Recent questions tagged q7

If $ | \overrightarrow a | = 2, |\overrightarrow b | = \sqrt 3\: and \: \overrightarrow a.\overrightarrow b = \sqrt 3.$ Find the angle between $ \overrightarrow a \: and \: \overrightarrow b.$

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find a matrix X such that 2A + 2B + X = 0, where $ A = \begin{bmatrix} -1 & 3 \\ 2 & 1 \end{bmatrix} $ and $ B = \begin{bmatrix} 1 & 5 \\ 3 & 2 \end{bmatrix} $

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Express $\begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ as sum of the symmetric and skew symmetric matrices.

asked Jan 24, 2013 by meena.p

0 answers

Find the value of x if $cosec^{-1}x=2\cot^{-1}7+\cot^{-1}\frac{3}{4}$

asked Jan 23, 2013 by meena.p

1 answer

What is the degree of the following differential equation ? $4 \bigg( \frac{dy}{dx} \bigg)^2 - 7y - \bigg( \frac{dy}{dx} \bigg)^3 + \sin x = 0 $

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Let $f :R \rightarrow R $ defined by $f(x) = (ax^2+b)^3$ find the function $g :R \rightarrow R $ such that $f(g(x)) = g(f(x))$

asked Jan 23, 2013 by meena.p

0 answers

Find the order and degree of the differential equation $\bigg[ 1+ \bigg(\large \frac{dy}{dx} \bigg)^2 \bigg]^{\large\frac{3}{2}} = \frac{d^2y}{dx^2} $

asked Jan 22, 2013 by thanvigandhi_1

1 answer

Solve the differential equation $\Large\frac{dy}{dx}\normalsize+1=e^{x+y}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Evaluate : $ \int\large \frac{1}{\sin^2x\cos^2x}$$dx.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

A vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2,3,-6.Find the direction cosines and components of $\overrightarrow{r}$,given that $\overrightarrow{r}$ makes an acute angle with x-axis.

asked Jan 17, 2013 by sreemathi.v

1 answer

Evaluate : $ \int \large\frac{\sin^2x}{1+\cos x}$$dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Find the area of the region bounded by the line $x=2$ and the parabola $y^2=8x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

$ \int_0^1 \large\frac{dx}{\sqrt{1-x^2}} $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate the following $\int\tan^2 x\sec^4 x\;dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Find the differential equation $ y=e^x+1$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3cm and 3.0005cm,respectively.

asked Jan 11, 2013 by sreemathi.v

1 answer

$ \int (ax^2+bx+c)dx.$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int ( \sin2x-4e^{3x})dx$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int\large \frac{2\cos x}{3\sin^2x}$$dx.$

asked Jan 9, 2013 by thanvigandhi_1

0 answers

A and B are two events such that $P(A)=\frac{1}{2},P(B)=\frac{1}{3} and\; P(A\cap B)=\frac{1}{4}$.Find:\[(i)\;P(A|B)\quad(ii)\;P(B|A)\quad(iii)\;P(A'|B)\quad(iv)\;P(A'|B')\]

asked Jan 8, 2013 by sreemathi.v

1 answer

Evaluate : $ \int \large\frac{\sin\: \sqrt x}{\sqrt x}$$dx.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

$ \int\: \frac{\large x^3+3x+4}{\large \sqrt x}dx.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Find the differential equation : $ y-\cos y = x.$

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Find the differential equation $y = x \sin x.$

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

asked Jan 3, 2013 by sreemathi.v

1 answer

Evaluate : $ \int \: \large\frac{cos\sqrt x}{\sqrt x}$$dx $

asked Jan 2, 2013 by thanvigandhi_1

0 answers

$ \int \: \large\frac{x^3+5x^2-4}{x^2}\normalsize dx. $

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}( x-a)\sin\large\frac{1}{x-a},\normalsize & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$ at $x=a$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find f(x) satisfying the following : $ \int \: e^x ( sec^2 x + tan \: x ) dx = e^x\: f (x) +C $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Write the value of $ \int_{\Large\frac{-\pi}{2}}^{\Large\frac{\pi}{2}} \sin^5 x dx $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Write the value of $ \int_{\Large\frac{-\pi}{2}}^{\Large\frac{\pi}{2}} \sin^5 xdx. $

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Using the properties of determinants, prove that: $\begin{vmatrix} y^2z^2 & yz &y+ z \\ z^2x^2 & zx & z+x \\ x^2y^2 & xy & x+y \end{vmatrix}\;=\;0$

asked Dec 24, 2012 by sreemathi.v

1 answer

$ \frac{d}{dx} ( log\: tan\: x)$ is equal to \[ \begin{array} ((A)\: 2\: sec\: 2x \quad & (B)\: 2\: cosec\: 2 x \\ (C)\: sec \: 2 x \quad & (D)\: cosec \: 2x \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

If $X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$ and $Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$, find $X + Y$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find the value of x from the following : $\begin {bmatrix} x & 4 \\ 2 & 2x \end {bmatrix} = 0 $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Find the real solution of the equation <BR>$\tan^{-1}\sqrt{x(x+1)}+\sin^{-1}\sqrt{x^2+x+1}=\frac{\pi}{2}$

asked Dec 20, 2012 by sreemathi.v

1 answer

Evaluate : $\int_0^1 \mathrm \: \large\frac{dx}{1+x^2} $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function?If g is described by $g(x)=\alpha x+\beta$,then what value should be assigned to $\alpha\;and\;\beta.$

asked Dec 18, 2012 by sreemathi.v

1 answer

Find the intercepts cut off by the plane $2x + y -z = 5.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \bigg( \sqrt {\frac{1-cos \: x}{1 + cos \: x}} \bigg), x < \pi\]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the values of a,b,c and d from the question:
$\begin{bmatrix}a-b & 2a+c\\2a-b & 3c+d\end{bmatrix}$ = $\begin{bmatrix}-1 & 5\\0 & 13\end{bmatrix}$

asked Dec 7, 2012 by sreemathi.v

1 answer

Find the unit vector in the direction of the vector $ \overrightarrow a = \hat i + \hat j + 2\hat k$ .

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int x^2(1-\frac{1}{x^2})\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Evaluate the product $(3\overrightarrow a − 5\overrightarrow b) ⋅ (2\overrightarrow a + 7\overrightarrow b)$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $x\;\sqrt{x+2}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin4x\;\sin8x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x-1}{\sqrt{x^2-1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{x}{(x^2+1)(x-1)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Let the vectors $ \overrightarrow a, \overrightarrow b, \overrightarrow c$ be given as $a_1\hat i + a_2\hat j + a_3\hat k, \: b_1\hat i + b_2\hat j + b_3\hat k, \: c_1\hat i + c_2\hat j + c_3\hat k $. Then show that $ \overrightarrow a × (\overrightarrow b + \overrightarrow c) = \overrightarrow a × \overrightarrow b + \overrightarrow a × \overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

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