Recent questions tagged q8

Verify Rolles theorem for the function $f(x)=\sin 2x \;in\;\bigg[0,\Large\frac{\pi}{2}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

The cartesian equation of a line AB is $ \large\frac{2x-1}{\sqrt 3} = \frac{y+2}{2} = \frac{z-3}{3} $. Find the direction cosines of a line parallel to AB.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If $ A = \begin{bmatrix} 4 & 1 \\ 5 & 8 \end{bmatrix},$ show that A + A' is symmetric matrix.

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Prove that $ \begin{vmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ca & bc & (a+b)^2 \end{vmatrix}=2abc(a+b+c)^2$ (Use properties to prove the above)

asked Jan 24, 2013 by meena.p

0 answers

If $\cos^{-1}x=\tan^{-1}x,\;show\;that\;\sin(\cos^{-1}x)=x^2$

asked Jan 23, 2013 by meena.p

1 answer

The coordinates of P and Q are (2, -3) and (1, -2) respectively. Find the coordinates of the position vector, equivalent to $ \overrightarrow {PQ} $.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $f(x)=\frac{5x+3}{4x-5}\big(x\neq\frac{5}{4}\big),$find g(x) such that $gof(x) = x$

asked Jan 23, 2013 by meena.p

0 answers

Find the value of $ \lambda $ so that the vectors $ \overrightarrow a = 2\hat i + \lambda\hat j + \lambda\hat k \: and \: \overrightarrow b = \hat i - 2\hat j + 3\hat k$ are perpendicular.

asked Jan 22, 2013 by thanvigandhi_1

0 answers

Solve:$y\;dx-x\;dy=x^2y\;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find a vector in the direction of vector $ 5\hat i - \hat j + 2\hat k $ which has magnitude 8 units.

asked Jan 17, 2013 by thanvigandhi_1

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FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $ \overrightarrow a. \hat i = \overrightarrow a. (\hat i + \hat j ) = \overrightarrow a.(\hat i + \hat j + \hat k )=1.$then find $ \overrightarrow a$.

asked Jan 16, 2013 by thanvigandhi_1

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Sketch the region $\{(x,0):y=\sqrt {4-x^2}$} and $x$-axis.Find the area of the region using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Evaluate the product of $ (3\overrightarrow a - 5\overrightarrow b ).(2\overrightarrow a + \overrightarrow b)$

asked Jan 15, 2013 by thanvigandhi_1

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Evaluate the following $\int\frac{(\sin x+\cos x)}{\sqrt {1+\sin 2x}}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Represent graphically a displacement of 40 km , $ 30^{\circ} $ east of length.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A man, 2m tall, walks at the rate of $1\frac{2}{3}m/s$ towards a street light which is $5\frac{1}{3}m$ above the ground.At what rate is the tip of his shadow moving?At what rate is the length of the shadow changing when he is $3\frac{1}{3}m$ from the base of the light?

asked Jan 11, 2013 by sreemathi.v

1 answer

If $ \overrightarrow P (1, 5, 4) \: and \overrightarrow Q (4, 1, -2),$ find the dr. of $ \overrightarrow {PQ}.$

asked Jan 10, 2013 by thanvigandhi_1

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If $ \overrightarrow a $ x $ \overrightarrow b = \overrightarrow c$ x $ \overrightarrow d$ and $ \overrightarrow a$ x $ \overrightarrow c = \overrightarrow b $ x $ \overrightarrow d $ show that $ \overrightarrow a - \overrightarrow d$ is parallel to $ \overrightarrow b-\overrightarrow c$ where $ \overrightarrow a \neq \overrightarrow d$ and $ \overrightarrow b \neq \overrightarrow c.$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Find the projection of $ \overrightarrow a $ on $ \overrightarrow b $ if $ \overrightarrow a . \overrightarrow b = 8 $ and $ \overrightarrow b = 2\hat i + 6\hat j + 3\hat k $.

