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Recent questions tagged q9-a

Four candidates A,B,C,D have applied for the assignment to coach a school cricket team.If A is twice as likely to be selected as B,and B and C are given about the same chance of being selected,while C is twice as likely to be selected as D,what are the probabilities that C will be selected?

asked Jul 7, 2014 by sreemathi.v

1 answer

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

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

Using Demoivre's theorem,find the least value of $n\in N$ for which the expression $(i+1)^n+(1-i)^n$ is equal to $-2^{\large\frac{n+2}{2}}$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the cube roots of -27 and show that the sum of the cube roots is equal to zero.

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that $(1+i\sqrt 3)^8+(1-i\sqrt 3)^8=-2^8$ by using De Moiver's Theorem.

asked Apr 16, 2013 by sreemathi.v

0 answers

If the ratio $\large\frac{z-i}{z-1}$ is purely imaginary,prove that the point $z$ lies on the circle whose centre is the point $\large\frac{1}{2}\normalsize(1+i)$ and radius is $\large\frac{1}{\sqrt 2}$.

asked Apr 15, 2013 by sreemathi.v

0 answers

If $z=\large\frac{13-5i}{4-9i}$,prove by using De Moivre's theorem that $z^6=-8i$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Solve the differential equation : $(y+\log x)dx-xdy=0$,given that $y=0$,when $x=1$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Using De moivre's theorem,find the value of : $(1+i\sqrt 3)^6+(1-i\sqrt 3)^6$

asked Apr 11, 2013 by sreemathi.v

0 answers

Using De Moivre's theorem prove that : $\bigg(\large \frac{1+cos\; \theta+isin\;\theta}{1+cos\; \theta-i sin\;\theta}\bigg)^n\normalsize$$ =cos \;n\theta+i \sin n\theta,$where $i=\sqrt {-1}.$

asked Apr 10, 2013 by sreemathi.v

0 answers

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