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Math
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Math
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Physics
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Recent questions in ISC XII Math
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ISC XII Math
ISC XII Math
Model Papers
Questions from: ISC XII Math
Two lines of regression are given by x+2y-5=0, 2x+3y-8=0 and σ2x("sigma squared"x)=12, Calculate the mean value of x and y, variable of Y and the coefficient of correlation between x and y.
asked
Jul 6, 2015
by
sahunitinkumar68
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
asked
Jul 6, 2015
by
sahunitinkumar68
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
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
asked
Apr 22, 2013
by
sreemathi.v
1
answer
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
Find the middle term in the binomial expansion of $\begin{pmatrix}\large\frac{x^2}{4}-\frac{4}{x^2}\end{pmatrix}^{10}$
isc
class12
modelpaper
2003
part-1
sec-a
q1
q1-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Solve the differential equation $\large\frac{d^2y}{dx^2}\normalsize=\sin 2x$
isc
class12
modelpaper
2004
part-2
sec-d
q16
q16-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Using DeMoivre's theorem find the value of $(2-2i)^{\large\frac{1}{3}}$.
isc
class12
modelpaper
2004
part-2
sec-d
q16
16-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Solve the differential equation $(1-x^2)\large\frac{dy}{dx}\normalsize-xy=x$. Given $y=2$ when $x=0$.
isc
class12
modelpaper
2004
part-2
sec-d
q15
q15-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Given $z=x+iy$ and $z_1=1+2i$ determine the region in the complex plane represented by $I<\mid z-z_1\mid\leq 3$.Represent it on the Argand plane.
isc
class12
modelpaper
2004
part-2
sec-d
q15
q15-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
If $z=x+iy$ and $\mid 2z+1\mid=\mid z-2i\mid$ show that $3(x^2+y^2)+4(x+y)=3.$
isc
class12
modelpaper
2004
part-2
sec-d
q14
q14-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Solve the differential equation $2\large\frac{dy}{dx}\normalsize=\large\frac{y}{x}\normalsize+\large\frac{y^2}{x^2}$ by substituting $y=vx$.
isc
class12
modelpaper
2004
part-2
sec-d
q14
q14-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
A bag has 4 red and 5 black balls,a second bag has 3 red and 7 black balls.One ball is drawn from the first bag and two from the second.Find the probability that two balls are black and one is red.
isc
class12
modelpaper
2004
part-2
sec-c
q13
q13-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
A dice is tossed three times.Getting a '3' or a '5' is considered a success.Find the probability of at least two successes.
isc
class12
modelpaper
2004
part-2
sec-c
q13
q13-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Calculate the lower $(Q_1$) and upper $(Q_3)$ quartiles for the following distribution :
isc
class12
modelpaper
2004
part-2
sec-c
q12
q12-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
The number of letters in hundreds received in a town on each day of a fortnight is given below :
isc
class12
modelpaper
2004
part-2
sec-c
q12
q12-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
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