Recent questions tagged modelpaper

Find the vector and cartesian equations of the plane through the points $(1 , 2 , 3 )$and $(2 , 3 , 1 )$ perpendicular to the plane $ 3x-2y+4z-5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Show that the lines $\large \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{3}$ and $\large\frac{x-2}{1}=\frac{y-1}{2}=\frac{-z-1}{1}$ intersect and find their point of intersection.

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the following two lines are skew lines: $\overrightarrow{r}=(\overrightarrow{3i}+\overrightarrow{5j}+\overrightarrow{7k})+ t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}) + s (\overrightarrow{7i}-\overrightarrow{6j}+\overrightarrow{7k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the following lines. $\large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-4}{6}$ and $ x+1=\large\frac{y+2}{2}=\frac{z-4}{2}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line through the point $(3 , -4 , -2 )$ and parallel to vector $\overrightarrow{9i} +\overrightarrow{6j} +\overrightarrow{2k}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the d . c. s of a vector whose direction ratios are $2 , 3 , -6.$

asked Apr 6, 2013 by poojasapani_1

1 answer

Verify $(\overrightarrow{a}\times\overrightarrow{b}) \times (\overrightarrow{c}\times\overrightarrow{d})=[\overrightarrow{a} \overrightarrow{b} \overrightarrow{d} ] \overrightarrow{c} - [\overrightarrow{a} \overrightarrow{b} \overrightarrow{c} ] \overrightarrow{d}$, For $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},\overrightarrow{ b}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{c}=\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k}.$

asked Apr 6, 2013 by poojasapani_1

1 answer

For any vector $\overrightarrow{a}$ Prove that $\overrightarrow{i} \times (\overrightarrow{a}\times\overrightarrow{i})+ \overrightarrow{j} \times (\overrightarrow{a}\times\overrightarrow{j})+ \overrightarrow{k } \times(\overrightarrow{a}\times\overrightarrow{k})=\overrightarrow{2a}$

asked Apr 6, 2013 by poojasapani_1

1 answer

if $\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $ Verify that $ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$

asked Apr 5, 2013 by poojasapani_1

1 answer

The volume of a parallelopiped whose edges are represented by $-\overrightarrow{12i}+\lambda\overrightarrow{k}, \overrightarrow{3j}-\overrightarrow{k}, \overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{15k} $ is $546;\quad$ find the value of $\lambda$.

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

A force magnitude $5$ units acting parallel to $\overrightarrow{2i}-\overrightarrow{2j}+ \overrightarrow{k}$ displaces the point of application from $(1,2,3)$to $(5,3,7) $ find the work done.

asked Apr 4, 2013 by poojasapani_1

1 answer

Prove that $\begin{bmatrix} x+y & x & x \\ 5x+4y & 4x & 2x \\ 10x+8y & 8x & 3x \end{bmatrix}=x^3$

asked Apr 3, 2013 by meena.p

1 answer

Solve the equation $x^{4}-4x^{3}+11x^{2}-14x+10=0$ if one root is $1+2i$.

asked Apr 3, 2013 by geethradh

1 answer

Prove by the vector method , cos$(A+B)=$ cos$A$ cos$B$ - sin$A$ sin$B$

asked Apr 3, 2013 by poojasapani_1

1 answer

Solve the equation $x^{4}-8x^{3}+24x^{2}-32x+20$ = 0 if $3+\mathit{i}$ is a root.

asked Apr 3, 2013 by geethradh

1 answer

Show that the vectors $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k},\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{5k}$ and $\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{4k}$ form a right angled tringle.

asked Apr 3, 2013 by poojasapani_1

1 answer

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (iii) Write the elements $a_{13},a_{21}.a_{33},a_{24},a_{23}$ .

asked Apr 3, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (ii) The number of elements .

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : $ (iii)\begin{bmatrix} -1&5&6 \\ \sqrt 3 & 5&6\\2 &3&-1 \end{bmatrix} $.

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : $ (ii)\begin{bmatrix} 1&-1 \\ 2 & 3 \end{bmatrix} $.

