Recent questions tagged class12

Find the amplitude of the complex number $\sin\large\frac{6\pi}{5}\normalsize+i\begin{pmatrix}1-\cos\large\frac{6\pi}{5}\end{pmatrix}$.

asked Apr 17, 2013 by sreemathi.v

0 answers

A performance test was conducted among seven candidates.They scored the following marks : 7,10,12,15,17,19,25.Calculate the interquartile range and the standard deviation.

asked Apr 17, 2013 by sreemathi.v

0 answers

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random.What is the probability that the ticket has a number which is a multiple of 3 or 7.

asked Apr 17, 2013 by sreemathi.v

1 answer

A radioactive substance disintegrates at a rate proportional to its mass. When its mass is $10 $mgm, the rate of disintegration is $0.051$ mgm per day. How long will it take for the mass to be reduced from $10$mgm to $5$mgm.$ [\log_{e}$$2=0.6931]$

asked Apr 17, 2013 by poojasapani_1

1 answer

The points (0,4) and (0,2) are the vertex and focus of a parabola.Find the equation of the parabola.

asked Apr 17, 2013 by sreemathi.v

0 answers

Evaluate $\int\large\frac{\cos x}{\sin x+\sqrt \sin x}\normalsize dx.$

asked Apr 17, 2013 by sreemathi.v

0 answers

If $\sin(xy)+\cos(xy)=1$ and $\tan(xy)\neq 1$,then show that $\large\frac{dy}{dx}=-\frac{y}{x}$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the foci and latus rectum for the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{5}=\frac{1}{2}$

asked Apr 17, 2013 by sreemathi.v

0 answers

The rate at which the population of a city increases at any time is propotional to the population at that time. If there were $1,30,000$ people in the city in $1960 $ and $1,60,000$ in $1990$ what population may be anticipated in $2020$.$[\log_{e}(\large\frac{16}{13})=$$.2070;$$e^{.42}=1.52]$

asked Apr 17, 2013 by poojasapani_1

1 answer

A straight line $y=mx$ passes through the intersection of the straight lines $x+2y-1=0$ and $2x-y+3=0.$Find the value of m.

asked Apr 17, 2013 by sreemathi.v

1 answer

Given that $A=\begin{bmatrix}\cos x & \sin x\\-\sin x& \cos x\end{bmatrix}$ and $A(adj. A)=K\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$,find the value of K.

asked Apr 17, 2013 by sreemathi.v

0 answers

A cup of coffee at temperature $100^{\circ}$$C$ is placed in a room whose temperature is $15^ {\circ}$$C$ and it cools to $60^{\circ}$$C$ in $5$ minutes . Find its temperature after a further interval of $5$ minutes.

asked Apr 17, 2013 by poojasapani_1

1 answer

A company has two plants which manufacture scooters.Plant I manufactures 80% of the scooters while Plant II manufactures 20% of the scooters.At plant I ,85 out of 100 scooters are rated as being of standard quality,while at Plant II only 65 out of 100 scooters are rated as being of standard quality.If a scooter is of standard quality,what is the probability that it came from Plant I?

asked Apr 17, 2013 by sreemathi.v

1 answer

Four dice are thrown simultaneously.If the occurrence of an odd number in a single dice is considered a success,find the probability of at most 2 successes.

asked Apr 17, 2013 by sreemathi.v

0 answers

A television manufacturer finds that the total cost for the production and marketing of $x$ number of television sets is : $c(x)=300x^2+4200x+13,500.$Each product is sold for Rs.8,400.Determine the break-even points.

asked Apr 17, 2013 by sreemathi.v

2 answers

The sum of Rs $1000$ is compounded continuously, the nominal rate of interest being four percent per annum. In how many years will the amount be twice the original principal ? $(\log_{e}$$2=0.6931)$

asked Apr 17, 2013 by poojasapani_1

1 answer

Mr.Agarwal buys goods worth Rs.2,800 payable 8 months. Hence he pays Rs.400 at the end of the second month and Rs.600 at the end of the third month.Find the number of months after which the balance will become due.

asked Apr 17, 2013 by sreemathi.v

0 answers

The price of a tape recorder is Rs. 1,561.A person purchases it by paying Rs. 300 in cash and the balance is to be paid with due interest in 3 half yearly equal installments.If the dealer charges interest at the rate of 10% per annum compounded half yearly,find the value of each installment.

