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Recent questions and answers in Model Papers
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ISC XII Math
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Model Papers
There are two series of index numbers : P for price index and S for stock of a commodity.The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively.The correlation coefficient between the two series is 0.4,with these data,obtain the regression lines of P on S and S on P.
isc
class12
modelpaper
2005
sec-a
q7
q7-b
answered
Dec 9
by
adv.rathore1974
1
answer
Solve the following linear equations using the matrix method : $x+y+z=9,2x+5y+7z=52,2x+y-z=0$.
isc
class12
modelpaper
2009
sec-a
q2
q2-b
answered
Jul 18
by
pady_1
1
answer
A wire of length 20m is available to fence off a flower bed in the form of a sector of a circle.What must be the radius of the circle,if we wish to have a flower bed with the greatest possible area?
isc
class12
modelpaper
2009
sec-a
q5
q5-b
answered
Apr 5
by
anukriti.maths
1
answer
Three persons A,B and C shoot to hit a target.If in trials,A hits the target 4 times in 5 shots,B hits 3 times in 4 shots and C hits 2 times in 3 trials.Find the probability that :
isc
class12
modelpaper
2012
sec-a
q1
q1-9
answered
Oct 20, 2016
by
pady_1
1
answer
A problem in mathematics is given to three students A,B and C.Their chances of solving the problem are $\large\frac{1}{3}$,$\large\frac{1}{4}$ and $\large\frac{1}{5}$ respectively.Calculate the probability that the problem will be solved.
isc
class12
modelpaper
2003
part-2
sec-c
q13
q13-b
answered
Mar 26, 2016
by
nihar.more33
1
answer
A candidate is selected for interview of management trainees for 3 companies.For the first company,there are 12 candidates,for the second there are 15 candidates and for the third,there are 10 candidates.Find the probability that he is selected in at least one of the companies.
isc
class12
modelpaper
2005
sec-a
q8
q8-b
answered
Sep 4, 2015
by
Anjanatadiboyina12
1
answer
A plane passes through the point (4,2,4) and is perpendicular to the planes $2x+5y+4z+1=0$ and $4x+7y+6z+2=0$.Find the equation of the plane.
isc
class12
modelpaper
2005
sec-b
q10
q10-a
answered
Sep 3, 2015
by
meena.p
1
answer
A straight line is parallel to the x-axis and passes through the intersection of the lines $x+2y+1=0$ and $y=x+7$.Find the equation of the straight line.
isc
class12
modelpaper
2006
sec-a
q1
q1-2
answered
Sep 2, 2015
by
vijayalakshmi.r
1
answer
A straight line $y=mx$ passes through the intersection of the straight lines $x+2y-1=0$ and $2x-y+3=0.$Find the value of m.
isc
class12
modelpaper
2005
sec-a
q1
q1-2
answered
Sep 2, 2015
by
vijayalakshmi.r
1
answer
Two lines of regression are given by x+2y-5=0, 2x+3y-8=0 and Ïƒ2x("sigma squared"x)=12, Calculate the mean value of x and y, variable of Y and the coefficient of correlation between x and y.
answered
Jul 7, 2015
by
meena.p
1
answer
Solve the following system of liner questions by matrix inverse method. 2x+2y+6z=52, 3x+2y+z=26, 2x+2y+6z=18
answered
Jul 7, 2015
by
meena.p
1
answer
Find the value of $\lambda$ for which the four points with position vectors $2\hat{i}+5\hat{j}+\hat{k},-\hat{j}-4\hat{k},3\hat{i}+\lambda\hat{j}+8\hat{k}$ and $-4\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.
isc
class12
modelpaper
2010
sec-b
q10
q10-a
answered
Jan 1, 2015
by
siddharth.sharma3
2
answers
Draw a rough sketch of the curve $y^2+1=x,x\leq 2$.Find the area enclosed by the curve and the line $x=2$.
isc
class12
modelpaper
2008
sec-a
q6
q6-b
cbse
sec-b
ch8
additionalproblem
math
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
Evaluate $\large \int \frac{2\sin 2 x -\cos x }{6-\cos^2x -4\sin x }$$dx$.
