
p19
medium
sec-b
math
asked
Nov 15, 2012
by
vaishali.a
1
answer
Consider \( f:R_+ \to [4,\infty)\)given by \(f(x)=x^2 +4\). Show that \(f\) is invertible with the inverse \(f^{-1}\)of \(f\) given by \(f^{-1}(y) = \sqrt {y-4}\),where $R_+$ is the set of all non-negative real numbers.
cbse
class12
bookproblem
ch1
sec3
q8
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Consider $f:R \to R$ given by $f(x)=4x+3$. Show that $f$ is invertible. Find the inverse of $ f$
cbse
class12
bookproblem
ch1
sec3
q7
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Show that $f : [-1,1]$ $ \rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow $ Range $ f$.
cbse
class12
bookproblem
ch1
sec3
q6
p18
medium
sec-b
math
asked
Nov 14, 2012
by
vaishali.a
1
answer
Find $ \frac {dy}{dx} $ in the following: $ \sin^2x +\cos^2y = 1 $
cbse
class12
bookproblem
ch5
sec3
q8
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find \( \frac {dy}{dx} \) in the following: \( sin^2y + cos \: xy = k \)
cbse
class12
bookproblem
ch5
sec3
q7
p169
exercise5-3
sec-b
medium
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ x^3 +x^2y + xy^2 +y^3 = 81 $
cbse
class12
bookproblem
ch5
sec3
q6
p169
exercise5-1
easy
sec-a
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ x^2 +xy + y^2 = 100 $
cbse
class12
bookproblem
ch5
sec3
q5
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $ \frac {dy}{dx} $ in the following: $ xy +y^2 = tan \: x + y $
cbse
class12
bookproblem
ch5
sec3
q4
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $ax +by^2 = cos \: y$
cbse
class12
bookproblem
ch5
sec3
q3
p169
sec-a
easy
exercise5-3
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: y$
cbse
class12
bookproblem
ch5
sec3
q2
p169
exercise5-3
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: x$
cbse
class12
bookproblem
ch5
sec3
exercise5-3
169
q-1
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} \large\frac{k\cos x}{\pi - 2x}\normalsize,& \quad { if \; x \neq \large\frac{\pi}{2} }\\ \normalsize 3 ,& \quad { if \; x = \large\frac{\pi}{2} }\\ \end{array} \right. \qquad at \; x = \; \large\frac{\pi}{2} $
cbse
class12
bookproblem
ch5
sec1
q26
p161
sec-b
easy
modelpaper
2012
q14
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $a$ and $b$ such that the function defined by $ f(x) = \left\{ \begin{array} {1 1} 5 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ ax+b,& \quad \text{if $2$ < x<10}\\ 21,& \quad \text{if $ x $ \(\geq 10\)}\\ \end{array} \right.$ is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q30
p161
sec-b
medium
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ \(\leq 5\)}\\ 3x-5,& \quad \text{if $x$ > 5}\\ \end{array} \right.\qquad at \; x = 5 $
cbse
class12
bookproblem
ch5
sec1
q29
p161
sec-b
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ \(\leq \pi\)}\\ \cos x,& \quad \text{if $x$ > \(\pi\)}\\ \end{array} \right.$ at $x = \pi$
cbse
class12
bookproblem
ch5
sec1
q28
p161
sec-a
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx^2 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ 3,& \quad \text{if $x$ > 2}\\ \end{array} \right. \qquad at \;x = 2 $
cbse
class12
bookproblem
ch5
sec1
q27
p161
sec-b
easy
math
asked
Nov 11, 2012
by
thanvigandhi_1
1
answer
Examine the continuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \sin x - \cos x,& \quad\text{ if \(x\) \(\neq\) 0 }\\ -1 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q25
p160
sec-b
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
Determine if $f$ defined by $f(x) = \left\{ \begin{array} {1 1} x^2sin \large\frac{ 1 }{x},\normalsize & \quad\text{ if x \(\neq\) 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $ is a continuous function?
cbse
class12
bookproblem
ch5
sec1
q24
p160
sec-a
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
Find all points of discontinuity of \(f\), where $ f(x) = \left\{ \begin{array} {1 1} \large\frac {sinx} {x},\normalsize & \quad\text{ if \(x\) < 0 }\\ x + 1 ,& \quad \text{if $x$ \( \geq 0\)}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q23
p160
sec-b
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
For what value of \( \lambda \) is the function defined by \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ \(\leq 0\)}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right. $ Continuous at \(x = 0\)?
cbse
class12
bookproblem
ch5
sec1
q18
q18-1
p160
sec-a
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
Find the relationship between \(a\) and \(b\) so that the function \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} ax + 1 ,& \quad\text{ if $ x $ \(\leq 3\)}\\ bx + 3,& \quad \text{if $x$ > 3}\\ \end{array} \right. $ is continuous at \(x = 3\).
cbse
class12
bookproblem
ch5
sec1
q17
p160
sec-b
easy
math
asked
Nov 10, 2012
by
thanvigandhi_1
1
answer
State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)
cbse
class12
bookproblem
ch1
sec3
q5
p18
q5-3
sec-a
easy
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
If $f(x) = \frac { (4x+3) } { (6x-4) }, x \neq \frac {2} {3}$, show that $ f(x) =x $, for all $ x \neq \frac {2} {3}$. What is the inverse of $f$
cbse
class12
bookproblem
ch1
sec3
q4
p18
medium
sec-b
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f+g) oh = foh + goh\]
cbse
class12
bookproblem
ch1
sec3
q2
p18
easy
sec-a
q2-1
math
asked
Nov 9, 2012
by
vaishali.a
1
answer
Let $f:\{1,3,4\} \to \{1,2,5\} $ and $g:\{1,2,5\}\to\{1,3\}$ be given by $f = \{(1, 2), (3, 5), (4, 1)\}$ and $ g = \{(1, 3), (2, 3), (5, 1)\}$. Write down $gof$.
cbse
class12
bookproblem
ch1
sec3
q1
p18
easy
sec-a
math
asked
Nov 9, 2012
by
vaishali.a
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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