Recent questions tagged modelpaper

Show that the differential equation $(x-y) \large\frac{dy}{dx}$$ = x+2y$ is homogenous and solve it

asked Jan 23, 2015 by meena.p

1 answer

Determine the product of $\begin{bmatrix}-4 & 4 & 4\\ -7 & 1 & 3\\ 5 & -3 & -1\end{bmatrix}$ and $\begin{bmatrix}1 & -1 & 1 \\ 1 & -2 & -2\\ 2 & 1 & 3\end{bmatrix}$ Use this product to solve the system of equations $x-y+z=4, x-2y-2z=9$ and $2x+y+3z=1$

asked Jan 23, 2015 by meena.p

1 answer

Using matrix method , solve the following system of linear equations: $5x+y-z=7, 4x-2y-3z=5, 7x+2y+2z=7.$

asked Jan 23, 2015 by meena.p

1 answer

A company produces two types of goods $A$ and $B$ that require gold and silver. Each unit of type $A$ requires $1\; gm$ of silver and $2 \;gm$ of gold. Type $B$ requires(each unit) $2\; gm$ of silver and $1\;gm$ of gold. The company has only $80\; gm$ of gold. Each unit of type A brings profit of $Rs. 500$ and each unit of type $B$ brings profit of $Rs. 400.$ Find the no of units of each type the company should produce to maximize the profit.

asked Jan 23, 2015 by meena.p

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There are $80$ workers in a publication house. Out of which $20$ are hardworking and honest. Three workers are selected at random out of them. Write the probability distribution for the selected workers who are hardworking and honest. Also find the mean of the distribution. Write the importance of hardworking and honesty in one’s life.

asked Jan 23, 2015 by meena.p

1 answer

Differentiate w.r.t x $y= e^{\sin x } +(\tan x) ^x $

asked Jan 23, 2015 by meena.p

1 answer

Show that the lines $\overrightarrow{r} = (\overrightarrow{i} +\overrightarrow{j} - \overrightarrow{k} ) + \lambda (4 \overrightarrow{i} -\overrightarrow{k})+ \mu ( 2 \overrightarrow{i} +3 \overrightarrow{k}) $ intersect. Find their point of intersection.

asked Jan 23, 2015 by meena.p

1 answer

Prove that $tan^{-1} \large\frac{3}{4} $$ + tan^{-1}\large\frac{3}{5} $$+ tan^{-1} \large\frac{8}{19} = \frac{\pi}{4}$

asked Jan 23, 2015 by meena.p

0 answers

Use this to evaluate $\int \limits_0^2 x \sqrt {2-x} dx$

asked Jan 23, 2015 by meena.p

1 answer

Prove that $\int \limits_0^a f(x)dx =\int \limits_0^a f(a-x)dx$

asked Jan 23, 2015 by meena.p

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An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second urn. Find the probability that it is a white ball.

asked Jan 23, 2015 by meena.p

1 answer

Find the equation of the two planes through the points $(4,2,1),(2,1,-1)$ and making angles of $\large\frac{\pi}{4}$ with the plane $x-4y+z-9=0$

asked Jan 23, 2015 by meena.p

1 answer

Find the coordinates of the point where the line passing through the points $(3,4,1)$ and $(5,1,6)$ crosses the xy plane

asked Jan 23, 2015 by meena.p

1 answer

Evaluate $\int \cos 2x \log \sin x dx $

asked Jan 23, 2015 by meena.p

1 answer

Evaluate $\int \large\frac{1+\tan x}{x+ lo \sec x}$

asked Jan 23, 2015 by meena.p

1 answer

Find the angle of intersection of the curves $x^2+4y^2=8$ and $x^2-2y^2=4$

asked Jan 23, 2015 by meena.p

1 answer

Find the equation of the normal to the point of the curve $x^2+2y^2-4x-6y+8=0$ at the point whose abscissa is $2$

asked Jan 23, 2015 by meena.p

1 answer

$f(x) = \left\{ \begin{array} {1 1} 5, & \quad\text{ if x_1 \leq x \leq \sqrt 2 } \\ ax+b ,& \quad \text{if $2x$ < 10 }\\ 21 ,& \quad \text{if $x$ \geq 10 } \end{array} \right. $ Find the values of a and b

asked Jan 23, 2015 by meena.p

1 answer

If $ y = \large\frac {\sqrt{1- \sin x}}{\sqrt{1+\sin x} }$ then show that $ \large\frac{dy}{dx} $$+ \sec^2 \bigg( \large\frac{\pi}{4} $$-x \bigg)=0$

asked Jan 23, 2015 by meena.p

0 answers

Using Rolle’s theorem, find the points on the curve $Y= x^2, x\in [-2,2]$ where the tangent is parallel to the x-axis.

asked Jan 23, 2015 by meena.p

1 answer

A binary operation is defined by $ab = 2^{ab}.$ Determine whether $$ is commutative or associative?

asked Jan 23, 2015 by meena.p

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Using the properties of determinants prove that $\begin{vmatrix} x+y & x & x \\ 5x+4y & 4x & 2x \\10x+8y & 8x & 3x \end{vmatrix}=x^3$

asked Jan 23, 2015 by meena.p

0 answers

Write the degree of the equation, $\sqrt{\large\frac{d^2y}{dx^2}}+y=\sin x$

asked Jan 23, 2015 by meena.p

1 answer

A line makes an angle of $\large\frac{\pi}{4}$ with each of $x$ - axis and $y$ - axis. Find the angle between the line and the $z$ -axis.

