Recent questions tagged medium

The equation of normal to the curve $3x^2-y^2=8$ which is parallel to the line x+3y=8 is\begin{array}{1 1}(A)\;3x-y=8 & (B)\;3x+y+8=0\\(C)\;x+3y-8=0 & (D)\;x+3y=0\end{array}

asked Jan 11, 2013 by sreemathi.v

1 answer

A ladder, 5 meter long,standing on a horizontal floor,leans against a vertical wall.If the top of the ladder slides downwards at the rate of 10cm/sec,then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 meters from the wall measure in "radian/seconds" is?

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the dimentions of the rectangle of perimeter 36cm which will sweep out a volume as large as possible,when revolved about one of its sides.Also find the maximum volume.

asked Jan 11, 2013 by sreemathi.v

1 answer

An open box with square base is to be made of a given quantity of card board of area $ c^2$.Show that the maximum volume of the box is $\Large \frac{c^3}{6\sqrt 3}$ cubic units.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the points of local maxima,local minima and the points of inflection of the function $f(x)=x^5-5x^4+5x^3-1$. Also find the corresponding local maximum and local minimum values.

asked Jan 11, 2013 by sreemathi.v

1 answer

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\Large \frac{1}{3}$

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that for a$\quad 1,f(x)=\sqrt 3\sin x-\cos x-2ax+b$ is decreasing in R.

asked Jan 11, 2013 by sreemathi.v

1 answer

Show that the line $\Large \frac{x}{a}+\frac{y}{b}\normalsize=1$,touches the curve $y=b.e^{\Large \frac{-x}{a}}$ at the point where the curve intersects the axis of y.

asked Jan 11, 2013 by sreemathi.v

1 answer

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

asked Jan 11, 2013 by sreemathi.v

1 answer

Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $xy=4$ and $x^2+y^2=8$ touch each other.

asked Jan 11, 2013 by sreemathi.v

1 answer

The volume of a cube increases at a constant rate.Prove that the increase in its surface area varies inversely as the length of the side.

asked Jan 11, 2013 by sreemathi.v

1 answer

A swimming pool is to be drained for cleaning .If L represents the number of litres of water in the pool seconds after the pool has been plugged off to drain and $L=200(10-t)^2$.How fast is the water running out at the end of 5 seconds?What is the average rate at which the water flows out during the first 5 seconds?

asked Jan 11, 2013 by sreemathi.v

1 answer

A kite is moving horizontally at a height of 151.5 meters If the speed of kite is 10m/s,how fast is the string being let out,when the kite is 250m away from the boy who is flying the kite?The height of boy is 1.5m

asked Jan 10, 2013 by sreemathi.v

1 answer

Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix} $ is a symmetric matrix.

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Two cards are drawn successively without replacement from a well shuffled deck of cards.Find the mean and standard variation of the random variable X where X is the number of aces.

asked Jan 9, 2013 by sreemathi.v

1 answer

A bag contains (2n+1) coins.It is known that n of these coins have a head on both sides where as the rest of the coins are fair.A coin is picked up at random from the bag and is tossed.If the probability that the toss results in a head is $\Large \frac{31}{42}$,determine the value of n.

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability distribution of a discrete random variable X is given as under:

asked Jan 9, 2013 by sreemathi.v

1 answer

An item is manufactured by three machines A,B and C.Out of the total number of items manufactured during a specified period,50% are manufactured on A,30% on B and 20% on C.2% of the items produced on A and 2% of items produced on B are defective,and 3% of these produced on C are defective.All the items are stored at one godown.One item is drawn at random and is found to be defective.What is the probability that it was manufactured on machine A?

asked Jan 9, 2013 by sreemathi.v

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 suffers from TB.A person is selected at random and is diagnosed to have TB.What is the probability that he actually has TB?

asked Jan 9, 2013 by sreemathi.v

1 answer

There are three urns containing 2 white and 3 black balls,3 white and 2 black balls,and 4 white and 1 black balls,respectively.There is an equal probability of each urn being chosen.A ball is drawn at random from the chosen urn and it is found to be white.find the probability that the ball drawn was from the second urn.

