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Recent questions and answers in Model Papers
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Model Papers
Let A = N x N and * be a binary operation on A defined by (a,b)*(c,d)=(ac,bd), show that : (i) (A*) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.
cbse
class12
modelpaper
2012
sec-c
q23
math
answered
Jul 8
by
s.kpandey26
1
answer
Show that of all the rectangles of given area, the square has the smallest perimeter.
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Jun 9
by
anshikamaheshwari28
1
answer
For what value of k is the following function continuous at x = 2? $ f(x) = \left\{ \begin{array}{l l} 2x+1, & \quad { x < 2}\\ k, & \quad \text{ $x$ = 2} \\ 3x-1, & \quad \text{ $x$ > 2} \end{array}. \right.$
cbse
class12
modelpaper
2012
sec-b
q14
math
answered
May 29
by
dwivediprachi09
1
answer
Give an example of relation which is reflexive but neither symmetric nor transitive.
cbse
class12
modelpaper
2012
sec-a
q1
math
answered
Apr 11
by
harishahmad6
1
answer
A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that volume of the box is maximum?
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Apr 9
by
rahulrkchauhan123456789
1
answer
A coin is based so that the head is 3 times as likely to occur as tail. If the coin is tossed three times, find the probabilty distribution of number of tails.
cbse
class12
modelpaper
2011
sec-b
q22
math
answered
Mar 20
by
akkhola2000
1
answer
A catering agency has two kitchens to prepare food at two places A and B. From these place " Mid-day meal' is to be supplied to three different schools situated at P, Q, R. The monthly requirements of the schools are respectively 40, 40 and 50 food packets. A packet contains lunch for 1000 students. Preparing capacity of kitchen A and B are 60 and 70 packets per month respectively. The transportation cost per packet for the kitchen to school is given below. How many packets from each kitchen should be transported to school so that the cost of transportation is minimum? Also find the minimum cost.
cbse
class12
modelpaper
2008
sec-b
q24
math
answered
Mar 20
by
prakashkumarsingh.ktr
1
answer
An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.
cbse
class12
modelpaper
2012
sec-c
q33
math
answered
Feb 23
by
pady_1
1
answer
A metal has a threshold wavelength of $6000 ^{\circ} A$. Calculate its 1) threshold frequency and 2) work function of the metal in eV.
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
Jan 31
by
arunamansingh5
1
answer
Solve the following differential equation : $ \cos^2\: x\large\frac{dy}{dx}$$+y=\tan x$
cbse
class12
modelpaper
2012
sec-b
q18
math
answered
Jan 27
by
chodadeepak14
1
answer
Two cards are drawn one by one without replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
cbse
class12
modelpaper
2012
sec-b
q15
math
answered
Jan 17
by
mahawarravi036
2
answers
Probabilities of solving a specific problem independently by A and B are \( \frac{1}{2} \: and \frac{1}{3} \) respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.
cbse
class12
modelpaper
2012
sec-b
q22
math
answered
Jan 14
by
next2unonu
1
answer
There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.
cbse
class12
modelpaper
2012
sec-b
q21
math
answered
Jan 3
by
zawude.tame
1
answer
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contains atleast 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 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
modelpaper
2012
sec-c
q29
math
answered
Dec 2, 2017
by
taha.ba16
1
answer
Evaluate : $ \begin{bmatrix} a+ib & c+id \\ -c+id & a-ib \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
math
answered
Nov 22, 2017
by
rabindrasinghrouth
1
answer
Find the differential equation of the family of ellipses having foci on y- axis and centre at the origin.
cbse
class12
modelpaper
2012
sec-b
q11
math
answered
Nov 12, 2017
by
sharmaeku25
1
answer
Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point ( x, y ) is equal to the sum of the coordinates of the point
cbse
class12
modelpaper
2012
sec-b
q19
math
answered
Nov 11, 2017
by
debnathsunita69
1
answer
Four hydrogen nuclei combine to form a helium nucleus, what amount of energy in mev will a released in this process?