asked Jan 23, 2015 by meena.p

1 answer

If $f(x) =a ^x.x^2$, find $f'(x) $

asked Jan 23, 2015 by meena.p

1 answer

Find the domain of the function $f(x) = \sqrt{(9-x^2 )}$

asked Jan 23, 2015 by meena.p

1 answer

What is the value of $tan^{-1} \bigg(cos^{-1}\large\frac{8}{17}\bigg)$ ?

asked Jan 23, 2015 by meena.p

1 answer

For the determinant $\begin{vmatrix}3 & -2 & 1\\4 & 6 & 5\\0 & 1 & 1\end{vmatrix}$ , find the minor $M_{32}$ and cofactor $A_{12}$

asked Jan 23, 2015 by meena.p

1 answer

Find the length and foot of the perpendicular from the point $(1,1,2)$ to the plane $\overrightarrow{r}(\hat i - 2 \hat j + 4 \hat k) +5=0$

asked Jan 21, 2015 by meena.p

1 answer

A dealer wishes to purchase a number of fans and radio. He has only $\$5760$ to invest and has a space for atmost 20 items. A fan costs him $\$360$ and a radio $\$240$. His expectation is this he can sell a fan at a profit of $\$22$ and a radio at a profit of $\$18$ . Assuming that he can sell all the items that he buys, how should be invert his money for maximum profit? Translate the problem as LPP and solve it graphically . What is the importance of electricity in our life .

asked Jan 21, 2015 by meena.p

1 answer

By examining the chest X-ray , the probability that TB is detected when a person is actually suffering is $0.99$ . The probability of an healthy person diagnosed to have TB is $0.001$ . In a certain city, 1 in 1000 people suffer from TB. A person selected at random and is diagnosed to have TB. What is the probability that be action has TB?

asked Jan 21, 2015 by meena.p

1 answer

Find the area enclosed by the curve $y=1x$ and $y= -|x-1|+1$

asked Jan 21, 2015 by meena.p

1 answer

find the area bounded by the lines $y= 4x+5,y=5-x$ and $4y= x+5$

asked Jan 21, 2015 by meena.p

1 answer

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi/2} \large\frac{\cos x}{1+ \cos x+ \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi} \large\frac{x}{1- \cos \alpha \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

The cost of $4kg$ Onion,$3kg$ wheat and $2kg$ rice is $\$60$. The cost of $2\;kg$ onion,$4\;kg$ wheat and $6\;kg$ rice is $\$90$. The cost of $6\;kg$ onion, $2\;kg$ wheat and $3\;kg$ rice is $\$70$. Find the cost of each item per kg by matrix method.

asked Jan 21, 2015 by meena.p

1 answer

If $x \sqrt {1+y} +y\sqrt {1+x}=0$. Then prove that $(1+x)^2 \large\frac{dy}{dx}$$+1=0$

asked Jan 21, 2015 by meena.p

0 answers

A coin is biased , so that head is 3 times as to occur as tail. If the coin is tossed twice. Find the probability distribution of number of tails.

asked Jan 21, 2015 by meena.p

1 answer

In a die game , a player pays a stake of $\$1$ for each throw of a die. She receives $\$5$, if the die shows a 3, $\$2$ if the die shows 1 or 6 and nothing otherwise. What is the player expected profit per throw over a long series of throws?

asked Jan 21, 2015 by meena.p

1 answer

The volume of a cube is increasing at a rate of $9\;cm^2/s$ . How fast is the surface area increasing . When the length of the edge is $10\;cm$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\tan \bigg[\sin^{-1}\bigg(\large\frac{2x}{1+x^2}\bigg)+$$\cos^{-1} \bigg( \large\frac{1-y^2}{1+y^2}\bigg)\bigg]$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\sin (2 \tan ^{-1} \large\frac{1}{3})$$+ \cos(\tan^{-1} 2 \sqrt 2)$

asked Jan 21, 2015 by meena.p

0 answers

Find the inverse of $A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$ by elementary transformation and hence solve the following system of linear equation : $2x+y=3; 4x+2y=6$

asked Jan 21, 2015 by meena.p

1 answer

If $f(x) = \left\{ \begin{array} {1 1} 1 & \quad, \text{ if $ x \leq$ 3 }\\ ax+b & \quad, \text{if $3 < x < 5$ } \\ 7 & \quad, \text{ if $ 5 \leq x $ } \end{array} \right.$ Determine the values if a and b so that $f(x)$ is continuous?

asked Jan 21, 2015 by meena.p

1 answer

If $ f(x) = \left\{ \begin{array} {1 1} \large\frac{ 2^{x+2}-16}{4^x-16}, & \quad\text{ if $x \neq 2$ } \end{array} \right. $ is a continuous at $x=2,$ then find k ?

asked Jan 21, 2015 by meena.p

1 answer

$\begin{align} \int \limits_{\large\frac{\pi}{3}}^{\large\frac{\pi}{2}}\frac{\sqrt {1+\cos x}}{(1- \cos x)^{5/2}}dx \end{align}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $ \int \large\frac{dx}{(x-1)\sqrt {2x+3}}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate = $\int \large\frac{x^2}{(x \sin x +\cos x)^2}$

asked Jan 21, 2015 by meena.p

1 answer

Solve the differential equation : $(x+2y^2) \large\frac{dy}{dx}$$=y$, given that when $x=2$ and $y=1$. If x devotes the percentage of who are intelligent and y denotes the percentage of people who are work holic, find x when $y=2 \%$ workoholics are always preferable. Do you agree ?

asked Jan 21, 2015 by meena.p

1 answer

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