asked Jan 9, 2013 by sreemathi.v

1 answer

Three bags contain a number of red and white balls as follows:

asked Jan 9, 2013 by sreemathi.v

1 answer

Find the probability distribution of the maximum of two scores obtained when a die is thrown twice .Determine also the mean of the distribution.

asked Jan 9, 2013 by sreemathi.v

1 answer

Suppose you have two coins which appear identical in your pocket.you know that one is fair and one is 2 headed.If you take one out,toss it and get a head,what is the probability that it was a fair coin?

asked Jan 9, 2013 by sreemathi.v

1 answer

Prove that $ \begin{bmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{bmatrix} = (5x+4)(4-x)^2. $

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Maximise $Z=x+y$.Subject to $x+4y\leq 8,2x+3y\leq 12,3x+y\leq 9,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Determine the maximum distance that the man can travel.

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The angle between the line $\overrightarrow{r}=(5\hat i-\hat j-\hat k)+\lambda(2\hat i-\hat j\;+\hat k)$ and the plane $\overrightarrow{r}.(3\hat i-4\hat j-\hat k)-5=0$ is $\sin^{-1}\large \frac{5}{2\sqrt 91}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

The plane 2x-3y+6z-11=0 makes an angle $\sin^{-1}(\alpha)$ with x-axis.The value of $\alpha$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

The area of the quadilateral $ABCD$ where $A(0,4,1),B(2,3,-1),C(4,5,0)$ and $D(2,6,2)$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

Distance of the point $(\alpha,\beta,\gamma)$ from y-axis is

asked Jan 4, 2013 by sreemathi.v

1 answer

Show that the points $ (\hat i-\hat j+3 \hat k)\; and\;3(\hat i+\hat j+\hat k)$ are equidistant from the plane $ \overrightarrow{r}.(5 \hat i+2 \hat j-7 \hat k)+9=0$ and lies on opposite side of it.

asked Jan 4, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the intersection of the planes $ \overrightarrow{r}.\quad(\hat i+3 \hat j)-6=0\; and\;\overrightarrow{r}.(3\hat i-\hat j-4 \hat k)=0,$ whose perpendicular distance from origin is unity.

asked Jan 4, 2013 by sreemathi.v

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} 3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{bmatrix} = 3(a + b + c)(ab+bc+ca) $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane which is perpendicular to the plane $5x+3y+6z+8=0$ and which contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the length and the foot of perpendicular from the point$\bigg(1,\large\frac{3}{2}$$,2\bigg)$ to the plane 2x-2y+4z+5=0

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the distance of a point(2,4,-1) from the line $\large \frac{x-5}{1}\;=\frac{y-3}{4}\;=\frac{z-6}{-9}$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the foot of perpendicular from the point(2,3,-8)to the line $\Large \frac{4-x}{2}\;=\frac{y}{6}\;=\frac{1-z}{3}$.Also,find the perpendicular distance from the given point to the line.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

asked Jan 3, 2013 by sreemathi.v

1 answer

The derivative of $\cos^{-1}(2x^2-1)$ w.r.t $\cos^{-1}x$ is

asked Jan 3, 2013 by sreemathi.v

1 answer

If $y=\sqrt{sin x+y}$, then $\Large \frac{dy}{dx}$ is equal to

asked Jan 3, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx},\normalsize if\;y=\large x^{tan x}+\sqrt{\large\frac{x^2+1}{2}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x^my^n=(x+y)^{m+n}$,Prove that $(i)\;\large\frac{dy}{dx}=\frac{y}{x}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the values of p and q so that $f(x)=\left \{\begin{array}{1 1}x^2+3x+p, & if \;x\leq\;1\\qx+2, & if\;x>\;1\end{array}\right.$is differentiable at $x=1.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using mean value theorem,prove that there is a point on the curve $y=2x^2-5x+3$ between the points $A(1,0)$ and $B(2,1)$where tangent is parallel to chord $AB$. Also find the point.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find a point on the curve $y=(x-3)^2$,where the tangent is parallel to the chord joining the point (3,0) and (4,1).

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sqrt {25-x^2}\;in\;[1,5].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sin x-\sin 2x\;in\;[0,\pi].$

asked Jan 2, 2013 by sreemathi.v

1 answer

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