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
Oct 17, 2017
by
balaramshil1
1
answer
Find the area of the smaller part of the circle \( x^2+y^2=a^2\) cut off by the line \( x=\large\frac{a}{\sqrt 2}\)
cbse
class12
modelpaper
2012
sec-c
q25
math
answered
Sep 15, 2017
by
kushagrapatel1997
2
answers
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Jul 28, 2017
by
pady_1
1
answer
A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment. Make it an L.P.P. and solve the above problem.
cbse
class12
modelpaper
2012
sec-c
q28
math
answered
Jul 28, 2017
by
yashingrodiya1212
1
answer
The total revenue received from the sale of x units of a product is given by $ R(x) = 13x^2 + 26x + 15 $ Find the marginal revenue when x = 7.
cbse
class12
modelpaper
2012
sec-a
q5
math
answered
Jun 3, 2017
by
ranjani.hogwarts
1
answer
The ground state energy of hydrogen atom is $-13.6\;eV$ 1.What are the potential and kinetic energy of an electron in the 3rd excited state? 2.If the electron jumps to the ground state from the third excited state, calculate the frequency of the photon emitted.
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
May 11, 2017
by
balaramshil1
1
answer
A company has two plants to manufacture bicycles. Plant I manufactures 70% of the bicycles and plant II manufactures 30%. At plant I 80% of the bicycles are rated as of standard quality and a plant II 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II?
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Apr 14, 2017
by
shrutibhagat2215
1
answer
A company sells two different products A and B. The products are produced in a common production process which has total capacity of 500 man hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The demand in the market shows that the maximum number of units of A that can sold is 70 and that of B is 125. Profit on each unit of A is Rs. 20 and on B is Rs.15. How many units of A and B should be produced to maximise the profit? Form an L.P.P and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
math
answered
Feb 16, 2017
by
meena.p
1
answer
If $( \overrightarrow a \: and \: \overrightarrow b)$ are two vectors such that $( | \overrightarrow a. \overrightarrow b| = | \overrightarrow a x \overrightarrow b |)$, then what is the angle between $( \overrightarrow a \: and \: \overrightarrow b)?$
cbse
class12
modelpaper
2012
sec-a
q9
math
answered
Feb 16, 2017
by
suganyadevi.p
1
answer
Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $
cbse
class12
modelpaper
2012
sec-b
q12
ch4
bookproblem
misc
q5
p141
math
answered
Feb 16, 2017
by
meena.p
1
answer
Solve the differential equation : $(x+y)dy + (x-y) dx=0$
cbse
class12
modelpaper
2012
sec-c
q26
math
answered
Feb 16, 2017
by
suganyadevi.p
1
answer
If vectros $ \overrightarrow a = 2\hat i + 2\hat j +3\hat k , \overrightarrow b = -\hat i + 2\hat j +\hat k \: and \: \overrightarrow c = 3\hat i + \hat j $ are such that $( \overrightarrow a +\lambda \overrightarrow b)$ is perpendicular to $( \overrightarrow c )$, then find the value of $( \lambda )$
cbse
class12
modelpaper
2012
sec-b
q20
math
answered
Feb 16, 2017
by
suganyadevi.p
1
answer
The scalar product of the vector $ \overrightarrow a = \hat i + \hat j + \hat k$ with a unit vector along the sums of vectors $ \overrightarrow b = 2 \hat i + 4\hat j - 5 \hat k$ and $ \overrightarrow c = \lambda \hat i + 2 \hat j + 3 \hat k\;$ is equal to one. Find the value of $ \lambda $ and hence find the unit vector along $ \overrightarrow b + \overrightarrow c$
modelpaper-2014-chennai
cbse
class12
math
sec-b
answered
Feb 16, 2017
by
meena.p
1
answer
Evaluate : \[ \int_{-a}^a \sqrt{\frac{a-x}{a+x}}dx \]
cbse
class12
modelpaper
2012
sec-c
q26
math
answered
Feb 16, 2017
by
meena.p
1
answer
If $x^{my^n}=(x+y)^{m+n}$, prove that $\large\frac{dy}{dx}=\frac{y}{x}$
cbse
class12
math
modelpaper
mock-test-series-2015
sec-b
answered
Feb 15, 2017
by
meena.p
1
answer
If $A$ is a square matrix such that $A^2=A$, then write the value of $7A -(I+A)^3$ where $I$ is an identity matrix.
modelpaper-2014-chennai
cbse
class12
math
sec-a
answered
Feb 15, 2017
by
meena.p
1
answer
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
cbse
class12
modelpaper
2005
sec-c
q17
math
answered
Feb 15, 2017
by
meena.p
1
answer
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is \( \frac{5}{6} \), What is the probability that he will knock down fewer than 2 hurdles.
cbse
class12
modelpaper
2012
sec-b
q21
math
answered
Feb 15, 2017
by
meena.p
1
answer
Assume that the chances of a patient having a heart attack is 40%. It is assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is 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 meditation and yoga?
