Recent questions tagged part-2

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.

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve : $(1+y+x^2y)dx+(x+x^3)dy=0$

asked Apr 22, 2013 by sreemathi.v

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Solve : $\large \frac{d^2y}{dx^2}\normalsize =\log x$

asked Apr 22, 2013 by sreemathi.v

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Find the real values of $x$,$y$ satisfying the equality $\large \frac{x-2+(y-3)i}{1+i}\normalsize=1-3i$

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.

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve : $\large\frac{dy}{dx}=\frac{(1+\cos ^2x)\sin^2y}{(1+\sin^2y)\cos^2x}$

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.

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.

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 :

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 :

asked Apr 22, 2013 by sreemathi.v

1 answer

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 :

asked Apr 22, 2013 by sreemathi.v

0 answers

Prove that every element a in Boolean algebra has a unique inverse.

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.

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 $a\ast b=a+b+\large\frac{ab}{2}\normalsize,\forall a,b,\in R$.

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.

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 $\hat{i}+2\hat{j}-\hat{k}$

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.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $y=e^{m\cos^{-1}x}$,prove that $(1-x^2)\large\frac{d^2y}{dx^2}-\normalsize x\large\frac{dy}{dx}\normalsize=m^2y.$

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 $\large\frac{a^2}{12}$.

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.

asked Apr 22, 2013 by sreemathi.v

1 answer

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 $x^2+y^2+z^2=4r^2$

asked Apr 22, 2013 by sreemathi.v

0 answers

Show that : $\sin^{-1}\large\frac{4}{5}\normalsize+\cos^{-1}\large\frac{2}{\sqrt 5}\normalsize =\cot^{-1}\large\frac{2}{11}$.

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.

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 $pq=-1$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Using matrices,solve the following system of equations : $x+2y=5,y+2z=8,2x+z=5$.

asked Apr 22, 2013 by sreemathi.v

2 answers

Using properties of determinants,find the value of the following determinant : $\begin{vmatrix}x^3 & x^2 & x\\y^3 & y^2 & y\\z^3 & z^2 & z\end{vmatrix}$.

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.

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 $n\in N$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve the differential equation $\large\frac{d^2y}{dx^2}\normalsize=\sin 2x$

asked Apr 19, 2013 by sreemathi.v

0 answers

Using DeMoivre's theorem find the value of $(2-2i)^{\large\frac{1}{3}}$.

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 $x=0$.

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.

asked Apr 19, 2013 by sreemathi.v

0 answers

If $z=x+iy$ and $\mid 2z+1\mid=\mid z-2i\mid$ show that $3(x^2+y^2)+4(x+y)=3.$

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 $y=vx$.

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.

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.

asked Apr 19, 2013 by sreemathi.v

1 answer

Calculate the lower $(Q_1$) and upper $(Q_3)$ quartiles for the following distribution :

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 :

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.

asked Apr 19, 2013 by sreemathi.v

0 answers

If a,b,c are elements of Boolean Algebra,prove that $ab+c(a'+b')=ab+c$.

asked Apr 19, 2013 by sreemathi.v

0 answers

Write the Boolean expression for the following circuit :

asked Apr 19, 2013 by sreemathi.v

0 answers

Prove the right cancellation law in a group.

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,$x\in S$.

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 $2\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$.

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.

asked Apr 19, 2013 by sreemathi.v

0 answers

If $x=\sin^3t$ and $y=a\cos^3t$,find $\large\frac{dy}{dx}$.

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.

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.

asked Apr 19, 2013 by sreemathi.v

1 answer

Evaluate :$\Large \int_{\normalsize 0}^{\large \frac{1}{2}} \large \frac{\sin^{-1}x}{(1-x^2)^\frac{3}{2}}$$dx$

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).

asked Apr 18, 2013 by sreemathi.v

1 answer

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