Recent questions tagged q13

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

asked Apr 3, 2013 by poojasapani_1

1 answer

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

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate: $\int\large \frac{cos 2x-cos 2\alpha}{cos x-cos\alpha}$$dx$

asked Mar 20, 2013 by sreemathi.v

1 answer

Using properties of determinants,prove the following $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}=9y^2(x+y)$

asked Mar 20, 2013 by sreemathi.v

1 answer

If $\begin{vmatrix}4+x& 4-x & 4-x\\4-x & 4+x & 4-x\\4-x & 4-x & 4+x\end{vmatrix}$,then find the values of x.

asked Mar 18, 2013 by sreemathi.v

1 answer

Find the simplified form of $cos^{-1}(\frac{3}{5}cos x+\frac{4}{5}sin x),$where $x\in (\frac{-3}{4},\frac{3}{4})$

asked Feb 19, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\alpha & \beta\\\gamma & -\alpha\end{bmatrix}$ is such that $A^2=I,$ then which of the following is true:

asked Feb 19, 2013 by sreemathi.v

1 answer

Find the value of $ \lambda $ so that the line $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $$\: and \; \large\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are perpendicular to each other.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Using the properties of determinants, prove the following : \[ \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & c+a \\ a+b & b+c & c+a \end{vmatrix} = 2(a+b+c)(ab+bc+ca-a^2-b^2-c^2).\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Using the properties of determinants, prove the following : \[ \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c).\]

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Prove that $ \begin{vmatrix} 1 & a & a^3 \\ 1 & b & b^3 \\ 1 & c & c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c).$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Using the properties of determinants, prove the following : \[ \begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix} = 2 \begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix} \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

prove that : $ \begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = abc \bigg( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+1 \bigg) = (bc+ca+ab+abc).$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If a,b and c are real number and $ \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c \\ a+b & b+c & c+a \end{vmatrix} $Show that either $a+b+c=0 \: or \: a=b=c$

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Express the following matrix as the sum of a symmetric (B) and skew symmetric matrix (C) $\begin{bmatrix} 3 & -2 & -4 \\ 3 & -2 & -5 \\ -1 & 1 & 2 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation : $ (1+x^2)\large\frac{dy}{dx}$$+2xdy=\large\frac{1}{1+x^2},$ given y = 0 when x = 1.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Prove, using properties of determinants $ \begin{vmatrix} y+k & y & y \\ y & y+k & y \\ y & y & y+k \end{vmatrix} = k^2(3y+k) $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that cards are a king, queen and a jack

asked Feb 5, 2013 by meena.p

0 answers

Evaluate : $ \int_0^1 \log \bigg(\large\frac{1}{x}-1\bigg)$$dx $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane through the points (-1,1,1) and (1,-1,1) perpendicular to the plane x+2y+2z = 5

asked Feb 5, 2013 by meena.p

1 answer

Using properties of determinants, solve the following for x : $ \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Let $ \bar{a},\bar{b},\;and\;\bar{c}$ be three vectors such that $|\bar{a}|=3,|\bar{b}|=4,|\bar{c}|=5$ and each one of them being perpendicular to sum of the other two, find $ |\bar{a}+\bar{b}+\bar{c}|$

asked Feb 4, 2013 by meena.p

1 answer

Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Solve the following differential equation: $ (1+y^2)(1+\log x)dx+xdy=0$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the area included between the curves $ (x-1)^2+y^2=1\;and\;x^2+y^2=1$

asked Feb 4, 2013 by meena.p

0 answers

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

using properties of determinants, prove that $ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix} = (ab+bc+ca)^2 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Using elements transformation find the inverse of $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

If none of a,b and c is zero, using properties of determinants, prove that $ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix} = (bc=ca+ab)^3 $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Principal and staff of a school decided to award prizes to their students for three values Honesty (x), cleanliness (y) and punctuality (z) in two groups. Group A (upto class VIII) and group B (IX-XII). It is decided that Rs. 12000 for three values (x,y,z) for 3,4,5 students of group A and Rs. 11040 for 5,4,3 students of group B respectively. If all the three prizes together amount to Rs. 2880 then, (i) Represent above situation by a matrix equation and form linear equation using matrices. (ii)Is it possible to solve the system of linear equations so obtained using matrices.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

Assuming that petrol burnt per hour in driving a motor boat varies as the cube of its velocity. Show that the most economical speed when going against a current of k km/hour is $ \large\frac{3k}{2} $ km/hour.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

