Recent questions tagged q7

Find the vector and cartesian equations of the plane containing the line $\Large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{3}$ and parallel to the line $\Large\frac{x+1}{3}=\frac{y-1}{2}=\frac{z+1}{1}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line joining the points $(1 , -2 , 1 )$ and $(0 , -2 , 3 ).$

asked Apr 6, 2013 by poojasapani_1

1 answer

If $ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{5k}, \overrightarrow{b}= -\overrightarrow{1}+ \overrightarrow{j}+ \overrightarrow{2k}$ and $ \overrightarrow{c}= \overrightarrow{4i}- \overrightarrow{2j}+ \overrightarrow{3k}, $ Show that $( \overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c} \neq \overrightarrow{a} \times( \overrightarrow{b}\times \overrightarrow{c})$

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove that sin $(A - B)$= sin $ A$ cos $B$ - cos $A$ sin $B$.

asked Apr 5, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{3j}-\overrightarrow{2k}$ and $\overrightarrow{b}=\overrightarrow{-i}+\overrightarrow{3k}$ than find $\overrightarrow{a}\times\overrightarrow{b}$. Verify that $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to$\overrightarrow{a}\times\overrightarrow{b}$ separately.

asked Apr 4, 2013 by poojasapani_1

1 answer

The constant forces $\overrightarrow{2i}-\overrightarrow{5j}+ \overrightarrow{6k}, -\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{k},$and $\overrightarrow{2i}+\overrightarrow{7j} $ act on a particle which is displaced from position $\overrightarrow{4i}-\overrightarrow{3j}-\overrightarrow{2k}$ to position $\overrightarrow{6i}+\overrightarrow{j}-\overrightarrow{3k}$. find the work done.

asked Apr 4, 2013 by poojasapani_1

1 answer

If arg $\left ( z-1 \right )$ = $\large\frac{\pi}{6}$ and arg $\left ( z+1 \right )$ = 2$\large\frac{\pi}{3}$ then prove that $\left | z \right |=1$

asked Apr 2, 2013 by geethradh

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -1 & -2 & -2 \\2 & 1 & -2 \\2 & -2 & 1 \end{bmatrix}$ is$\; 3A^T.$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the length of the perpendicular drawn from the origin to the plane 2X-3Y+6Z+21=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find $\mid\overrightarrow{x}\mid$,if for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a}).(\overrightarrow{x}+\overrightarrow{a})=15.$

asked Mar 20, 2013 by sreemathi.v

1 answer

P and Q are two points with position vectors $3\overrightarrow{a}-2\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ respectively.Write the position vector of a point R which divides the line segment PQ in the ratio 2 : 1 externally.

asked Mar 20, 2013 by sreemathi.v

1 answer

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(ii) $f : R\; \to R\; defined \; by \; f(x)\; =\; 1+x^2$

asked Mar 18, 2013 by meena.p

1 answer

Prove the following function: 7.$ tan^{-1}\frac{63}{16} = sin^{-1} \frac{5}{13}+cos^{-1} \frac {3}{5}$

asked Mar 14, 2013 by balaji.thirumalai

1 answer

State whether the function is one-one, onto or bijective.

$f : R\; \to R$ defined by $f(x)\; =\; 1+x^2$

asked Mar 6, 2013 by meena.p

1 answer

Find the values of $x$, if $ \text{: } \begin{vmatrix} 2&3 \\ 4&5 \end{vmatrix} = \begin{vmatrix} x&3 \\ 2x&5 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

$ (ii)$ Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix. $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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 a matrix $Z$ such that $X+Y+Z$ is a zero matrix.

asked Mar 4, 2013 by sreemathi.v

1 answer

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 $2X-3Y$

asked Mar 4, 2013 by sreemathi.v

1 answer

Evaluate : $ \int \large\frac{\sec^2x}{3+\tan\:x}$$dx $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ |\overrightarrow a|=\sqrt 3, |\overrightarrow b|=2$ and the angle between $ \overrightarrow a \: and \: \overrightarrow b$ is $ 60^{\circ}$, find $ \overrightarrow a.\overrightarrow b$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

