Recent questions tagged sec4

Let the vectors $ \overrightarrow a$ and $ \overrightarrow b$ be such that $| \overrightarrow a | = 3$ and $ |\overrightarrow b | = \frac{\large \sqrt 2}{\large 3}$ , then $\overrightarrow a \times \overrightarrow b$ is a unit vector, if the angle between $ \overrightarrow a$ and $ \overrightarrow b$ is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Area of a rectangle having vertices $A, B, C$ and $D$ with position vectors $ -\hat i + \large\frac{1}{2}$$ \hat j + 4\hat k, \: \hat i +\large \frac{1}{2}$$ \hat j + 4\hat k, \: \hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ and $-\hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ respectively is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the general solution $\large\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx} $$=\sqrt {4-y^2} \; (-2\lt y \lt 2) $

asked Nov 30, 2012 by sreemathi.v

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Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $y\;\log\: y\;dx-x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $x^5\large\frac{dy}{dx}$$=-y^5$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=$$\sin^{-1}x$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $e^x\tan y\;dx+(1-e^x)\sec ^2y\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(x^3+x^2+x+1)\large\frac{dy}{dx}$$=2x^2+x;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $x(x^2-1)\large\frac{dy}{dx}$$=1;y=0\;when\;x=2$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}=$$y\tan x;\;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

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Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y'=e^x\;\sin x.$

asked Nov 30, 2012 by sreemathi.v

1 answer

For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve,the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

asked Nov 30, 2012 by sreemathi.v

1 answer

At any point (x,y) of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3).Find the equation of the curve given that it passes through (-2,1).

asked Nov 30, 2012 by sreemathi.v

1 answer

In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3units and after 3seconds it is 6units.Find the radius of balloon after t seconds.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a bank, principal increases continuously at the rate of $5\%$ per year. An amount of $Rs.1000$ is deposited with this bank, how much will it work after $10$ years $(e^{0.5}=1.648)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?

asked Nov 30, 2012 by sreemathi.v

1 answer

The general solution of the differential equation$\frac{\large dy}{\large dx}=e^{x+y}$is

asked Nov 30, 2012 by sreemathi.v

1 answer

If $\Delta = \begin{vmatrix} a_11&a_12&a_13 \\ a_21&a_22&a_23 \\ a_31&a_32&a_33 \end{vmatrix} $ and $A_y$ is Cofactor of $a_y$, then value of $\Delta$ is:

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of third column, evaluate $ \Delta = \begin{vmatrix} 1&x&yz \\ 1&y&zx \\ 1&z&xy \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of second row, evaluate $ \Delta = \begin{vmatrix} 5&3&8 \\ 2&0&1 \\ 1&2&3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 2&-4 \\ 0&3 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

asked Nov 27, 2012 by balaji.thirumalai

1 answer

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0, if he opposed, and X = 1, if he is in favour. Find E(X) and Var (X).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

asked Nov 27, 2012 by balaji.thirumalai

2 answers

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the mean number of heads in three tosses of a fair coin.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

The random variable X has a probability distribution P(X) of the following form, where k is some number : \[ P(X) = \left\{ \begin{array}{l l} k & \quad \text{if $x$ = 0}\\ 2k & \quad \text{if $x$ = 1} \\ 3k & \quad \text{if $x$ = 2} \\ 0 & \quad \text{otherwise} \end{array} \right. \] (a) Determine the value of k. (b) Find $P (X \lt 2), P (X \leq 2), P(X \geq 2).$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given the following probability distribution, $\begin{matrix} \text{X} & 0 &1 &2 &3&4&5&6&7\\ \text{P(X)}&0&k&2k&2k&3k&k^2&2k^2&7k^2+k \end{matrix}$ \[\]determine $\;(i) k\quad (ii) P(X \lt 3)\quad (iii) P(X \gt 6)\quad (iv) P(0 \lt X \lt 3)$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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

asked Nov 27, 2012 by balaji.thirumalai

1 answer

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as \[ \text {(i) number greater than 4 (ii) six appears on at least one die} \]

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

State which of the following is a probability distributions of a random variable. Give reasons for your answer.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

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