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Recent questions tagged q28
Questions
The vector $\hat i+\lambda\hat j+\hat k,\hat i+\hat j-\hat k$ and $3\hat i+6\hat j-5\hat k$ are coplanar if
cbse
class12
ch10
q28
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
A housewife wishes to mix up two kind of foods X and Y in such a way that mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food X and 1 kg of food Y are as given in the table : If 1 kg of food X costs Rs. 6 and 1 kg of food Y costs Rs. 10, find the least cost of the mixture which will produce the desired diet.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is \begin{array}{1 1}(A)\;2 sq.units & (B)\;4 sq.units\\(C)\;3 sq.units & (D)\;1sq.units \end{array}
cbse
class12
ch8
q28
p178
objective
exemplar
sec-b
easy
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
A factory owner wants to purchase two types of machines. A and B for his factory. The machine A requires an area of 1000 \( m^2\) and 12 skilled men for running it and its daily output is 50 units, whereas the machine B requires 1200 \( m^2\) area and 8 skilled men and its daily output is 40 units. If an area of 7600 \( m^2\) and 72 skilled men be available to operate the machine, how many machines of each type should be bought to maximise the daily output.? Keeping unemployment in mind justify the values to be promoted for selection of the manually operated machine.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Evaluate the following as limits of sums: $ \int\limits_0^2e^xdx$
cbse
class12
ch7
q28
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Show that \( \int_0^{\pi} \frac{\large x\: sin\: x}{\large 1+sin \: x}= \frac{\large \pi}{\large 2}(\pi-2) \)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 13, 2013
by
thanvigandhi_1
0
answers
Show that \( \int_0^{\pi} \log(1+tan \: \theta ) d\theta. \)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 13, 2013
by
thanvigandhi_1
0
answers
If the straight line $x\cos\alpha+y\sin\alpha=p$ touches the curve $\Large\frac{x^2}{a^2}\;\;\frac{y^2}{b^2}=\normalsize 1$,then prove that $a^2\cos^2\alpha+b^2\sin^2\alpha=p^2$.
cbse
class12
ch6
q28
p137
exemplar
math
sec-b
asked
Jan 11, 2013
by
sreemathi.v
0
answers
Find the angle between the planes \( 4x+8y+z-8=0 \: and \: y+z-4=0. \)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
A farmer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2/kg and the type II costs Rs. 3/kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum?
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of one kg food is given below : One kg of food x costs Rs.16 and one kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
A die is thrown three times.Let X be 'the number of twos seen'.Find the expectation of X.
cbse
class12
ch13
q28
p274
short-answer
exemplar
easy
sec-a
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
There are two types of fertilisers \( F_1 and F_2. F_1\) contain 10% nitrogen and 6% phosphoric acid and \( F_2\) consists of 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14kg of phosphoric acid for the crop. If \( F_1 \) costs Rs.6/kg and \( F_2 \) costs Rs. 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
cbse
class12
modelpaper
2012
q28
math
sec-c
asked
Jan 8, 2013
by
thanvigandhi_1
0
answers
Solve the following linear programming problem graphically Minimize \( Z = x-5y+20\). Subject of the constraints : $ \begin{array} xx-y \geq 0 \\ -x+2y \geq 2 \\ x \geq 3 \\ y \leq 4 \\ x,y \geq 0. \end{array} $
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
If $l_1,m_1,n_1,l_2,m_2,n_2,l_3,m_3,n_3$ are direction cosines of three mutually perpendicular lines,prove that the line whose direction cosines are proportional to $l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3$ make equal angles with them.
cbse
class12
ch11
q28
p237
exemplar
difficult
sec-c
math
asked
Jan 4, 2013
by
sreemathi.v
1
answer
A toy company manufactures two types of dolls, A and B. Markets 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 almost 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 almost 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
modelpaper
2012
sec-c
q28
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Show that the lines : $ \frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \: and \: \frac{x-2}{4}=\frac{y-1}{3}=\frac{z+1}{-2}. $
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
Find the co-ordinates of the image of the point ( 1, 3, 4 ) in the plane \( 2x-y+z+3=0\)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
A farmer mixes two brands P and Q of cattle feed. Brand P costing Rs. 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B and 3 units of element C . The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units, respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Differentiate the following w.r.t $x$ : $log\begin{bmatrix}log\bigg(log x^5\bigg)\end{bmatrix}$.
