Recent questions tagged set-1

A dietician wants to develop a special diet using two foods X and Y. Each packet (contains 30g) of food X contains 12 units of calcium , 4 units of iron, 6 units of cholesterol and $6 \;units$ of vitamin A. Each packet of the same quantity of food Y contains 3 units of calcium, 20 units of iron , 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium , at least 460 units of iron and at most 300 units of cholesterol. Make an LPP to find how many packets of each food should be used to minimise the amount of vitamin A in the diet, and solve it graphically.

asked Mar 23, 2015 by meena.p

1 answer

A dealer deals in two items only - item A and item B . He has $Rs. 50,000$ to inverst and a space to store at most 60 items. An item A cost $Rs. 2500$ and item B costs $Rs. 500$. A net profit to him on item A is $Rs. 500$ and on item B is $Rs. 150$. If he can sell all the items that he purchases , how should he inverst his amount to have maximum profit ? Formulate an LPP and solve is graphically .

asked Mar 23, 2015 by meena.p

1 answer

Assume that the chances of a patient having a heart attack is $40\%$ . It is also assumed that a meditation and yoga course reduces the risk of heart attack by $30\%$ and the prescription of a certain drug reduces its chance by $25\%$ . At a time a patient can choose any one of the two options with equal probabilities . Its given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of mediation and yoga.

asked Mar 23, 2015 by meena.p

1 answer

Find the vector and cartesian equation of the plane passing through the intersection of the planes $\overrightarrow {r} . (\hat i +\hat j+ \hat k)=6$ and $\overrightarrow {r} . (2\hat i +3\hat j+ 4 \hat k)=-5$ and the point $(1,1,1)$

asked Mar 23, 2015 by meena.p

1 answer

Solve the following differential equation , given that $y=0$ , then $ x= \large\frac{\pi}{4}: $$ \sin 2x \large\frac{dy}{dx}$$-y =\tan x$

asked Mar 23, 2015 by meena.p

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Find the general Solution of the differential equation $\large\frac{dy}{dx}=\frac{y^2}{xy-x^2}$

asked Mar 23, 2015 by meena.p

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Find the point on the curve $y= \large\frac{x}{1+x^2} $, Where the tangent to the curve has the greatest slope.

asked Mar 23, 2015 by meena.p

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Using integration , find the area bounded by the curve $y= |x-1|$ and $y= 3-|x|$

asked Mar 23, 2015 by meena.p

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Show that the relation R in the set $A= [1,2,3,4,5]$ given by $R= [(a,b):|a-b|] $ is divisible by 2. It is an equivalence relation . Show that all the elements of $[1,3,5]$ are related to each other and all the elements of $[2,4]$ are related to each other , but no element of ${1,3,5}$ is related to any element of $[2,4]$

asked Mar 22, 2015 by meena.p

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From a set of 100 cards numbered 1 to 100 , one card is drawn at random. Find the probability that the number on the card is divisible by 6 or 8, but not by 24.

asked Mar 22, 2015 by meena.p

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Find the vector and cartesian equations of the plane which bisects the line joining the points $(3,-2,1) $ and $(1,4,-3)$ at right angles.

asked Mar 22, 2015 by meena.p

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Let $P(3,2,6)$ be a point in the space and Q be a point on the line $ \overrightarrow{r} =(\hat i - \hat j +2 \hat k) +\mu (-3 \hat i +\hat j +5 \hat k ), $ then find the value of $\mu $ for ehich the vector $\overrightarrow{PQ}$ is parallel to the plane $x -4y+3z=1$

asked Mar 22, 2015 by meena.p

1 answer

Show that the lines $\large\frac{x-1}{3} =\frac{y-1}{-1}$$,z+1=0$ and $\large\frac{x-4}{2} =\frac{z+1}{3}$$,y=0$ intersect each other . Also find their point of intersection .