isc
class12
modelpaper
2010
sec-a
q6
q6-a
answered
Dec 22, 2013
by
balaji.thirumalai
1
answer
Using Demoivre's theorem,find the least value of n for which $\bigg(\large\frac{i+\sqrt 3 i}{\sqrt 2(1+i)}\bigg)^n$ is purely imaginary.
isc
class12
modelpaper
2003
part-2
sec-d
q16
q16-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Solve : $(1+y+x^2y)dx+(x+x^3)dy=0$
isc
class12
modelpaper
2003
part-2
sec-d
q16
q16-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Solve : $\large \frac{d^2y}{dx^2}\normalsize =\log x$
isc
class12
modelpaper
2003
part-2
sec-d
q15
q15-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the real values of $x$,$y$ satisfying the equality $\large \frac{x-2+(y-3)i}{1+i}\normalsize=1-3i$
isc
class12
modelpaper
2003
part-2
sec-d
q15
q15-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the locus of a complex number $z=x+iy$ satisfying the relation $\mid12z+3i\mid\geq \mid 2z+5\mid$.Illustrate the locus in the Argand plane.
isc
class12
modelpaper
2003
part-2
sec-d
q14
q14-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Solve : $\large\frac{dy}{dx}=\frac{(1+\cos ^2x)\sin^2y}{(1+\sin^2y)\cos^2x}$
isc
class12
modelpaper
2003
part-2
sec-d
q14
q14-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
The probability that a contractor will get a plumbing contract is $\large\frac{2}{3}$ and an electric contract is $\large\frac{4}{9}$.If the probability of getting at least one contract is $\large\frac{4}{5}$,find the probability that he will get both the contracts.
isc
class12
modelpaper
2003
part-2
sec-c
q13
q13-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Construct the consumer price index number for 1990,taking 1989 as the base year and using simple average of price relative method for the following data :
isc
class12
modelpaper
2003
part-2
sec-c
q12
q12-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Sample of polythene bags from a manufacturer are tested by a buyer for bursting pressure with the following data :
isc
class12
modelpaper
2003
part-2
sec-c
q12
q12-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
A psychologist had a random sample of 22 students.He grouped them into 11 pairs.In each pair,one student was taught by method A and other by method B and were examined after the completion of the course.The marks obtained by them are tabulated below :
isc
class12
modelpaper
2003
part-2
sec-c
q11
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Prove that every element a in Boolean algebra has a unique inverse.
isc
class12
modelpaper
2003
part-2
sec-b
q10
10-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
$x,y$ and $z$ represent three switches in an position and $x^1,y^1$ and $z^1$ represent the three switches in an off position.Construct a switching circuit representing the polynomial $(x^1+y^1)(x+z^1)+y^1(y+z)$.Using the laws of Boolean algebra,show that the above polynomial is equivalent to $x^1z^1+y^1$ and construct an equivalent switching circuit.
isc
class12
modelpaper
2003
part-2
sec-b
q10
q10-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the value of $x$,if $1\ast(x\ast 2)=8$,where the operation $\ast$ is defined by $a\ast b=a+b+\large\frac{ab}{2}\normalsize,\forall a,b,\in R$.
isc
class12
modelpaper
2003
part-2
sec-b
q9
q9-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
A set $S=\{x : x\in R,x\neq -2 \}$ is given.A binary operation $ \ast $ on S is defined by $a \ast b=a+b+\large\frac{ab}{2}\normalsize,\forall a,b,\in R$.Prove that $(S,\ast)$ is an abelian group.
isc
class12
modelpaper
2003
part-2
sec-b
q9
q9-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the volume of the parallelopiped whose three co-terminus edges are represented by the vectors $\hat{i}+\hat{j}+\hat{k},\hat{i}-\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}-\hat{k}$
isc
class12
modelpaper
2003
part-2
sec-b
q8
q8-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
The position vectors of the vertices of a triangle are given as $2\hat{i}-\hat{j}+\hat{k},\hat{i}-3\hat{j}-5\hat{k}$ and $3\hat{i}-4\hat{j}-4\hat{k}$.Prove that it is a right-angled triangle.
isc
class12
modelpaper
2003
part-2
sec-b
q8
q8-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
If $y=e^{m\cos^{-1}x}$,prove that $(1-x^2)\large\frac{d^2y}{dx^2}-\normalsize x\large\frac{dy}{dx}\normalsize=m^2y.$
isc
class12
modelpaper
2003
part-2
sec-a
q7
q7-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Show that the area included between the $x$-axis and the curve $a^2y=x^2(x+a)$ is $\large\frac{a^2}{12}$.