cbse
class12
ch5
q28
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the equation of the curve passing through the origin and satisfying the differential equation \((1 + x^2) \frac{dy}{dx} + 2xy = 4x^2 \)
cbse
class12
modelpaper
2012
sec-b
q28
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Evaluate : $ \int\: \large\frac{dx}{(x^2-3x+2) \sqrt {x-1}} $
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
A merchant plans to sell two types of personal computer - a desk top model and a portable model that will cost Rs. 25,000 and Rs. 40,000 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 should stock to get a maximum profit if he does not want to invest more than 70 lakh and if his profit on the desktop model is Rs. 4,500 and the portable is Rs. 5,000.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
The number of distinct real roots of $\begin{vmatrix}\sin x & \cos x & \cos x\\\cos x & \sin x & \cos x\\\cos x & \cos x &\sin x\end{vmatrix}=0\;$ in the interval $\large \frac{-\pi}{4}$$ \leq x \leq\large \frac {\pi}{4}$ is
cbse
class12
ch4
sec-a
q28
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
From a pack of 52 cards, a card is lost. Fro the remaining 51 cards, two cards are drawn at random ( without replacement ) and are found to be both diamonds. What is the probability that the lost card was a card of heart?
cbse
class12
modelpaper
2011
sec-c
q28
math
asked
Dec 26, 2012
by
thanvigandhi_1
0
answers
An aerolpane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves atleast 20 seats for the executive class. However, at least 4 times as many passengers prefer to travel by ecenomy class, than by the executive class. Determine how many tickets of each type must be sold, inorder to maximise the profit for the airline. What is the maximum profit? Make an L.P.P. and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
Evaluate : $ \int \:\large \frac{2\sin2\theta -\cos \theta}{6-\cos^\theta - 4\sin\theta}$$d\theta$
cbse
class12
modelpaper
2008
sec-c
q28
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
Find the solution of the differential equation \( (x^2 + y^2) dx = 2xy \: dy\)
cbse
class12
modelpaper
2012
sec-b
q28
math
asked
Dec 22, 2012
by
thanvigandhi_1
0
answers
If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(i)\quad(2A+B)'=2A'+B'$
cbse
class12
ch3
q28
q28-1
p56
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
The value of $\cos^{-1}\bigg(\cos\frac{3\pi}{2}\bigg)$ is equal to:
cbse
class12
ch2
q28
p38
objective
exemplar
easy
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760, to invest and has a space for at most 20 items. A fan cost him Rs.360 and a sewing machine Rs.240. His expectation is that he can sell a fan at a profit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit ? Formulate this as a linear programming problem and solve it graphically.
cbse
class12
modelpaper
2009
sec-c
q28
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are listed below. He has maximum area of 9000 \( m^2 \) available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximise the daily output.
cbse
class12
modelpaper
2008-1
sec-c
q28
math
asked
Dec 19, 2012
by
thanvigandhi_1
0
answers
Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$. If a is congruent to b where $a,b\in T$, then $R$ is:
cbse
class12
ch1
q28
p13
objective
exemplar
sec-a
math
asked
Dec 19, 2012
by
sreemathi.v
1
answer
Integrate the function\[\frac{\cos x}{\sqrt{1+\sin x}}\]
cbse
class12
bookproblem
ch7
sec2
q28
p307
sec-a
easy
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Evaluate the definite integrals\[\int\limits_\frac{\pi}{6}^\frac{\pi}{3}\frac{\sin x+\cos x}{\sqrt{\sin2x}}dx\]
cbse
class12
bookproblem
ch7
misc
q28
p353
sec-b
difficult
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
cbse
class12
bookproblem
ch6
misc
q10
242
sec-b
easy
modelpaper-2014
modelpaper-2012
q28
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
For all real values of \(x\), the minimum value of \( \large\frac{1-x+x^2}{1+x+x^2}\) is
cbse
class12
bookproblem
ch6
sec5
q28
p234
sec-b
easy
math
asked
Nov 27, 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
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