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the Banker's discount and the discounted value of a bill worth Rs.600 drawn on May 15,2005 for 3 months and discounted on July 20,2005 at 5% per annum.

asked Apr 17, 2013 by sreemathi.v

0 answers

Radium disappears at a rate propotional to the amount present .If $5\%$ of the original amount disappears in $50$ years , how much will remain at the end of $100$ years [Take $A_{0}$ as a intial amount.]

asked Apr 17, 2013 by poojasapani_1

1 answer

The table below gives details of the electricity generated in million kilowatt hours in each quarter for the years 2002 to 2004.

asked Apr 17, 2013 by sreemathi.v

0 answers

The quotations for four different commodities for the years 2000 and 2005 are given below.Calculate the index number for 2005 with 2000 as the base year by using the weighted average of price relatives method.

asked Apr 17, 2013 by sreemathi.v

0 answers

The vectors $\hat{i}+3\hat{j},5\hat{k}$ and $\lambda\hat{i}-\hat{j}$ are coplanar.Find the value of $\lambda$.

asked Apr 17, 2013 by sreemathi.v

0 answers

The vectors $-2\hat{i}+4\hat{j}+4\hat{k}$ and $-4\hat{i}-2\hat{k}$ represent the diagonals BD and AC of a parallelogram ABCD.Find the area of the parallelogram.

asked Apr 17, 2013 by sreemathi.v

0 answers

Show that the equation to a sphere passing through three points (2,0,0),(0,2,0) and (0,0,2) and having its centre on the plane $2x+3y+4z=27$ is $x^2+y^2+z^2-6x-6y-6z+8=0.$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the equations to be two planes passing through the points (0,4,-3) and (6,-4,3),if the sum of their intercepts on the three axes is zero.

asked Apr 17, 2013 by sreemathi.v

0 answers

Solve the differential equation : $y dx-(x+2y^2)dy=0$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the cube roots of -27 and show that the sum of the cube roots is equal to zero.

asked Apr 16, 2013 by sreemathi.v

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A card is drawn at random from a pack of 52 playing cards.What is the probability that the card drawn is neither a spade nor a queen?

asked Apr 16, 2013 by sreemathi.v

0 answers

A and B throw two dice each.If A gets a sum of 9 on his two dice ,then find the probability of B getting a higher sum.

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that $\left ( 1+\mathit{i} \right )^{4n}$ and $\left ( 1+\mathit{i} \right )^{4n+2}$ are real and purely imaginary respectively.

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \cos \; \theta + \mathit{i}\sin \; \theta \right )^{\mathit{n}} + \left ( 1+ \cos \; \theta - \mathit{i}sin \; \theta \right )^{\mathit{n}} = 2^{\mathit{n+1}} \cos ^{\mathit{n}}\left ( \large\frac{\theta}{2} \right )$$ \cos \;\large\frac{n\theta }{2}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \mathit{i\sqrt{3}} \right )^{\mathit{n}} + \left ( 1- \mathit{i\sqrt{3}} \right )^{\mathit{n}} = 2^{n+1} \cos \; \large\frac{n\pi}{3}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$

asked Apr 16, 2013 by geethradh

1 answer

The following table shows the sales and advertisement expenditure of a firm :

asked Apr 16, 2013 by sreemathi.v

1 answer

Calculate Spearman's rank correlation coefficient between the advertisement cost and sales from the following data :

asked Apr 16, 2013 by sreemathi.v

1 answer

The region bounded by the curve $y^2=x(x-1)^2$,the x-axis and the lines $x=1,x=0$,is rotated through four right angles about the x-axis.Calculate the volume of the solid of revolution so formed.

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that $\int_0^{2\pi}\large\frac{x\cos x}{1+\cos x}\normalsize dx=2{\pi}^2.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the volume of the largest cone that can be inscribed in a sphere of radius R.

asked Apr 16, 2013 by sreemathi.v

0 answers

Verify Rolle's theorem for the function $f(x)=e^{2x}(\sin 2x-\cos 2x)$ defined in the interval $\begin{bmatrix}\large\frac{\pi}{8},\frac{5\pi}{8}\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

1 answer

If $y=\large\frac{\sin^{-1}x}{\sqrt{1-x^2}}$,prove that $(1-x^2)\large\frac{dy}{dx}-\normalsize xy=1.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that : $\sin^{-1}\bigg(\large\frac{1}{\sqrt {17}}\bigg)\normalsize+\cos^{-1}\bigg(\large\frac{9}{\sqrt{85}}\bigg)\normalsize=\tan^{-1}\bigg(\large\frac{1}{2}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the following differential equation; $(3D^{2}+4D+1)$$y=3e^{-\Large\frac{x}{3}}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+2D+3)$$y=\sin$$2x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+5)$$y=\cos^{2}$$x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation;$(D^{2}-1)$$y=\cos$$2x-2\sin$$2x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation;$(D^{2}-6D+9)$$y=x+e^{2x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $D^{2}$$y=-9\sin$$3x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}-2D-3)$$y=\sin$$x\cos$$x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+3D-4)$$y=x^{2}$

asked Apr 16, 2013 by poojasapani_1

1 answer

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