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Three events A,B and C have probabilities $\Large \frac{2}{5},\frac{1}{3}$ and $\Large \frac{1}{2}$,respectively.Given that $P(A\cap C)=\frac{1}{5}\;and\;P(B\cap C)=\frac{1}{4}$,find the value of $P(C|B)\; and \;P(A'\cap C').$

asked Jan 8, 2013 by sreemathi.v

1 answer

Find the value of $ p$ if $ (2\hat i + 6\hat j + 27\hat k) \times (\hat i + 3\hat j + p\hat k) =0.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

If $ \overrightarrow a = \hat i - 2\hat j + 3\hat k \: and \: \overrightarrow b = -2\hat i + 3\hat j - 4\hat k \: and \: \overrightarrow c = \hat i - 3\hat j - \lambda \hat k $ are coplanar if $ \lambda = 5.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Write two different vectors having same direction.

asked Jan 4, 2013 by thanvigandhi_1

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Compute the magnitude of the following vectors : $ \overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - 7\hat j - 3\hat k\: and \: \overrightarrow c = \frac{1}{\sqrt 3}\hat i + \frac{1}{\sqrt 3}\hat j - \frac{1}{\sqrt 3}\hat k $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Find the equation of a plane which is at a distance $3\sqrt 3$ units from origin and the normal to which is equally inclined to coordinate axis.

asked Jan 3, 2013 by sreemathi.v

1 answer

Show that the vectors : $ \overrightarrow a = -4\hat i - 6\hat j - 2\hat k, \overrightarrow b = -\hat i + 4\hat j + 3\hat k \: and \: \overrightarrow c = -8\hat i - \hat j + 3\hat k $ are coplanar.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Find the value of the parallelopipped whose edges are $ \overrightarrow a = 2\hat i - 3\hat j + 4\hat k, \overrightarrow b = \hat i - 2\hat j - \hat k \: and \: \overrightarrow c = 2\hat i - \hat j + 2\hat k $

asked Jan 2, 2013 by thanvigandhi_1

0 answers

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

asked Dec 31, 2012 by sreemathi.v

1 answer

In a triangle ABC, the sides AB and BC are represented by vectors $ 2\hat i - \hat j + 2\hat k, \hat i + 3\hat j + 5\hat k$ respectively. Find the vector representing CA.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the position vector of the midpoint of the line segment joining the points $ A ( 5\hat i + 3\hat j )\: and \: B ( 3\hat i - \hat j ) $.

asked Dec 26, 2012 by thanvigandhi_1

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Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).

asked Dec 25, 2012 by thanvigandhi_1

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Using the properties of determinants, Prove that$\begin{vmatrix} y+z & z & y \\ z & z+x & x \\ y & x & x+y \end{vmatrix}\;=\;4xyz$

asked Dec 24, 2012 by sreemathi.v

1 answer

The rate of change of the area of a circle with respect to its radius r when r = 6 is \[ \begin{array} ((A) \: 10 π \quad & (B) \: 12 π \\ (C) \: 8 π \quad & (D)\: 11 π \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

Find non-zero values of $x$ satisfying the matrix equation $x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\(10) & 6x\end{bmatrix}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Find the value of p if $ ( 2\hat i + 6\hat j + 27\hat k )$ x $ ( \hat i + 3\hat j + p\hat k ) = \overrightarrow 0. $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Find the value of the expression $\sin \bigg(2\tan^{-1}{\frac{1}{3}}\bigg)+\cos \big(\tan^{-1}2\sqrt 2\big)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find a unit vector in the direction of $ \overrightarrow a = 3\hat i - 2\hat j + 6\hat k $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Are the following set of ordered pairs function?If so,examine whether the mapping is injective or subjective $\;\{(x,y)\;:\;x \;is \;a \;person,y\; is\; the\; mother\; of\; x\}$

asked Dec 18, 2012 by sreemathi.v

1 answer

Find the equation of the plane with intercept 3 on the y - axis and parallel to ZOX plane.

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \bigg( \frac{cos\: x - sin\: x}{cos\: x + sin\: x} \bigg) , 0 < x < \pi \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

$A=[a_{ij}]_{m \times n}$ is a square matrix if

asked Dec 7, 2012 by sreemathi.v

1 answer

Find the unit vector in the direction of vector $ \overline{PQ}$, where $P$ and $Q$ are the points $(1, 2, 3)$ and $(4, 5, 6)$ respectively.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int(ax^2+bx+c)\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the magnitude of two vectors $ \overrightarrow a$ and $\overrightarrow b$ , having the same magnitude and such that the angle between them is $60^{\omicron}$ and their scalar product is $\large \frac{1}{2}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $x\;\sqrt{1+2x^2}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{1-\cos x}{1+\cos x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x^2}{\sqrt{x^6+a^6}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

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

asked Dec 5, 2012 by sreemathi.v

1 answer

If either $ \overrightarrow a = \overrightarrow 0 $ or $ \overrightarrow b = \overrightarrow 0 $ then $ \overrightarrow a × \overrightarrow b = \overrightarrow 0$. Is the converse true? Justify your answer with an example.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

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