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Recent questions tagged bookproblem
Questions
Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?
cbse
class12
bookproblem
ch5
sec5
q17
p178
easy
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Find the derivative of the function given by $f(x) =( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)$ and hence find $ f' (1).$
cbse
class12
bookproblem
ch5
sec5
q16
p178
easy
sec-b
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Find $\large\frac{dy}{dx}$ of the function $xy = e^{\large(x-y)}$
cbse
class12
bookproblem
ch5
sec5
q15
p178
medium
sec-a
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Find $\large\frac{dy}{dx}$ of the function $(\cos x)^{\large y} = (\cos y)^{\large x}$
cbse
class12
bookproblem
ch5
sec5
q14
p178
sec-a
medium
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Find $\large\frac{dy}{dx}$ of the functions given in $ y^{\large x} = x^{\large y} $
cbse
class12
bookproblem
ch5
sec5
q13
p178
sec-a
easy
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Find $\large\frac{dy}{dx}$ of the functions given in $ x^{\large y }+ y^{\large x }= 1 $
cbse
class12
bookproblem
ch5
sec5
q12
p178
sec-c
difficult
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ (x \cos x )^{\large x} + (x\sin x)^{\Large\frac{1}{x}} $
cbse
class12
bookproblem
ch5
sec5
q11
p178
sec-c
difficult
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ x^{\large x \cos x} + \large\frac{x^2 + 1}{x^2 - 1} $
cbse
class12
bookproblem
ch5
sec5
q10
p178
sec-c
medium
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ x ^{\large\sin x} + (\sin x)^{\large\cos x} $
cbse
class12
bookproblem
ch5
sec5
q9
p178
difficult
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x$ : $ (\sin x )^{\large x} + \sin^{-1} \sqrt x $
cbse
class12
bookproblem
ch5
sec5
q8
p178
medium
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $y=(\log x)^{\large x}+x^{\large\log x}$
cbse
class12
bookproblem
ch5
sec5
q7
p178
sec-b
medium
modelpaper
2012
q12
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ (x + \large\frac{1}{x})^{\large x}$$ + x ^{\large (1 + \Large\frac{1}{x})} $
cbse
class12
bookproblem
ch5
sec5
q6
p178
medium
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Let \(f : X \to Y\) be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.
cbse
class12
bookproblem
ch1
sec3
q12
p19
easy
sec-a
math
asked
Nov 16, 2012
by
vaishali.a
1
answer
Differentiate the functions given in w.r.t. $x : $ $ (x + 3)^2 \: . \: (x + 4)^3 \: . \: (x + 5)^4 $
cbse
class12
bookproblem
ch5
sec5
q5
p178
easy
sec-b
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ x^{\large x} - 2^{\large sin \: x} $
cbse
class12
bookproblem
ch5
sec5
q4
p178
easy
sec-b
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ ( \log \; x )^{\large cos \: x} $
cbse
class12
bookproblem
ch5
sec5
q3
p178
easy
sec-a
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x :$ $ \sqrt {\large\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}} $
cbse
class12
bookproblem
ch5
sec5
q2
p178
easy
sec-b
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ \cos \: x \: . \cos \: 2x \:. \cos \: 3x $
cbse
class12
bookproblem
ch5
sec5
q1
p178
sec-b
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
If a matrix has 24 elements, what are the possible orders it can have? What if it has 13 elements?
cbse
class12
bookproblem
sec1
q2
math
sec-a
asked
Nov 16, 2012
by
mahuya_bh
0
answers
Differentiate the following w.r.t. $ x: $ $ cos \: ( log\: x + e^x ), x > 0 $
cbse
class12
bookproblem
ch5
sec4
q10
p174
easy
sec-a
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x: \large \frac {\cos x}{\log x}$,$\; x > 0 $
cbse
class12
bookproblem
ch5
sec4
q9
p174
easy
sec-a
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x :$$ log ( log \: x ), x > 1 $
cbse
class12
bookproblem
ch5
sec4
q8
p174
easy
sec-a
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : \sqrt {e^\sqrt x}, x > 0 $
cbse
class12
bookproblem
ch5
sec4
q7
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : e^x + e^{x^2} + \: ... + e^{x^5} $
cbse
class12
bookproblem
ch5
sec4
q6
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : \log\;( cos \: e^x ) $
cbse
class12
bookproblem
ch5
sec4
q5
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : sin\;( tan^{-1} e^{-x}) $
cbse
class12
bookproblem
ch5
sec4
q4
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
The volume of a cube is increasing at the rate of $ 8\;cm^ 3/s$ . How fast is the volume of a cube is increasing at the rate of $8\;cm^ 3 /s$ . How fast is the surface area increasing when the length of an edge is $12 cm$?
cbse
class12
bookproblem
ch6
sec1
q2
p197
sec-a
easy
math
asked
Nov 16, 2012
by
kasturi.c
1
answer
Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$
cbse
class12
bookproblem
ch6
sec1
q1
q1-a
p197
sec-a
easy
math
asked
Nov 16, 2012
by
kasturi.c
1
answer
Differentiate the following w.r.t. $x : e^{x^{3} } $
cbse
class12
bookproblem
ch5
sec4
q3
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : e^{sin^{-1} x} $
cbse
class12
bookproblem
ch5
sec4
q2
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Differentiate the following w.r.t. $x : \large \frac{e^x}{sin\;x}$
cbse
class12
bookproblem
ch5
sec4
q1
p174
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
1
answer
Find $\large \frac {dy}{dx} $ in the following: $ y = sec^{-1} \left(\large\frac{1}{2x^2 - 1}\right), 0 < x < \; { \frac{1}{\sqrt2} } \\ $
cbse
class12
bookproblem
ch5
sec3
q15
p169
exercise5-3
easy
sec-a
math
asked
Nov 16, 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
Find $\large \frac {dy}{dx} $ in the following: $y = \sin^{-1} \big( 2x \sqrt{1 -x^2} \big), -\;{ \frac{1}{\sqrt2} }\;< x < \;{\frac{1}{\sqrt2} }\\ $
cbse
class12
bookproblem
ch5
sec3
q14
p169
exercise5-3
sec-a
easy
math
asked
Nov 16, 2012
by
thanvigandhi_1
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
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
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