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Recent questions tagged modelpaper
Questions
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.
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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 .
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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.
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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 $(1,1,1)$
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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$
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
asked
Mar 23, 2015
by
meena.p
1
answer
Find the general Solution of the differential equation $\large\frac{dy}{dx}=\frac{y^2}{xy-x^2}$
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
asked
Mar 23, 2015
by
meena.p
1
answer
Find the point on the curve $y= \large\frac{x}{1+x^2} $, Where the tangent to the curve has the greatest slope.
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
asked
Mar 23, 2015
by
meena.p
1
answer
Using integration , find the area bounded by the curve $y= |x-1|$ and $y= 3-|x|$
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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 $[2,4]$
class12
cbse
boardexam
2015
set-1
sec-c
math
modelpaper
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.
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
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.
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
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 $x -4y+3z=1$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
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 .
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 22, 2015
by
meena.p
1
answer
Evaluate : $\lim \int \limits _0^{\pi} \large\frac{x \tan x }{\sec x . \tan x}$$dx$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 22, 2015
by
meena.p
1
answer
Find $\int \limits_0^2 (x^2+e^{2x+1)}dx$ as the limit of a sum
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 22, 2015
by
meena.p
1
answer
Evaluate : $\int x. \sin ^{-1}x dx$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
asked
Mar 20, 2015
by
meena.p
1
answer
Find : $\int \large\frac{1- \cos x}{\cos x (1+\cos x)}$$dx$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
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$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 20, 2015
by
meena.p
1
answer
If $y=x^{2^{-x^2}}$, find $\large\frac{dy}{dx}$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
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 $x=4$
class12
cbse
boardexam
2015
set-1
sec-b
math
modelpaper
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 $A^{-1} .A =I$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
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.
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
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}$$=0$ , then using properties of determinants, prove that $a+b+c=0$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
If $\tan ^{-1} x+\tan ^{-1}y+\tan ^{-1} z= \large\frac{\pi}{2}$$,x,y,z>0$, then find the value of $xy+yz+zx$
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
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 ?
class12
cbse
2015
set-1
sec-b
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write the direction cosines of the normal to the plane $3x+4y+12z=52$
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write the value of $\hat i. (\hat j \times \hat k) + \hat j .( \hat k \times \hat i) +\hat k.(\hat i \times \hat j)$.
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
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 $\hat i +\hat j$
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
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 .
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
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$
class12
cbse
2015
set-1
sec-a
math
boardexam
modelpaper
asked
Mar 19, 2015
by
meena.p
1
answer
Write a $ 3\times 3$ skew symmetric matrix
class12
cbse
2015
set-1
summative-2
sec-a
math
boardexam
modelpaper
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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 $\Delta ABC.$
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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?
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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 $\large\frac{2hsec \alpha}{tan \beta -tan \alpha}.$
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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 $24\;cm$?
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-d
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
asked
Feb 19, 2015
by
meena.p
0
answers
How many numbers of two digits are divisible by 7?
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
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 $\angle BAC + \angle AC = 90^{\circ}$
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
asked
Feb 19, 2015
by
meena.p
0
answers
Find the value of ‘k’, if the points $A(8,1), B(3,-4)$ and $C(2,k)$ are collinear
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
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.
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
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 $\angle BAC + \angle ACD = 90^{\circ}$
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
asked
Feb 19, 2015
by
meena.p
0
answers
Solve by the method of completing the squares: $3x^2 + 2x-1=0$
cbse
class10
math
sa-2
modelpaper
mock-test-series-2015
sec-c
asked
Feb 19, 2015
by
meena.p
1
answer
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