asked Mar 22, 2015 by meena.p

1 answer

Evaluate : $\lim \int \limits _0^{\pi} \large\frac{x \tan x }{\sec x . \tan x}$$dx$

asked Mar 22, 2015 by meena.p

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Find $\int \limits_0^2 (x^2+e^{2x+1)}dx$ as the limit of a sum

asked Mar 22, 2015 by meena.p

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Evaluate : $\int x. \sin ^{-1}x dx$

asked Mar 20, 2015 by meena.p

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Find : $\int \large\frac{1- \cos x}{\cos x (1+\cos x)}$$dx$

asked Mar 20, 2015 by meena.p

1 answer

If $y= \sqrt {x+1} -\sqrt {x-1} $, prove that $(x^2-1) \large\frac{d^2y}{dx^2} $$+x\large\frac{dy}{dx} -\frac{1}{4}$$y=0$

asked Mar 20, 2015 by meena.p

1 answer

If $\log \sqrt {x^2+y^2}=\tan ^{-1} \bigg( \large\frac{x}{y} \bigg)$, then show that $\large\frac{dy}{dx}=\frac{y-x}{y+x}$

asked Mar 20, 2015 by meena.p

1 answer

If $y=x^{2^{-x^2}}$, find $\large\frac{dy}{dx}$

asked Mar 20, 2015 by meena.p

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If function $f(x) =|x-3| +|x-4| $, then show that $f(x)$ is not differentiable at $x=3$ and $x=4$

asked Mar 20, 2015 by meena.p

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Find the inverse of matrix $A=\begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix}$ and hence show that $A^{-1} .A =I$

asked Mar 19, 2015 by meena.p

1 answer

If $ X\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}=\begin{bmatrix} -7 & -8 & -9 \\2 & 4 & 6 \end{bmatrix}$, then find the matrix X.

asked Mar 19, 2015 by meena.p

1 answer

If $ a \neq b \neq c$ and $\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end{vmatrix}$$=0$ , then using properties of determinants, prove that $a+b+c=0$

asked Mar 19, 2015 by meena.p

1 answer

If $\tan ^{-1} x+\tan ^{-1}y+\tan ^{-1} z= \large\frac{\pi}{2}$$,x,y,z>0$, then find the value of $xy+yz+zx$

asked Mar 19, 2015 by meena.p

1 answer

There are 3 families A,B and C. The number of men , women and children in these are as under : Dairy expense of men , women and children are $ Rs 200, Rs .150$ and $Rs 200$ respectively. Only men and women earn and children or not. using matrix multiplication , calculate the dairy expenses of each family. What impact does more children in the family create on the society ?

asked Mar 19, 2015 by meena.p

1 answer

Write the direction cosines of the normal to the plane $3x+4y+12z=52$

asked Mar 19, 2015 by meena.p

1 answer

Write the value of $\hat i. (\hat j \times \hat k) + \hat j .( \hat k \times \hat i) +\hat k.(\hat i \times \hat j)$.

asked Mar 19, 2015 by meena.p

1 answer

Write the projection of vector $2 \hat i +3 \hat j - \hat k$ along the vector $\hat i +\hat j$

asked Mar 19, 2015 by meena.p

1 answer

Write a differential equation $y= A \cos \alpha x + B \sin \alpha x$ , where A and B are arbitrary constants .

asked Mar 19, 2015 by meena.p

1 answer

Find the product of the order and degree of the following different equation : $x \bigg(\large\frac{d^2y}{dx^2} \bigg) +\bigg(\large\frac{dy}{dx}\bigg)^2$$+y^2=0$

asked Mar 19, 2015 by meena.p

1 answer

Write a $ 3\times 3$ skew symmetric matrix

asked Mar 19, 2015 by meena.p

1 answer

From each end of solid metal was scooped out in hemispherical form of same diameter . The height of the cylinder is 10 cm and its base is of radius $4.2 \;cm$ . The rest of the cylinder is melted and covered into a cylindrical wire of $1.4\;cm$ thickness . Find the length of the wire $(\pi=\large\frac{22}{7})$

