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Recent questions tagged 2011

If $ y =\large\frac{\log_{\Large e}x}{x}$ and $z= \log_ ex,$ then $\large\frac{d^2y}{dz^2}+\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

1 answer

If $f(x) =|x|+ | \sin x|$ for $x \in \bigg(-\large\frac{\pi}{2},\frac{\pi}{2}\bigg),$ then its left hand derivative at $x=0$ is

asked Sep 20, 2013 by meena.p

1 answer

If $\cos^{-1}\bigg(\large\frac{x^2-y^2}{x^2+y^2}\bigg)=k$ (a constant ), then $\large\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

1 answer

If $y=(1+x)(1+x^2)(1+x^4)........(1+x^{2^{n}}),$ then $\bigg(\large\frac{dy}{dx}\bigg)_{x =0}=$

asked Sep 20, 2013 by meena.p

1 answer

If [x] denotes the greatest integer not exceeding x and if the function f defined by \[f(x) = \left\{ \begin{array}{l l} \frac{a+2 \cos x}{x^2} & \quad ( x < 0) \\ b\;\tan \frac{\pi}{[x+4]} & \quad (x \geq 0) \end{array} \right. \] is continuous at $x=0,$ then the ordered pair $(a,b)=$

asked Sep 20, 2013 by meena.p

1 answer

$\lim\limits_{x \to 8} \large\frac{\sqrt {1+\sqrt {1+x}}-2}{x-8}=$

asked Sep 19, 2013 by meena.p

1 answer

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

asked Jul 14, 2013 by sreemathi.v

1 answer

The profit of a soft drink firm (in thousands of rupees) during each month of the year is as given below :

asked Apr 11, 2013 by sreemathi.v

0 answers

The price quotations of four different commodities for 2001 and 2009 are as given below.Calculate the index number for 2009 with 2001 as the base year by using weighted average of price relative method.

asked Apr 11, 2013 by sreemathi.v

0 answers

Given that the total cost function for x units of a commodity is : $C(x)=\large \frac{x^3}{3}\normalsize +3x^2-7x+16$

asked Apr 11, 2013 by sreemathi.v

1 answer

If the difference between Banker's discount and True discount of a bill for 73 days at 5% per annum is Rs.10,find (i) the amount of the bill (ii) the banker's discount.

asked Apr 11, 2013 by sreemathi.v

0 answers

A manufacturer manufactures two types of tea-cups,A and B.Three machines are needed for manufacturing the tea cups.The time in minutes required for manufacturing each cup on the machines is given below :

asked Apr 11, 2013 by sreemathi.v

1 answer

The price of a tape recorder is Rs. 1,661.A person purchases it by making a cash payment of Rs. 400 and agrees to pay the balance with due interest in 3 half-yearly equal installments.If the dealer charged interest at the rate of 10% per annum compounded half-yearly.Find the value of the installment.

asked Apr 11, 2013 by sreemathi.v

0 answers

Bag contains 2 white,1 black and 3 red balls,Bag B contains 3 white ,2 black and 4 red balls and Bag C contains 4 white ,3 black and 2 red balls.One Bag is chosen at random and 2 balls are drawn at random from that Bag.If the randomly drawn balls happen to be red and black,what is the probability that both balls come from Bag B?

asked Apr 11, 2013 by sreemathi.v

1 answer

A box contains 4 red and 5 black marbles.Find the probability distribution of the red marbles in a random draw of three marbles.Also find the mean and standard deviation of the distribution.

asked Apr 11, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the points $A(2,1,-3),B(-3,-2,1)$ and $C(2,4,-1).$

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the vector equation of the line passing through the points $(-1,2,1)$ and parallel to the line $\overrightarrow{r}=2\hat{i}+3\hat{j}-\hat{k}+\lambda\big(\overrightarrow{i}-2\hat{j}+\hat{k}\big)$.Also,find the distance between these lines.

asked Apr 11, 2013 by sreemathi.v

0 answers

If D,E,F are mid-points of the sides of a triangle ABC,Prove by vector method that : Area of ADEF=$\frac{1}{4}$(Area of $\Delta$ABC).

asked Apr 11, 2013 by sreemathi.v

0 answers

Prove that : $\begin{bmatrix}\overrightarrow{a}+\overrightarrow{b}& \overrightarrow{b}+\overrightarrow{c}&\overrightarrow{c} +\overrightarrow{a}\end{bmatrix}=2\begin{bmatrix}\overrightarrow{a}&\overrightarrow{b}&\overrightarrow{c}\end{bmatrix}$

asked Apr 11, 2013 by sreemathi.v

0 answers

Solve the following differential equation for a particular solution : $y-x\large\frac{dy}{dx}\normalsize=x+y\large\frac{dy}{dx}$,when $y=0$ and $x=1$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Using De moivre's theorem,find the value of : $(1+i\sqrt 3)^6+(1-i\sqrt 3)^6$

asked Apr 11, 2013 by sreemathi.v

0 answers

Aman and Bhavan throw a pair of dice alternately.In order to win,they have to get a sum of 8.Find their respective probabilities of winning if Aman starts the game.

asked Apr 11, 2013 by sreemathi.v

0 answers

A purse contains 4 silver and 5 copper coins.A second purse contains 3 silver and 7 copper coins.If a coin is taken out at random from one of the purses,what is the probability that it is a copper coin?

