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If * is a binary operation defined in $Q^+$ as $ab=\large\frac{ab}{3}$, then the inverse element of 46 is ?

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $[2x-3]=5$, what are the values of $x$ where $[.]$ is greatest integer function

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^2$ $g(x)=sinx$, $\forall x\in R$, then the set of all $x$ satisfying $fogogof(x)=gogof(x)$ is

asked May 7, 2013 by rvidyagovindarajan_1

1 answer

The domain of $y=sin^{-1}(1+3x+2x^2)$ is

asked May 7, 2013 by rvidyagovindarajan_1

1 answer

The value of $\alpha$ for which the function $f(x)=1+\alpha x,\:\:\alpha\neq 0$ is the inverse of itself is:

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

What is the inverse of the function $f(x)=\large\frac{e^x-e^{-x}}{e^x+e^{-x}}$

asked May 2, 2013 by rvidyagovindarajan_1

1 answer

The no. of subsets of a finite set A is 56 more than the no. of subsets of another finite set B. What is the no. of elements of A?

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

If n(A) = 4, n(B) = 6, then the number of 1-1 functions from A to B is

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3,4\}$ and $B=\{1,2\}$, then the number of onto functions from $A$ to $B$ is

asked Apr 28, 2013 by rvidyagovindarajan_1

1 answer

Using vector method prove that : $d)\;\cos (A+B)=\cos A\cos B+\sin A\sin B$

asked Apr 22, 2013 by sreemathi.v

1 answer

Using vector method prove that : $c)\;\cos (A+B)=\cos A\cos B-\sin A\sin B$

asked Apr 22, 2013 by sreemathi.v

1 answer

Using vector method prove that : $b)\;\sin (A-B)=\sin A\cos B-\cos A\sin B$

asked Apr 22, 2013 by sreemathi.v

1 answer

Solve the equation: $\sin^{-1}(6x) + \sin^{-1}(6\sqrt 3 x) =-\large \frac{\pi}{2}$

asked Apr 22, 2013 by smanpreet070

1 answer

The rate at which the population of a city increases at any time is propotional to the population at that time. If there were $1,30,000$ people in the city in $1960 $ and $1,60,000$ in $1990$ what population may be anticipated in $2020$.$[\log_{e}(\large\frac{16}{13})=$$.2070;$$e^{.42}=1.52]$

asked Apr 17, 2013 by poojasapani_1

1 answer

Evaluate $\left|\begin{array}{ccc} 1 & \omega^n & \omega^{2n} \\ \omega^{2n} & 1 & \omega^{n} \\ \omega^n & \omega^{2n} & 1 \end{array}\right|$

asked Apr 4, 2013 by meena.p

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

Evaluate : $ \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$

asked Apr 3, 2013 by meena.p

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

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 : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$

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

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

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

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

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;7x\;+\;3y\;=\;-1\;,\;2x\;+\;y\;=\;0$

asked Mar 29, 2013 by poojasapani_1

1 answer

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

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

Evaluate :$\int\limits_0^{2{\pi}}\large\frac{1}{1+e^{sin x}}$$dx$

asked Mar 20, 2013 by sreemathi.v

1 answer

Consider $( f:R_+ \to [4,\infty)$ given by $(f(x)=x^2 +4)$. Show that $(f)$ is invertible with the inverse $(f^{-1})$ of $(f)$ given by $(f^{-1}(y) = \sqrt {y-4})$,where $R_+$ is the set of all non-negative real numbers.

asked Mar 20, 2013 by sreemathi.v

1 answer

A binary operation $\ast$ on the set $\{0, 1, 2, 3, 4, 5\}$ is defined as
$a * b= \left\{ \begin{array}{1 1} a+b & \quad if\;a+b < 6\\ a+b-6 & \quad if a+b \geq 6 \end{array} \right.$

asked Mar 20, 2013 by balaji.thirumalai

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

\(sin^{-1}\:is\:>\:cos^{-1}x\:in\:which\:interval?\)

asked Mar 15, 2013 by rvidyagovindarajan_1

1 answer

If A+B+C=0,then prove that $\begin{vmatrix}1& cosC &cos B\\cos C& 1 &cos A\\cos B & cos A &1\end{vmatrix}=0.$

asked Mar 15, 2013 by sreemathi.v

1 answer

Evaluate $\tan^{-1} \left (\large \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right )$$,\frac{-1}{\sqrt2} \leq x \leq 1$

asked Mar 14, 2013 by balaji.thirumalai

1 answer

Evaluate $\cot^{-1} \left ( \large \frac {{\sqrt {1+\sin x}}+{\sqrt {1-\sin x}}}{{\sqrt {1+\sin x}}-{\sqrt {1-\sin x}}} \right ) = \large \frac {x}{2}$$ , x \in \left ( 0, \frac{\pi}{4} \right )$

asked Mar 14, 2013 by balaji.thirumalai

1 answer

Find the value of the following function: $tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}$

asked Mar 14, 2013 by balaji.thirumalai

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

What does $cos^{-1} \frac {12}{13} +sin^{-1} \frac{3}{5}$ reduce to?

asked Mar 14, 2013 by balaji.thirumalai

1 answer

What does $sin^{-1} \frac{8}{17} +sin^{-1} \frac{3}{5}$ reduce to?

asked Mar 14, 2013 by balaji.thirumalai

1 answer

What does $2sin^{-1} \frac{3}{5}$ reduce to?

asked Mar 14, 2013 by balaji.thirumalai

1 answer

By using the properties of determinants show that $ (ii) \begin{vmatrix} x+y+2z&x&y \\ z&y+z+2x&y \\ z&x&z+x+2y \end{vmatrix} = 2(x+y+z)^3 $

asked Mar 11, 2013 by sreemathi.v

1 answer

By using the properties of determinants show that $ (ii) \begin{vmatrix} y+k&y&y \\ y&y+k&y \\ y&y&y+k \end{vmatrix} = k^2 (3y+k)$

asked Mar 11, 2013 by sreemathi.v

1 answer

The relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $ R = \{(a,b) |a-b|$ is a multiple of 4$\}$. Is the relation reflexive, symmetrical or transitive?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Show that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda \;and\;\frac{x-4}{5}=\frac{y-1}{2}=z=\mu\;$intersect. Also,find thier point of intersection.

asked Mar 7, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\-2 & 1\end{bmatrix},B=\begin{bmatrix}2 & 3\\3 & -4\end{bmatrix}\;and\;C=\begin{bmatrix}1 & 0\\-1 & 0\end{bmatrix},verify:(ii)\;A(B+C)=AB+AC$

asked Mar 5, 2013 by sreemathi.v

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iv) \begin{bmatrix} 1 & 5 \\ -1 & 2 \end{bmatrix} $

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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

asked Mar 5, 2013 by balaji.thirumalai

1 answer

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