$\Large\int \frac {dx}{x\sqrt{1-x^3}} =$\[\begin {array} {1 1} (a)\;\frac{1}{3} log \bigg | \frac {\sqrt {1-x^2}+1}{\sqrt {1-x^2}-1}\bigg | & \quad (b)\;\frac{1}{3} log \bigg |\frac{\sqrt {1-x^2}-1}{\sqrt {1-x^2}+1}\bigg| & \quad \\(c)\;\frac{2}{3} log \bigg |\frac{1}{\sqrt {1-x^3}}\bigg| & \quad(d)\;\frac{1}{3} log | 1-x^3 | \end {array}\]

asked Jan 31, 2013 by meena.p

0 answers

There are two families P and Q. There are 3 men, 3 women and 12 children in family P and 2 men, 2 women and 4 children in family Q. The recommended daily allowance for calories is : Man : 2400, woman : 2000, child: 1400 and man : 60 g for proteins is : woman: 40 g and child: 35 g. (i) Represent the above information by matrices. Using matrix multiplication, calculate the total requirement of calories and proteins of each of the two families.

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove that $ \begin{bmatrix} 2ab & a^2 & b^2 \\ a^2 & b^2 & 2ab \\ b^2 & 2ab & a^2 \end{bmatrix} = -(a^3+b^3)^2$

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Using elementary transformation, find the inverse of the matrix $\begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $

asked Jan 30, 2013 by thanvigandhi_1

1 answer

The surface area of a spherical bubble is increasing at the rate of 2 $cm^2$/sec. Find the rate at which the volume of the bubble is increasing at the instant its radius is 6 cm.

asked Jan 30, 2013 by fingeazy

0 answers

The total monthly earnings of a worker in a factory is given by $ I=p+qx+ry$, where X denotes the number of points of honesty and Y denotes the number of points of punctuality. Data for three months are as follows : (a) represent the above data by linear equations and write its matrix form. (b) Is it possible to solve the system of equations so obtained using matrices?

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If the line ax+by+c = 0 is normal to the curve xy = 1 then \[(a)\;a>0,b>0 \qquad (b)\;a<0,b<0 \qquad(c)\;a<0,b>0\qquad(d)\;a<0,b<0.\]

asked Jan 28, 2013 by meena.p

1 answer

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

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{bmatrix},$ show that $ A^2-7A+10I=0.$ Hence , find $ A^{-1} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

(i)A sum of rupees ten thousand is put into three investments at the rate of 10%, 12% and 15% p.a. The combined income of first and second investment is Rs. 620 more of the income of third investment. If the combined income is Rs. 2420, then find the investment in each using matrices.(ii)"One can buy many things with very little savings".Explain the importance of savings in student's life.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Represent the following problem by a system of linear equations. Rs.188000 is the cost of 3 cycles, 1 motorbike and 1 car, the cost of 2 cycles, 2 motorbikes and 1 car is Rs.228000. The cost of 4 cycles 2 cars and 1 motorbike is Rs. 330000. Use matrix to find the cost of each.

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Is the function $ f(x)=\Large\frac{3x+4\tan x}{x}$ continuous at x = 0? If not, how may the function be defined to make it continuous at this point.

asked Jan 25, 2013 by meena.p

1 answer

Solve for x : $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1} \bigg(\large\frac{8}{31} \bigg) $

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Prove that $ 2\tan^{-1} \large\frac{1}{5}$$ + \tan^{-1} \large\frac{1}{8}$$ = \tan^{-1}\large \frac{4}{7} $

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Prove that $\begin{bmatrix} (a+1) & (a+2) & (a+2) & 1 \\ (a+2) & (a+3) & (a+3) & 1 \\(a+3) & (a+4) & (a+4) & 1 \end{bmatrix}=-2$

asked Jan 24, 2013 by meena.p

0 answers

Let $ \overrightarrow a, \overrightarrow b, \overrightarrow c$ be three vectors of magnitude 3, 4, 2 respectively. If ech one is perpendicular to sum of other two vectors, prove that $ | \overrightarrow a + \overrightarrow b + \overrightarrow c | = \sqrt {29} .$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If $ \cos^{-1}\frac{x}{a}+\cos^{-1}\frac{y}{b}=\alpha,$prove that $\frac{x^2}{a^2}-\frac{2xy}{ab}\cos \alpha+\frac{y^2}{b^2}=\sin^2\alpha.$

asked Jan 23, 2013 by meena.p

1 answer

If $f(x)=log \big(\frac{1+x}{1-x}\big)$ show that $f(x)+f(y)=f \big(\frac{x+y}{1+xy}\big)$

asked Jan 23, 2013 by meena.p

0 answers

Two firms X and Y decided to award prizes to their employees for three norms Obedience (O), Punctual (P), Quality of work (Q). Firm X decided to award Rs. 40000 for the three values to 2, 4, 7 employees respectively while Y decided to award Rs. 51000 to 4, 2, 8 employees respectively. If all the three prizes together amount to Rs. 8750, then (i) Represent the above situation by a matrix equation and form linear equation using matrix multiplication. (ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why?

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Ask Questions, Get Answers