Recent questions tagged class12

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

A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(\large\frac{\pi}{2}<x<\frac{3\pi}{2})$

asked Apr 19, 2013 by poojasapani_1

1 answer

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 random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(0<x<\large\frac{\pi}{2})$

asked Apr 19, 2013 by poojasapani_1

1 answer

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 random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{1 1} k & \quad 0 < x < 2n \\ 0 & \quad \text{else where} \end{array} \right.$ Find $k$

asked Apr 19, 2013 by poojasapani_1

1 answer

A continuous random variable $x$ has the p.d.f defined by $f(x) = \left\{ \begin{array}{1 1} ce^{-ax} & \quad 0 < x < \infty \\ 0 & \quad \text{else where} \end{array} \right.$ Find the value of $c$ if $a>0$

asked Apr 19, 2013 by poojasapani_1

1 answer

If $x+\large\frac{1}{x}$$ =2\cos\;\theta $ and $y+\large\frac{1}{y}=$$2 \cos \;\phi$ show that $\large\frac{x^{m}}{y^{n}}+ \frac{y^{n}}{x^{m}} $$= 2 \cos \left ( m\theta -n\phi \right )$

asked Apr 19, 2013 by geethradh

1 answer

For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate $p(x>0.75)$

asked Apr 19, 2013 by poojasapani_1

1 answer

For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate $p(x\leq0.5)$

asked Apr 19, 2013 by poojasapani_1

1 answer

For the distribution function given by $f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{$0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$\[\] Find the density function. Also evaluate p(0.5< x <0.75)

asked Apr 19, 2013 by poojasapani_1

1 answer

The probability density function of a random variable $x$ is $f(x) = \left\{ \begin{array}{l l} kx^{\alpha-1}e^{-\beta\;x^{\alpha}}, & \quad \text{x,$\alpha$$,\beta$>$0$}\\ 0 ,& \quad \text{elsewhere} \end{array} \right.$, Find $p(x$>$10)$

asked Apr 19, 2013 by poojasapani_1

1 answer

If $\large\overrightarrow a\:and\:\overrightarrow b$ are unit vectors then prove that $ \large\frac{1}{2}|\overrightarrow a-\overrightarrow b|=sin\frac{\theta}{2}.$

asked Apr 19, 2013 by rvidyagovindarajan_1

1 answer

The probability density function of a random variable $x$ is $f(x) = \left\{ \begin{array}{l l} kx^{\alpha-1}e^{-\beta\;x^{\alpha}}, & \quad \text{x,$\alpha$$,\beta$>$0$}\\ 0 ,& \quad \text{elsewhere} \end{array} \right.$ \[\] Find $k$

asked Apr 19, 2013 by poojasapani_1

1 answer

For the p.d.f $f(x) = \left\{ \begin{array}{l l} cx(1-x)^{3}, & \quad \text{0 $<$ x$<$1}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ \[\]Find $p(x<\large\frac{1}{2})$

asked Apr 19, 2013 by poojasapani_1

1 answer

For the p.d.f $f(x) = \left\{ \begin{array}{l l} cx(1-x)^{3}, & \quad \text{0 $<$ x$<$1}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ \[\]Find the constant $c$

asked Apr 19, 2013 by poojasapani_1

1 answer

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

A discrete random variable $x$ has the following probability distribution. Find the value of $a$ \[\] $\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

0 answers

A discrete random variable $x$ has the following probability distributioxs.Find $p(x<3)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

1 answer

A discrete random variable $x$ has the following probability distributioxs. Find$ p(3$$<$$x$$<$$7)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

1 answer

If $x +\large\frac{1}{x} = $$2\; cos\;\theta $ prove that $x^{n} -\large \frac{1}{x^{n}}= $$2i\; sin\;n\theta $

asked Apr 18, 2013 by geethradh

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

Find the equation of a plane through the point (-1,-1,2) and perpendicular to the planes $3x+2y-3z=1$ and $5x-4y+z=5.$

asked Apr 18, 2013 by sreemathi.v

0 answers

Find the radius of the circular section of the sphere $x^2+y^2+z^2=49$ cut by a plane $2x+3y-z-5\sqrt{14}=0.$

asked Apr 18, 2013 by sreemathi.v

0 answers

Find the equation of a pair of straight lines represented by $8x^2+8xy+2y^2+26x+13y+5=0$ and show that the angle between them is $0^{\circ}$.

asked Apr 18, 2013 by sreemathi.v

0 answers

If $\; x+\large\frac{1}{x}= $$\;2\;\cos\;\theta \; $ prove that $\;x^{n}+\large\frac{1}{x^{n}}$$= \;2\;\cos\;n\theta\; $

asked Apr 18, 2013 by geethradh

1 answer

If $A=\begin{pmatrix}3 & -4\\1 & -1\end{pmatrix}$,show by mathematical induction that for any positive integer n, $A^n=\begin{pmatrix}1+2n&-4n\\n &1-2n\end{pmatrix}$

asked Apr 18, 2013 by sreemathi.v

0 answers

If $ \alpha$ and $\beta $ are the roots of $x^{2}-2x+4=0$. Prove that $\alpha ^{n}-\beta ^{n}=i2^{n+1}sin\large\frac{n\pi }{3}$ and calculate $\alpha ^{9}-\beta ^{9}$, where n $\in$ N?

asked Apr 18, 2013 by geethradh

1 answer

If $\alpha $ and $\beta$ are the roots of the equation $ x^{2}-2px+\left ( p^{2} + q^{2}\right )=0 $ and $ tan \; \theta =\large \frac{q}{y+p} $ show that $ \large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $ q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$

asked Apr 18, 2013 by geethradh

1 answer

Let $X$ be a random variable whose possible values $x_1, x_2, ..., x_n$ occur with probabilities $p(x_1), p(x_2), ..., p(x_n)$ respectively. Then if $\mu$ is the mean of $X$, what is the standard deviation of $X$?

asked Apr 18, 2013 by balaji.thirumalai

1 answer

A random variable X taking values 0, 1, 2, ..., n is said to have a binomial distribution with parameters n and p, if its probability distibution is given by what?

asked Apr 18, 2013 by balaji.thirumalai

1 answer

Verify that the following are probability density functions.$f(x)=\large\frac{1}{\pi}\frac{1}{(1+x^{2})'}$$-\infty$$<$$x$$<\infty $

asked Apr 18, 2013 by poojasapani_1

1 answer

According to Bayes Theorem, if $E_1, E_2, E_3.....E_n$ are a set of mutually exclusive and exhaustive events, then what is P$\large (\frac{E_i}{E})$?

asked Apr 18, 2013 by balaji.thirumalai

1 answer

Verify that the following are probability density functions.$f(x) = \left\{ \begin{array}{l l} \frac { 2x}{9} & \quad \text{0 $\leq$ x$\leq$3}\\ 0 & \quad \text{elsewhere} \end{array} \right.$

asked Apr 18, 2013 by poojasapani_1

1 answer

If n is the number of distinct elements in a sample space and m is the number of outcomes favorable to an event E, then express P(E') in terms of m and n.

asked Apr 18, 2013 by balaji.thirumalai

1 answer

Ask Questions, Get Answers