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the value of x if : $ \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix} $

asked Apr 2, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$

asked Apr 2, 2013 by poojasapani_1

1 answer

For what valus of $k$, the system of equations $kx+y+z=1\;,x+ky+z=1\;,x+y+kz=1\;,$have (i) unique solution (ii) more than one solution (iii) no solution.

asked Apr 2, 2013 by poojasapani_1

1 answer

Discuss the solutions of the system of equations for all values of $\lambda$. $ x+y+z=2\;,2x+y-2z=2\;,\lambda\;x+y+4z=2$

asked Apr 2, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y-z=1\;,2x+2y-2z=2\;,-3x-3y+3z=-3$

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6 $

asked Mar 30, 2013 by poojasapani_1

1 answer

A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation:$\;2x\;-\;y\;=7\;,\;3x\;-2y\;=11$

asked Mar 29, 2013 by poojasapani_1

1 answer

For $A=\begin{bmatrix} -1 & 2 & -2 \\4 & -3 & 4 \\4 & -4 & 5 \end{bmatrix}$ show that $A=A^{-1}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self

asked Mar 28, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that $(AB)^{-1}=B^{-1}A^{-1}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the inverse of following matrix :$\begin{bmatrix} 1 & 0 & 3 \\2 & 1 & -1 \\1 & -1 & 1 \end{bmatrix}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the adjoint of the matrix A =$\begin{bmatrix} 1 & 2 \\3 & -5 \end{bmatrix}$ and verify the result $ A\;(adj\; A)=(adj\;A)\;A=$|$A$|$.I$

asked Mar 28, 2013 by poojasapani_1

1 answer

Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$

asked Mar 27, 2013 by poojasapani_1

1 answer

Find the particular solution of the differential equation $\large\frac{dx}{dy}$$+x\cot y=2y+y^2\cot y,(y\neq 0)$,given that $x=0$ when $y=\large \frac{\pi}{2}$.

asked Mar 22, 2013 by sreemathi.v

1 answer

Find the area of the region $\{(x,4):y^2\leq 4x,4x^2+4y^2\leq9\}$ using method of integration.

asked Mar 22, 2013 by sreemathi.v

1 answer

Using properties of determinants,prove the following $\begin{vmatrix}3x& -x+y & -x+z\\x-y & 3y & z-y\\x-z & y-z & 3z\end{vmatrix}=3(x+y+z)(xy+yz+zx)$

asked Mar 22, 2013 by sreemathi.v

1 answer

If $x\sin (a+y)+\sin a \cos(a+y)=0$,Prove that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^3+1)}$

asked Mar 22, 2013 by sreemathi.v

1 answer

Using vectors,find the area of triangle ABC,whose vertices are $A(1,2,3),B(2,-1,4),C(4,5,-1).$

asked Mar 22, 2013 by sreemathi.v

1 answer

L and M are two points with position vectors $2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{a}+2\overrightarrow{b}$ respectively.Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.

asked Mar 22, 2013 by sreemathi.v

1 answer

If Matrix A = $\begin{bmatrix} 3 &-3 \\ -3 & 3 \end{bmatrix}$, and $A^2=\lambda A$, then write the value of $\lambda$.

asked Mar 22, 2013 by sreemathi.v

1 answer

Using the property of determinants, evalute: $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

What is the value of $tan\bigg(\frac{1}{2}sin^{-1}\frac{3}{4}\bigg)$

asked Mar 22, 2013 by balaji.thirumalai

1 answer

Show that the differential equation $[xsin^2\big(\frac{y}{x}\big)-y]dx+xdy=0.$ is homogeneous.Find the particular solution of this differential equation ,given that $y=\frac{\pi}{4}$ when x=1.

asked Mar 22, 2013 by sreemathi.v

1 answer

Find the area of the region $\{(x,y):y^2\leq 6ax$ and $x^2+y^2\leq 16a^2\}$ using method of integration.

asked Mar 22, 2013 by sreemathi.v

1 answer

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