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Recent questions tagged q14

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^{2\pi}\cos^5x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{(x^2+1)(x^2+4)}\]

asked Dec 3, 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

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 1&1+p&1+p+q\\ 2&3+2p&4+3p+2q\\ 3&6+3p&10+6p+3q \end{vmatrix}= 1.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{For the matrix A = } \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}, \text{ find the numbers a and b such that } A^{2} + aA + bI = O \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following $tan^{-1} \frac{1-x}{1+x} =\frac{1}{2} tan^{-1} x,(x>0)$

asked Nov 29, 2012 by vaishali.a

2 answers

Find a particular solution of the differential equation $(x+1)\frac{dy}{dx}=2e^{-y} -1$, given that $y = 0$ when $x = 0$.

asked Nov 28, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Solve the following $\tan^{-1} \sqrt{3} -sec^{-1} (-2)$:

asked Nov 28, 2012 by vaishali.a

2 answers

Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability \(\frac{1}{2}\)).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?

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

If A and B are two events such that \(A ⊂ B\) and \(P(B) ≠ 0\), then which of the following is correct?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Probability of solving specific problem independently by A and B are $\large \frac{1}{2} $ and $\large \frac{1}{3} $ respectively. If both try to solve the problem independently, find the probability that $ \text {(i) the problem is solved (ii) exactly one of them solves the problem.} $

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event - the sum of numbers on the dice is 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that $$ \begin{array}{l} (i) \qquad \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & -1 \\ 6 & 7 \end{bmatrix} \\[0.5em] (ii) \qquad \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \: \neq \: \begin{bmatrix} -1 & 1 & 0 \\ 0 & -1 & 1 \\ 2 & 3 & 4 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \end{array} $$

asked Nov 25, 2012 by pady_1

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(0, 5)$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Find the least value of a such that the function $f$ given by $f (x) = x^2 + ax + 1$ is strictly increasing on $(1, 2).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Show that zero is the identity for this operation and each element $a\neq0$ of the set is invertible with $6-a$ being the inverse of $a$.

asked Nov 22, 2012 by vaishali.a

1 answer

If the matrix A is both symmetric and skew symmetric, then

asked Nov 22, 2012 by pady_1

1 answer

If \( x \sqrt {1+y} + y \sqrt{1+x} = 0\), for, \(-1 < x < 1\), prove that $\large \frac{dy}{dx} = -\frac{1}{(1+x)^2} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If \( y = Ae^{mx} + Be^{nx}\), show that \( \large\frac{d^2y}{dx^2} -\normalsize ( m + n ) \large\frac{dy}{dx} +\normalsize mny = 0 \)

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Let \(f : R - \{ - \frac {4} {3} \} \to R \) be a function defined as \(f(x)= \frac {4x} {3x+4} \) .The inverse of \(f\) is the map \(g\): Range \(f \to R - \{ - \frac {4} {3} \} \) given by

asked Nov 19, 2012 by vaishali.a

1 answer

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

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large \frac {dy}{dx} $ in the following: $y = \sin^{-1} \big( 2x \sqrt{1 -x^2} \big), -\;{ \frac{1}{\sqrt2} }\;< x < \;{\frac{1}{\sqrt2} }\\ $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} \large\frac{k\cos x}{\pi - 2x}\normalsize,& \quad { if \; x \neq \large\frac{\pi}{2} }\\ \normalsize 3 ,& \quad { if \; x = \large\frac{\pi}{2} }\\ \end{array} \right. \qquad at \; x = \; \large\frac{\pi}{2} $

asked Nov 11, 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} 3 ,& \quad\text{ if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4,& \quad\text{if $ 1 $ < \(x\) < 3 }\\ 5 ,& \quad\text{ if $ 3 $ \(\leq x\) \(\leq10\)}\\ \end{array} \right. \]

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Let \(L\) be the set of all lines in \(XY\) plane and \(R\) be the relation in \(L\) defined as \(R = \{(L1, L2) : L1\:\) is parallel to \(L2\}\). Show that \(R\) is an equivalence relation. Find the set of all lines related to the line \(y = 2x + 4.\)

asked Nov 8, 2012 by vaishali.a

1 answer

If the points $( 1, 1 , p)$ and $(– 3 , 0, 1)$ be equidistant from the plane $\hat{r} . (3\hat{i} +4\hat{j} -12\hat{k} +13) = 0$ then find the value of $p$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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