Recent questions tagged modelpaper

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

1 answer

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

asked Mar 22, 2015 by meena.p

1 answer

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

asked Mar 20, 2015 by meena.p

1 answer

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

asked Mar 20, 2015 by meena.p

1 answer

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

1 answer

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

If $A(-2,-1), B(a,0), C(4,b)$ and $D(91,2)$ are the vertices of a parallelogram, find the values of a and b.

asked Feb 19, 2015 by meena.p

1 answer

Find the coordinates of the circumcentre of the triangle whose vertices are $(8,6),(8.2)$ and $(2,-2)$. Also find its circum-radius

asked Feb 19, 2015 by meena.p

1 answer

$ABC$ is a right angled triangle , right angled at A. Find the area of the shaded region if $AB = 6cm, BC = 10cm$ and $I$ is the centre of the incircle of $\Delta ABC.$

asked Feb 19, 2015 by meena.p

1 answer

Sonia buys a shop for $Rs. 1,20,000$. She pays half the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs. 5000$ each. If the rate of interest is $12 \%$ and she pays with the installment due on the unpaid amount, find the total cost of the shop.

asked Feb 19, 2015 by meena.p

0 answers

Ramesh has got $24000/$ - as Puja Bonus. He donated ` 5000/'- to temple. He gave $`12000/-$ to his wife, ` $2000/-$ to his servant and gave rest of the amount to his daughter. a. What is the probability of wife's share? b. Calculate the probability of servant's share? c. What is the probability of daughter's share? d. Which value are depicted by Ramesh from the way the amount is distributed?

asked Feb 19, 2015 by meena.p

1 answer

A fast train takes 3 hrs less than the a slow train for a journey of $600\;km$. If the speed of the slow train is 10km/hr less than that of the fast train, find the speeds of the two trains

asked Feb 19, 2015 by meena.p

1 answer

If two tangents are drawn to a circle from an external point, then prove that, a)They subtend equal angles at the centre b) They are equally inclined to the segment, joining the centre to that point.

asked Feb 19, 2015 by meena.p

0 answers

Two circles with centres A and B of radii $3\;cm$ and $4\;cm$ respectively intersect at two points C and D such that AC and BC are tangents to the two circles. Find the length of the common chord

asked Feb 19, 2015 by meena.p

1 answer

An aeroplane flying horizontally $1\;km$ above the ground is observed at an angle of elevation of $60^{\circ}$. After 10 seconds, its elevation is observed to be $30^{\circ}$. Find the speed of the aeroplane in km/hr

asked Feb 19, 2015 by meena.p

1 answer

If the angle of elevation of a cloud from a point h meteres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is $\large\frac{2hsec \alpha}{tan \beta -tan \alpha}.$

asked Feb 19, 2015 by meena.p

1 answer

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainer is $\large\frac{8}{9}$ of the curved surface of the whole cone, find the ratio of the line-segment into which the cone’s altitude is divided by the plane.

asked Feb 19, 2015 by meena.p

1 answer

Water flows at the rate of $10\;m$ per minute through a cylindrical pipe having its diameter as $5\;mm$. How much time will it take to fill a conical vessel whose diameter of base is $40\;cm$ and depth $24\;cm$?

asked Feb 19, 2015 by meena.p

1 answer

Draw a circle of radius $6\;cm$. From a point $10\;cm$ away from its centre, construct the pair of tangents to the circle and measure their lengths.

asked Feb 19, 2015 by meena.p

0 answers

How many numbers of two digits are divisible by 7?

asked Feb 19, 2015 by meena.p

1 answer

$O$ is the centre of the circle and $BCD$ is tangent to it at $C.$ Prove that $\angle BAC + \angle AC = 90^{\circ}$

asked Feb 19, 2015 by meena.p

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Find the value of ‘k’, if the points $A(8,1), B(3,-4)$ and $C(2,k)$ are collinear

asked Feb 19, 2015 by meena.p

1 answer

How many terms of the series $54,51,48…$ is taken so that their sum is $513?$ Explain the double answer.

asked Feb 19, 2015 by meena.p

1 answer

$O$ is the centre of the circle and $BCD$ is tangent to it at $C$. Prove that $\angle BAC + \angle ACD = 90^{\circ}$

asked Feb 19, 2015 by meena.p

0 answers

Solve by the method of completing the squares: $3x^2 + 2x-1=0$

asked Feb 19, 2015 by meena.p

1 answer

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