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Recent questions tagged part-2
ASK
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
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
The mathematical aptitude score (MAS) of ten computer programmers with job performance rating (JPR) is given below.Calculate Spearman's rating of rank correlation and state whether those who have aptitude for maths are likely to be better programmers.
isc
class12
modelpaper
2004
part-2
sec-c
q11
asked
Apr 19, 2013
by
sreemathi.v
0
answers
If a,b,c are elements of Boolean Algebra,prove that $ab+c(a'+b')=ab+c$.
isc
class12
modelpaper
2004
part-2
sec-b
q10
q10-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Write the Boolean expression for the following circuit :
isc
class12
modelpaper
2004
part-2
sec-b
q10
q10-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Prove the right cancellation law in a group.
isc
class12
modelpaper
2004
part-2
sec-b
q9
q9-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Consider the non empty set S={0,1,2,3,4}.Show that $(S,\oplus_5)$ is a group where $\oplus_5$ represents addition modulo 5.Also find 'x' if $x\oplus_5$ 3=4,$x\in S$.
isc
class12
modelpaper
2004
part-2
sec-b
q9
q9-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Find the unit vector perpendicular to the two vectors $\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$ and $2\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$.
isc
class12
modelpaper
2004
part-2
sec-b
q8
q8-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Show that the sum of the squares on the sides a parallelogram is equal to the sum of the squares on the diagonals of the parallelogram.
isc
class12
modelpaper
2004
part-2
sec-b
q8
q8-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
If $x=\sin^3t$ and $y=a\cos^3t$,find $\large\frac{dy}{dx}$.
isc
class12
modelpaper
2004
part-2
sec-a
q7
q7-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Sketch and shade the area of the region lying in the first quadrant and bound by $y=9x^2,x=0,y=1$ and $y=4$.Find the area of the shaded region.
isc
class12
modelpaper
2004
part-2
sec-a
q7
q7-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
A closed circular cylinder has a volume of 2156c.c.What will be the radius of its base so that its total surface area is minimum.Find the height of the cylinder when its total surface area is minimum.
isc
class12
modelpaper
2004
part-2
sec-a
q6
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Evaluate :$\Large \int_{\normalsize 0}^{\large \frac{1}{2}} \large \frac{\sin^{-1}x}{(1-x^2)^\frac{3}{2}}$$dx$
isc
class12
modelpaper
2004
part-2
sec-a
q5
q5-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
show that the function $f(x)=x^2-6x+1$ satisfies the Lagrange's Mean value Theoem.Also find the co-ordinate of a point at which the tangent to the curve represented by the above function is parallel to the chord joining A(1,-4) and B(3,-8).
isc
class12
modelpaper
2004
part-2
sec-a
q5
q5-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
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