asked Mar 17, 2015 by meena.p

0 answers

In the Figure $PQRS$ is a square laws with side $PQ= 42 meters$. Two circular flower beds are there on the sides $PS$ and $QR$ with center at $Q,$ the intersection of its diagonals. Find the total area of the two flower bed (shaded parts)

asked Mar 17, 2015 by meena.p

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Find the value of k so that the area of the triangle with verices $(1,-1) , (-4,2k)$ and $(-k,-5)$ is 24 sq.units

asked Mar 17, 2015 by meena.p

1 answer

A card is drawn at random from a well -shuffled deck of playing cards . Find the probability that the card drawn is (i) A card of spade or an ace (ii) a black king (iii) neither a jack nor a king (iv) either a king or a queen

asked Mar 17, 2015 by meena.p

1 answer

At a Point A, 20 metres above the level of water in a lake , the angle of elevation of a cloud is $30^{\circ}$ . The angle of depression of the reflection of the cloud in the lake, at A ia $60^{\circ}$ . Find the distance of the cloud from A.

asked Mar 17, 2015 by meena.p

1 answer

Construct a $\Delta ABC$ in which $AB= 6\;cm, \angle A=30^{\circ}$ and $ \angle B=60^{\circ}$ construct another $ \Delta AB'C'$ similar to $\Delta ABC$ with base $AB'= 8 \;cm$

asked Mar 17, 2015 by meena.p

0 answers

Prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc.

asked Mar 17, 2015 by meena.p

1 answer

Prove that the length of the tangents drawn from an external point to a circle are equal

asked Mar 17, 2015 by meena.p

1 answer

A train travels at a certain average speed for a distance of 54 km and then travels a distance of $63\;km$ at an average speed of $6\;km/h$ more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

asked Mar 17, 2015 by meena.p

1 answer

Find the 60th term of the AP $8,10,12....,$ if it has a total of 60 terms and hence find the sum of its last 10 terms .

asked Mar 17, 2015 by meena.p

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Find the 60th term of the AP $8,10,12....,$ if it has a total of 60 terms and hence find the sum of its last 10 terms .

asked Mar 17, 2015 by meena.p

1 answer

The diagonal of a rectangular field is 16 meters more than the shorter side. If the longer side is 14 meters more than the shorter side, then find the lengths of the sies of the field.

asked Mar 17, 2015 by meena.p

1 answer

The diagonal of a rectangular field is 16 meters more than the shorter side. If the longer side is 14 meters more than the shorter side, then find the lengths of the sies of the field.

asked Mar 17, 2015 by meena.p

0 answers

$504$ cones , each of diameter $3.5\;cm$ and height 3 cm, are melted and recast into a metallic sphere. find the diameter of the sphere and hence find its surface [use $\pi =\large\frac{22}{7}$ ]

asked Mar 17, 2015 by meena.p

1 answer

A cubical block of side 10 cm is surmounted by a hemisphere . What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of $5$ per $100 \;sq\;cm$ [Use $\pi = 3.14$]

asked Mar 17, 2015 by meena.p

1 answer

A hemispherical bowl of internal diameter $36\;cm$ contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm Find the height of the each bottle. If $10 \%$ liquid is wasted in this transfer .

asked Mar 17, 2015 by meena.p

1 answer

If the coordinates of points A and B are $(-2,-2)$ and $(2,-4)$respectively, find the coordinates of P such that $AP=\large\frac{3}{7} $$AB$, where P lies on the line segment AB.

asked Mar 17, 2015 by meena.p

1 answer

The angle of elevation of an aeroplane from a point A on the ground is $60^{\circ}$. After a flight of 15 seconds the angle of elevation changes to $30^{\circ}$. If the aeroplane is flying at a constant height of $1500 \sqrt 3\;m$ find the speed of the palne in km/hr

asked Mar 17, 2015 by meena.p

1 answer

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