asked Apr 11, 2013 by sreemathi.v

0 answers

Compute Karl Pearson's Coefficient of correlation between sales and expenditures of a firm for six months

asked Apr 11, 2013 by sreemathi.v

1 answer

The following observations are given : $(1,4),(2,8),(3,2),(4,12),(5,10),(16,14),(7,16),(8,6),(9,18)$.Estimate the value of $y$ when the value of $x$ when the value of $y=5$.

asked Apr 11, 2013 by sreemathi.v

0 answers

If $y=x^x$,prove that : $\large\frac{d^2y}{dx^2}-\large\frac{1}{y}\big(\large\frac{dy}{dx}\big)^2-\large\frac{y}{x}\normalsize =0$

asked Apr 11, 2013 by sreemathi.v

0 answers

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 $\large \frac{\pi}{3}$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Draw a rough sketch of the curves $y=(x-1)^2$ and $y=(x-1)$.Hence,find the area of the region bounded by these curves.

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\large\int\frac{x^2-5x-1}{x^4+x^2+1}\normalsize dx$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the equation of the hyperbola whose foci are (0,$\pm$ 13) and the length of the conjugate axis is 20.

asked Apr 11, 2013 by sreemathi.v

0 answers

Verify Lagrange's mean value theorem for the function $f(x)=\sin x-sin 2x$ in the interval [0,$\pi$].

asked Apr 11, 2013 by sreemathi.v

0 answers

P,Q and R represent switches in 'ON position' and $P^1,Q^1$ and $R^1$ represent switches in 'OFF position'.Construct a switching circuit representing the polynomial : $P(P+Q)Q(Q+R^1$)

asked Apr 11, 2013 by sreemathi.v

0 answers

Prove that : $2Tan^{-1}\large\frac{1}{5}\normalsize+Cos^{-1}\large\frac{7}{5\sqrt 2}\normalsize+2Tan^{-1}\large\frac{1}{8}=\large \frac{\pi}{4}$

asked Apr 11, 2013 by sreemathi.v

0 answers

Solve the following system of equations using matrix method : $\large\frac{2}{x}+\large\frac{3}{y}+\large\frac{10}{z}\normalsize=4,\large\frac{4}{x}-\large\frac{6}{y}+\large\frac{5}{z}\normalsize=1,\large\frac{6}{x}+\large\frac{9}{y}-\large\frac{20}{z}\normalsize=2$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Using properties of determinants,show that $P\alpha^2+2q\alpha+r=0$,given that :p,q and r are not in G.P and $\begin{vmatrix}1 & \large\frac{q}{p} & \alpha+\large\frac{q}{p}\\1 & \large\frac{r}{q} & \alpha+\large\frac{r}{q}\\p\alpha+q &q\alpha+r &0\end{vmatrix}=0$.

asked Apr 11, 2013 by sreemathi.v

2 answers

Solve the differential equation : $\large \frac{dy}{dx}=e^{x+y}+x^2e^y$

asked Apr 11, 2013 by sreemathi.v

0 answers

A word consists of 9 different alphabets,in which there are 4 consonants and 5 vowels.Three alphabets are chosen at random .What is the probability that more than one vowel will be selected?

asked Apr 11, 2013 by sreemathi.v

1 answer

Find the modulus and argument of the complex number $\large \frac{2+i}{4i+(1+i)^2}$

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\large \int_0^1\frac{xe^x}{(1+x)^2}\normalsize dx$

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\lim_{y\to 0}\large \frac{y-tan^{-1}y}{y-sin y}$

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\large \int \frac{cosec x}{\log \;\tan\big(\frac{x}{2}\big)}\normalsize dx.$

asked Apr 11, 2013 by sreemathi.v

0 answers

Two regression lines are represented by $2x+3y-10=0$ and $4x+y-5=0$.Find the line of regression of y on x.

asked Apr 11, 2013 by sreemathi.v

0 answers

Solve for x : $\sin(2\tan^{-1}x)=1$

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the values of k,if the equation $8x^2-16xy+ky^2-22x+34y=12$ represents an ellipse.

asked Apr 11, 2013 by sreemathi.v

0 answers

If A=$\begin{bmatrix}3 & -2\\4 & -2\end{bmatrix}$,find x such that $A^2=xA-2I.$Hence find $A^{-1}$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate :$ \int \: \sqrt {\large\frac{1- \sqrt x}{1+ \sqrt x}}$$ dx $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

A helicopter is flying along the curve \( y = x^2 + 2\). A soldier is placed at the point (3, 2) . Find the nearest distance between the soldier and the helicopter.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Two equal sides of an isosceles triangle with fixed base 'a' are decreasing at the rate of 9 cm/second. How fast is the area of the triangle decreasing when the two sides are equal to 'a'.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Let f, g : R \( \rightarrow \) R be defined as \( f(x) = |x| \: and \: g(x) = [x]\) where [x] denotes the greatest integer less than or equal to x, find the fog \( \bigg(\large \frac{5}{2} \bigg)\) and gof \( (-\sqrt 2) \).

asked Dec 29, 2012 by thanvigandhi_1

0 answers

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