Recent questions tagged modelpaper

Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{\pi}{6}}^{\large\frac{\pi}{3}}\large\frac{dx}{1+\sqrt{\tan x}}$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{0}^{3}\large\frac{\sqrt{x}dx}{\sqrt{x}+\sqrt{3-x}}$

asked Apr 27, 2013 by poojasapani_1

1 answer

Using Euler's theorem prove the following: if$\;u=\tan^{-1}\large[\frac{x^{3}+y^{3}}{x-y}]$ prove that $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}=$$\sin 2u$

asked Apr 26, 2013 by poojasapani_1

1 answer

Find $\large\frac{\partial w}{\partial u}$ and $\large\frac{\partial w}{\partial v}$ if$\;w=x^{2}+y^{2}$ where $x=u^{2}-v^{2},y=2uv$

asked Apr 26, 2013 by poojasapani_1

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following:$\;w=\large(\frac{x}{x^{2}+y^{2}})$ where $x=\cos t,y=\sin t.$

asked Apr 25, 2013 by poojasapani_1

1 answer

Varify $\large\frac{\partial^{2} y}{\partial x\partial y}=\frac{\partial^{2} y}{\partial y\partial x}$ for the following function;$\;u=\tan^{-1}\large(\frac{x}{y})$

asked Apr 25, 2013 by poojasapani_1

1 answer

Use differentials to find an approximate value for the given numbers $\sqrt{36.1}$

asked Apr 24, 2013 by poojasapani_1

1 answer

Trace the curve $y$=$x^{3}$ Discuss the following curves for extence,symmetry,Asymptotes and loops

asked Apr 24, 2013 by poojasapani_1

1 answer

Find$C$. $\mu$ and $c^{2}$ of the normal distribution whose probability function is given by $f{x}$=$C$$e^{\large -x^2+3x}$$,-\infty<$X$<\infty$.

asked Apr 23, 2013 by poojasapani_1

1 answer

Marks in an aptitude test given to $800$ students of a school was found to be normally distributed. $10\%$ of the students scored below $40$ marks and $10\%$ of the students scored above $90$ marks. Find the number of students scored between $40$ and $90$.

asked Apr 23, 2013 by poojasapani_1

1 answer

The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh more than $185$ pounds

asked Apr 22, 2013 by poojasapani_1

1 answer

The mean weight of $500 $ male students in a certain college in $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find how many students weigh between $120$ and $155$ pounds

asked Apr 22, 2013 by poojasapani_1

1 answer

Suppose that the amount of cosmic radiation to which a person is exposed when flying by jet across the united states is a random variable having a normal distribution with a mean of $4.35 m$ rem and standard deviation of $0.59m$ rem. What is the probability that a person will be exposed to than $5.20m$ rem of cosmic radiation of such flight.

asked Apr 22, 2013 by poojasapani_1

1 answer

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing.$P(85\leq$X$\leq$95$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

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

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilites by standardizing. $P(70$$<$X$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing. $P(65\leq$X$\leq$100$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

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

asked Apr 22, 2013 by sreemathi.v

0 answers

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing.$P(X\leq$80$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilities by standardizing. $P(X\leq$100$)$

asked Apr 22, 2013 by poojasapani_1

1 answer

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

asked Apr 22, 2013 by sreemathi.v

0 answers

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

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

If : $\begin{bmatrix}x^2 & 3 & 4\\1 & 9 & 8\end{bmatrix}+\begin{bmatrix}-3x & 1 & -5\\-3 & -2 & -6\end{bmatrix}=\begin{bmatrix}4 & 4 & -1\\-2 & 7 & 2\end{bmatrix}$,find the values of $x$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Evaluate : $\int_0^{\large\frac{\pi}{4}}\normalsize (\tan x+\cot x)^{-1}dx.$

asked Apr 22, 2013 by sreemathi.v

0 answers

Using vectors,show that the perpendiculars from the vertices to the opposite sides of the triangle ABC are concurrent.

asked Apr 22, 2013 by sreemathi.v

0 answers

Simplify : $(1-\omega)(1-{\omega}^2)(1-{\omega}^2)(1-{\omega}^3)$.

asked Apr 22, 2013 by sreemathi.v

0 answers

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