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Recent questions and answers in Model Papers
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
by
asewa44
1
answer
A man and his wife appear for an interview for two posts. The probability of husbandâ€™s selection is \( \frac{1}{7} \) and that of the wifeâ€™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
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
answered
Jun 2, 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
answered
Jun 2, 2016
by
meena.p
1
answer
Find the equation of plane passing through the point $A(3,2,1,) B(4,2,-1)$ and $C(6,5,-1)$ and $D(\lambda,5,5)$ are co planar
cbse
class12
math
sec-b
boardexam
2016
answered
Jun 1, 2016
by
meena.p
1
answer
Given that vectors $ \overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ from a triangle such that $\overrightarrow{a} = \overrightarrow{b}+ \overrightarrow{c}$. Find p,q,r,s such that area of triangle is $ 5 \sqrt 6$ where $\overrightarrow{a} = p \hat i +q \hat j +r \hat k$ ,$\overrightarrow{b} = s \hat i +3 \hat j +4 \hat k$ and $\overrightarrow{c} = 3 \hat i + \hat j -2 \hat k$
cbse
class12
math
sec-b
boardexam
2016
answered
Jun 1, 2016
by
meena.p
1
answer
There are two bags A and B . Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls . Three balls are drawn at random ( with out replacement ) from one of the bags and are found to be two white and one red. Find the probability that these were drqwn from bag B.
cbse
class12
math
sec-b
boardexam
2016
answered
Jun 1, 2016
by
meena.p
1
answer
Prove that $ 2\sin ^{-1} \bigg( \large\frac{3}{5} \bigg) - \tan ^{-1} \bigg(\large\frac{17}{31} \bigg) = \large\frac{\pi}{4}$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Ishan wants to donate a rectangular plot of land for a land for a school in his village . When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same. but if length is decreased by 10 m and breadth is decreased by 20 m. then its area will decrease by $5300\;m^2$ . Using matrices , find the dimension of the plot. Also give reasons why he wants to denote the plot for a school.
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Solve the differential equation : $ 2ye^{x/y} dx+ (y -2x e^{x/y})dy=0$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Solve the differential equation : $(x+1)\large\frac{dy}{dx}$$-y =e^{3x}(x+1)^3$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Evaluate : $\int \limits_0^1 \cot ^{-1} (1-x+x^2)dx$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Evaluate: $ \int \limits_0^{\large\frac{\pi}{2}} \large\frac{sin ^2 x}{\sin x + \cos x}$$dx$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Find $\{\int (\log (\log x)+\large\frac{1}{(\log x)^2}\}$$dx$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Find $\int \large\frac{1- \sin x}{\sin x (1+\sin x)}$$dx$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Find the equation of normal to the curve $ay^2 = x^3$ at the point whose x coordinate is $am^2$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Find k, if $f(x) = \left\{ \begin{array} {1 1} k \sin \frac{\pi}{2}(x+1), & \quad x \leq 0 \\ \frac{\tan x - \sin x}{x^3} ,& \quad x >0 \end{array} \right. $ is a continuous at x=0
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Differentiate $\tan ^{-1} \bigg( \large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\bigg)$ with respect to $ \cos ^{-1}x^2$
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
Differentiate $(\sin 2x)^x+ \sin ^{-1} \sqrt {3x}$ with respected to x
cbse
class12
math
sec-b
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
If $A = \begin{bmatrix} 0 & 3 \\2 & -5 \end{bmatrix}$ and $KA = \begin{bmatrix} 0 & 4a \\-8 & 5b \end{bmatrix}$ find the values of K and a
cbse
class12
math
sec-a
boardexam
2016
answered
May 31, 2016
by
meena.p
1
answer
If $A= \begin{bmatrix}1 & 2 \\ 3 & -1\end{bmatrix}$ and $B=\begin{bmatrix}1 & -4 \\ 3 & -2\end{bmatrix}$ find $|AB|$
cbse
class12
math
sec-a
boardexam
2016
answered
May 30, 2016
by
meena.p
1
answer
If A is a square matrix such that $|A|=5$ write the value of $|AA^T|$
cbse
class12
math
sec-a
boardexam
2016
answered
May 30, 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
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