Recent questions tagged modelpaper

One number is chosen at random from the numbers 1 to 21.Find the probability that may be a prime number.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $y=\tan^{-1}\bigg(\large\frac{2x}{1-x^2}\bigg)$,prove that $\large\frac{dy}{dx}=\frac{2}{1+x^2}$.

asked Apr 22, 2013 by sreemathi.v

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Find the cosine of the angle between the planes $x+2y-2z+6=0,2x+2y+z+8=0$.

asked Apr 22, 2013 by sreemathi.v

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The equation $y^2-4y-4x+16=0$ represents a parabola.Find its vertex and focus.

asked Apr 22, 2013 by sreemathi.v

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Find the angle between the straight lines represented by the equation $3x^2-y^2-\sqrt 3x+3y-2=0.$

asked Apr 22, 2013 by sreemathi.v

0 answers

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$ out of $1000$ taxi drivers find approximately the number of driver with more than $3$ accidents in a year $[e^{-3}=0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$. Out of $1000$ taxi drivers find approximately the number of driver with no accident in a year .$[e^{-3} = 0.0498].$

asked Apr 21, 2013 by poojasapani_1

1 answer

The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting at most two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously.what is the probability of getting at least two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting exactly $2$ heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \alpha e^{-\alpha x} ,& \quad \text{if $x$$>$$0$}\\ 0 ,& \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} \frac {1}{24} ,& \quad \text{-12$\leq$$ x$$\leq $$12$}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

The probability distribution of a random variable $x$ is given below: \[\] $\begin{array} {llllllll} \textbf{X:}& 0& 1& 2& 3 \\ \textbf{P(X=x):}& 0.1& 0.3 &0.5& 0.1& \end{array}$\[\] If $Y=X^{2}+2X$ find the mean and variance of $Y$.

asked Apr 20, 2013 by poojasapani_1

1 answer

In an entrance examination a student has to answer all the $120$ questions. Each question has four options and only one option is correct. A student gets $1$ mark for a correct answer and loses half mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?

asked Apr 20, 2013 by poojasapani_1

1 answer

Find the middle term in the binomial expansion of $\begin{pmatrix}\large\frac{x^2}{4}-\frac{4}{x^2}\end{pmatrix}^{10}$

asked Apr 19, 2013 by sreemathi.v

0 answers

If $x\;=\cos\;\alpha +i\sin\;\alpha\;;\; y\;= \cos\;\beta + i\sin \;\beta $ prove that $x^{m}y^{n} \;+\large \frac{1}{x^{m}y^{n}}$$= \;2\cos \;\left ( m\alpha + n\beta \right )$

asked Apr 19, 2013 by geethradh

1 answer

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

asked Apr 19, 2013 by sreemathi.v

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

asked Apr 19, 2013 by sreemathi.v

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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

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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

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

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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

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

asked Apr 19, 2013 by sreemathi.v

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Write the Boolean expression for the following circuit :

asked Apr 19, 2013 by sreemathi.v

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Prove the right cancellation law in a group.

asked Apr 19, 2013 by sreemathi.v

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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

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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

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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

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

asked Apr 19, 2013 by sreemathi.v

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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

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 $A=\begin{pmatrix}3 & -4\\1 & -1\end{pmatrix}$,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

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