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

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Determine order and degree of $ (y^{'''})^2+(y^{''})^3+(y^{'})^4+y^5=0 $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int (cosec^2x-\cot\: x)e^x\: dx $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $\int_{-\Large\frac{\pi}{2}}^{\Large\frac{\pi}{2}} \sin^7x\: dx$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Determine the order and degree of following differential equation $ \bigg(\large \frac{ds}{dt} \bigg)^4 +$$ 3s\bigg(\large \frac{d^2s}{dt^2} \bigg) $$= 0 $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_1^2 \bigg( \large\frac{1}{x} - \frac{1}{x^2} \bigg) $$e^x \: dx$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\limits_1^{\sqrt 3} \large\frac{dx}{1+x^2} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If on an average 1 ship in every 10 sinks, find the chance that out of 5 ships atleast 4 will arrive safely.

asked Feb 5, 2013 by meena.p

0 answers

Evaluate : $ \int \large\frac{dx}{\sqrt{1-x^2} } $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Solve the following LPP graphically. Maximize or minimize Z = 3x+5y subject to \[3x-4y\geq-12\]\[2x-y+2\geq0\]\[2x+3y-12\geq0\]\[0\leq x\leq4\]\[y\geq2\]

asked Feb 5, 2013 by meena.p

1 answer

Find the equation of the plane passing through the point (1,1,1) and perpendicular to each of the plane x+2y+3z = 7 and 2x-3y+4z = 0

asked Feb 5, 2013 by meena.p

0 answers

Prove that angle in a semi-circle is a right angle.

asked Feb 4, 2013 by meena.p

1 answer

Solve:\[(x+y)^2\frac{dy}{dx}=a^2\]

asked Feb 4, 2013 by meena.p

0 answers

Find the area of the region bounded by the curve C. $y=\tan x $ the tangent drawn to C at $x=\pi/4$ and the x-axis.

asked Feb 4, 2013 by meena.p

0 answers

Write the value of $ \int \large\frac{dx}{x^2+16} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove that $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ca & cb & -c^2 \end{vmatrix} = 4a^2b^2c^2 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin^{-1}x}{\sqrt{1-x^2}}$$dx $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

What is the degree of the following differential equation? $ y\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx} \bigg)^3$$=x \bigg( \large\frac{d^3y}{dx^3} \bigg)^2 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

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

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the differential equation that will represent the family of straight lines $ y=mx+c$, where m,c are parameters.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Without expanding, show that : $ \begin{vmatrix} 42 & 1 & 6 \\ 28 & 7 & 4 \\ 14 & 3 & 2 \end{vmatrix} = 0 $

asked Jan 31, 2013 by thanvigandhi_1

1 answer

$\Large\int \frac {\sqrt x}{\sqrt{a^3-x^3}} dx=$\[(a)\;\frac{2}{3}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad (b)\;\frac{2}{3}\sin^{-1}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad(c)\;\frac{2}{3}\cos {-1}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad(d)\;\frac{2}{3}\sin^{-1}\bigg(\frac{a}{x}\bigg)^{3/2}\]

asked Jan 30, 2013 by meena.p

0 answers

Find the direction ratio of a line parallel to the line joining the points (2,5,-3) and (3,-2,0).

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_{-\large\frac{\pi}{4}}^{\large\frac{\pi}{4}} x^3\sin^4x\: dx $

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $ y=a log|x|+bx^2+x $ has its extreme values at x = 1 and x = 2 then\[(a)\;a=2,b=-1\qquad(b)\;a=2,b=-1/2\qquad(c)\;-2,b=1/2\qquad(d)\;none\;of\;these\]

asked Jan 28, 2013 by meena.p

0 answers

Evaluate : $ \int_{-\pi}^{\pi} x^8\sin^5x dx. $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

If $ | \overrightarrow a | = 10, | \overrightarrow b | = 15 $ and the angle between the vector $ \overrightarrow a \: and \: \overrightarrow b \: is \:45^{\circ}, $ then find $ \overrightarrow a.\overrightarrow b$.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find f(x) satisfy the following : $ \int e^x (cosec^2x-\cot \: x)dx = e^x\: f(x)+C$

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Let $y=y=\sqrt{e^\sqrt x },x>0\;find\;\large\frac{dy}{dx}.$

asked Jan 25, 2013 by meena.p

1 answer

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