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Feb 15, 2017
by
meena.p
1
answer
If a point charge be rotated in an arc of radius r around a change q, what will be the workdone ? explain
cbse
class12
physics
ch-1
sec-a
q48
difficult
answered
Feb 15, 2017
by
meena.p
1
answer
Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semivertical angle $ \alpha, \: is \: \large\frac{4}{27}$$ \pi \: h^3\: tan^2\: \alpha $
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Feb 15, 2017
by
asewa44
1
answer
A man and his wife appear for an interview for two posts. The probability of husband’s selection is \( \frac{1}{7} \) and that of the wife’s selection is \( \frac{1}{5} \) . Find the probability that only one of them will be selected.
cbse
class12
modelpaper
2012
sec-b
q31
math
answered
Dec 5, 2016
by
meena.p
1
answer
Show that semi-vertical angle of the cone of maximum volume and of given slant height is \( \tan^{-1} \sqrt 2\).
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Nov 18, 2016
by
fizho0631
1
answer
Solve, using matrices : $ 2x-y+3z=5;3x+2y-z=7 ; 4x+5y-5z = 9$
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Sep 12, 2016
by
rakshitrabadiya
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 perunit 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 and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 6, 2016
by
meena.p
1
answer
Three numbers are selected at random (with out replacement ) from first six positive integers. If X denotes the smallest of the three numbers obtained , find the probability distribution of X.Also find the mean and variance of the distribution .
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 3, 2016
by
meena.p
1
answer
Find the equation of the plane containg two parallel lines $ \large\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z}{3} $ and $\large\frac{x}{4} = \frac{y-2}{-2} =\frac{z+1}{6}$ . Also find the plane thus obtained contains the line $ \large\frac{x-2}{3} =\frac{y-1}{1} =\frac{z-2}{5}$ or not .
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 3, 2016
by
meena.p
1
answer
Using integration find the area of the region $f(x,y): y^2 \leq 6ax$ and $ x^2+y^2 \leq 16a^2$
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 2, 2016
by
meena.p
1
answer
Determine the intervals in which the function $f(x)=x^4 -8x^3+22x^2-24 x +21$ is strictly increasing or strictly decreasing.
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 2, 2016
by
meena.p
1
answer
Using of elementary row operations, find the inverse of the following matrix : $\begin{bmatrix} 2 & -1 & 3\\ -5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$
cbse
class12
math
sec-c
boardexam
2016
answered
Jun 2, 2016
by
meena.p
1
answer
Find the maximum and minimum values of $f(x)=\sec x + \log \cos ^2x, 0 < x < 2 \pi$
cbse
class12
math
sec-c
boardexam
2016
asked
May 30, 2016
by
meena.p
0
answers
Using properties of determinant prove that : $\begin{bmatrix}(b+c)^2 & a^2 & bc \\ (c+a)^2 & b^2 & ca \\ (a+b)^2 & c^2 & ab \end{bmatrix}$ $=(a-b)(b-c)(c-a) (a+b+c)(a^2+b^2+c^2)$
cbse
class12
math
sec-c
boardexam
2016
asked
May 30, 2016
by
meena.p
1
answer
Find the coordinates of the point where the line $ \overrightarrow {r} =(-\hat {i} - 2 \hat {j} - 3 \hat {k} )+ \lambda ( 3\hat i + 4 \hat j +3 \hat k )$ meets the plane which is perpendicular to the vector $ \overrightarrow n= \hat i + \hat j + 3 \hat k$ and at a distance of $\large\frac{4}{\sqrt {11}}$ from origin .
cbse
class12
math
sec-b
boardexam
2016
asked
May 30, 2016
by
meena.p
1
answer
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