isc
class12
modelpaper
2003
part-2
sec-a
q7
q7-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Three numbers are given whose sum is $180$ and the ratio between first two of them is $1: 2$.If the product of the number is greatest,find the numbers.
isc
class12
modelpaper
2003
part-2
sec-a
q6
asked
Apr 22, 2013
by
sreemathi.v
0
answers
A sphere $x^2+y^2+z^2-3ax-3by-3cz=0$ has a constant radius $3r$.It cuts the axes at the point A,B and C.Show that the centroid of the triangle ABC lies on the sphere $x^2+y^2+z^2=4r^2$
isc
class12
modelpaper
2003
part-2
sec-a
q5
q5-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Show that : $\sin^{-1}\large\frac{4}{5}\normalsize+\cos^{-1}\large\frac{2}{\sqrt 5}\normalsize =\cot^{-1}\large\frac{2}{11}$.
isc
class12
modelpaper
2003
part-2
sec-a
q5
q5-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the equation of the ellipse whose foci are at $(-2,4)$ and $(4,4)$ and whose major and minor axes are 10 and 8 respectively.Also find the eccentricity of the ellipse.
isc
class12
modelpaper
2003
part-2
sec-a
q4
q4-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
If pairs of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair,prove that $pq=-1$.
isc
class12
modelpaper
2003
part-2
sec-a
q4
q4-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Using matrices,solve the following system of equations : $x+2y=5,y+2z=8,2x+z=5$.
isc
class12
modelpaper
2003
part-2
sec-a
q3
q3-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Using properties of determinants,find the value of the following determinant : $\begin{vmatrix}x^3 & x^2 & x\\y^3 & y^2 & y\\z^3 & z^2 & z\end{vmatrix}$.
isc
class12
modelpaper
2003
part-2
sec-a
q3
q3-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Using binomial expansion,calculate the value of $(98)^{\large\frac{1}{2}}$ correct to three places of decimal.
isc
class12
modelpaper
2003
part-2
sec-a
q2
q2-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Prove by the method of mathematical induction that $\large\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+....+\frac{1}{(3n+1)(3n+4)}=\frac{n}{4(3n+4)}$,for all $n\in N$.
isc
class12
modelpaper
2003
part-2
sec-a
q2
q2-a
asked
Apr 22, 2013
by
sreemathi.v
0
answers
If : $\begin{bmatrix}x^2 & 3 & 4\\1 & 9 & 8\end{bmatrix}+\begin{bmatrix}-3x & 1 & -5\\-3 & -2 & -6\end{bmatrix}=\begin{bmatrix}4 & 4 & -1\\-2 & 7 & 2\end{bmatrix}$,find the values of $x$.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-j
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Evaluate : $\int_0^{\large\frac{\pi}{4}}\normalsize (\tan x+\cot x)^{-1}dx.$
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-i
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Using vectors,show that the perpendiculars from the vertices to the opposite sides of the triangle ABC are concurrent.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-h
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Simplify : $(1-\omega)(1-{\omega}^2)(1-{\omega}^2)(1-{\omega}^3)$.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-g
asked
Apr 22, 2013
by
sreemathi.v
0
answers
One number is chosen at random from the numbers 1 to 21.Find the probability that may be a prime number.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-f
asked
Apr 22, 2013
by
sreemathi.v
0
answers
If $y=\tan^{-1}\bigg(\large\frac{2x}{1-x^2}\bigg)$,prove that $\large\frac{dy}{dx}=\frac{2}{1+x^2}$.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-e
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the cosine of the angle between the planes $x+2y-2z+6=0,2x+2y+z+8=0$.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-d
asked
Apr 22, 2013
by
sreemathi.v
0
answers
The equation $y^2-4y-4x+16=0$ represents a parabola.Find its vertex and focus.
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-c
asked
Apr 22, 2013
by
sreemathi.v
0
answers
Find the angle between the straight lines represented by the equation $3x^2-y^2-\sqrt 3x+3y-2=0.$
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-b
asked
Apr 22, 2013
by
sreemathi.v
0
answers
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