Recent questions tagged sec-b

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

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

If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]

asked Mar 15, 2013 by sreemathi.v

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

Using the properties of determinants,\[\begin{vmatrix}a^2+2a &2a+1 & 1\\2a+1 & a+2 & 1\\3 & 3 & 1\end{vmatrix}=(a-1)^3\]

asked Mar 15, 2013 by sreemathi.v

1 answer

What is the value of the function: $\large \frac{1}{4} $$\sin^{-1}\large\frac{2\sqrt 2}{3}$$+\sin^{-1}\large\frac{1}{3} $

asked Mar 14, 2013 by balaji.thirumalai

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

What is the value of $\tan^{-1}\large \frac{2}{11}$$ +tan^{-1} \large \frac{7}{24}$?

asked Mar 14, 2013 by balaji.thirumalai

1 answer

Using properties of determinants,solve for x,\[\begin{vmatrix}a+x & a-x& a-x\\a-x & a+x & a-x\\a-x & a-x & a+x\end{vmatrix}=0\]

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(vi)\;\; a \ast b = {ab}^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(v)\;\; a \ast b = \frac{ab}{4}$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iv)\;\; a \ast b = (a-b)^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iii)\;\; a \ast b = a+ab$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(ii)\;\; a \ast b = a^2+b^2 $ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

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

By using the properties of determinants show that $ (ii) \quad \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 Mar 6, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2\\4 & 1\\5 & 0\end{bmatrix},B=\begin{bmatrix}1 & 2\\6 & 4\\7 & 3\end{bmatrix},then\;verify\;that:(ii)\quad(A-B)'=A'-B'$.

asked Mar 6, 2013 by sreemathi.v

1 answer

$A=\begin{bmatrix}0 & -1 & 2\\4 & 3 & -4\end{bmatrix}\;and\;B=\begin{bmatrix}4 & 0\\1 & 3\\2 & 6\end{bmatrix},then\;verify \;that:(ii)\quad(AB)'=B'A'$

asked Mar 6, 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

Check the injectivity and surjectivity of the following functions:(iv) $f : N\to N\; given\; by\; f(x)\; = x^3 $

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: $f : R\to R $ given by $ f(x)\; = x^2 $

asked Mar 5, 2013 by meena.p

1 answer