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Recent questions tagged q15

Integrate the function $\int\cos^3x\;e^{log\sin x}dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

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

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} sin\alpha&cos\alpha&cos(\alpha+\delta)\\ sin\beta&cos\beta&cos(\beta+\delta)\\ sin\gamma&cos\gamma&cos(\gamma+\delta)) \end{vmatrix}= 0.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 2 &-3 & 5\\ 3& 2 & -4\\ 1& 1& -2 \end{bmatrix}$, $\;$ find $A^{-1}.\;$ Using $ A^{-1}$ solve the system of equations: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{For the matrix A = } \begin{bmatrix} 1&1&1 \\ 1& 2&- 3 \\ 2 &-1& 3 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 5A + 11I = O. \text{ Hence, find } A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer $\sin (\tan^{-1}x), |x| <1 $ is equal to

asked Nov 28, 2012 by vaishali.a

1 answer

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time.If the population was 20,000 in 1999 and 25000 in the year of 2004,what will be the population of the village in 2009?

asked Nov 28, 2012 by sreemathi.v

1 answer

Let $A$ be a square matrix of order $3 \times 3$, then $ |kA|$ is equal to:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius \(r\) is \( \large\frac{4r}{3}\)

asked Nov 28, 2012 by thanvigandhi_1

1 answer

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: $ \text {P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15}$. Evaluate the following probabilities \[ \text {(i) P(A fails | B has failed) (ii) P(A fails alone)} \]

asked Nov 27, 2012 by balaji.thirumalai

1 answer

The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers 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

One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independant if: E : the card drawn is a spade F : the card drawn is an ace

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two positive numbers \(x\) and \(y\) such that their sum is 35 and the product \(x^2 y^5\) is a maximum.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event - the coin shows a tail, given that - at least one die shows a 3.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?

asked Nov 26, 2012 by vaishali.a

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

Find $ A^2 -5A + 6I $ , if $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

Find the equation of the tangent line to the curve $y = x^2 - 2x +7$ which is $(a)$ parallel to the line $2x - y + 9 = 0$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by \( f(x) = x + \frac{1}{\large x}\) is strictly increasing on $I$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

If $A $ is a square matrix, such that $ A^2 = A $ , then $ (1 + A )^3 - 7A $ is equal to:

asked Nov 22, 2012 by pady_1

1 answer

Let \(f:W \to W\) be defined as $f(n)=n$ - $1$, if \(n\;is\;odd\;and\; f(n)=n+1,\;if\;n\;is\; even.\) Show that \(f\) is invertible. Find the inverse of \(f\). Here, \(W\) is the set of all whole numbers.

asked Nov 21, 2012 by vaishali.a

1 answer

If \(( x-a)^2 + (y-b)^2 = c^2\), for some \( c > 0\), prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of \(a\) and \(b\).

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If \( y = 500e^{\large 7x} + 600e^{\large -7x}\), show that \( \large\frac{d^2y}{dx^2}\normalsize = 49y\)

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the function $xy = e^{\large(x-y)}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large \frac {dy}{dx} $ in the following: $ y = sec^{-1} \left(\large\frac{1}{2x^2 - 1}\right), 0 < x < \; { \frac{1}{\sqrt2} } \\ $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} 2x ,& \quad\text{ if $ x $ < 0}\\ 0,& \quad\text{if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4x ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.

asked Nov 8, 2012 by vaishali.a

1 answer

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