Recent questions tagged sec-b

Prove that f: R → R is a bijection given by f(x) =$ x^3$ +3. Find$ {f}^{-1} (x).$ Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by shanthinig

0 answers

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

Prove the determinant $\begin{vmatrix} x & -\sin\alpha & \cos\alpha \\ \sin\alpha & -x & 1 \\ \cos\alpha & 1 & x \end{vmatrix}$ is independent as $\alpha$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $ \begin{vmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ca & bc & (a+b)^2 \end{vmatrix}=2abc(a+b+c)^2$ (Use properties to prove the above)

asked Jan 24, 2013 by meena.p

0 answers

Using properties of Determinants prove that : $ \begin{vmatrix} a^2 & bc & ac+c^2 \\ a^2+ab & b^2 & ac \\ab & b^2+ac & c^2 \end{vmatrix}=4a^2b^2c^2$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $\begin{vmatrix} x-3 & x-4 & x-a \\ x-2 & x-3 & x-b \\ x-1 & x-2 & x-c \end{vmatrix}=0,$ where a,b,c are in A.P

asked Jan 24, 2013 by meena.p

0 answers

If $ \begin{bmatrix} p & q \\ r & -p \end{bmatrix}$ is such that $A^2=1$ then find the value of $1-p^2+qr$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $f: \text{R} \rightarrow \text{R}$ is a bijection given by $f(x) = x^3 + 3$. Find $f^{-1}(x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by pady_1

0 answers

On the set N of natural numbers, define the operation * on N by mn=gcd(m,n) for all m, n$ \varepsilon$ N. Show that is commutative as well as associative.

asked Jan 23, 2013 by meena.p

0 answers

Let X = {1,2,3,4,5,6,7,8,9}. Let $ R_1\;andR_2$ be relations in x given by \[R_1=\{(x,y):x-y\;is\;divisible\;by\;3\}\;and\]\[R_2=\{(x,y)!\{x,y\} \varepsilon \{1,4,7\}or\{x,y\} \varepsilon \{2,5,8\}\]\[or \{x,y\} \varepsilon \{3,6,9\}\}.\; Show\; that \;R_1=R_2.\]

asked Jan 23, 2013 by meena.p

0 answers

Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.

asked Jan 23, 2013 by meena.p

1 answer

Show that the function $ f:N \rightarrow N$ given by $f(x) = x -(-1)^x\;for\;all\;x\; \varepsilon\;N $ is a bijection.

asked Jan 23, 2013 by meena.p

0 answers

Define a binary operation $^$ on the set A = {0,1,2,3,4,5} as \[ab=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\]Show that zero is an identity element for this operation and each element a of the set is invertiable with 6-a being the inverse of a.

asked Jan 23, 2013 by meena.p

0 answers

Let f and g be real valued functions, such that $(fog)(x)=\cos x^3\; and\;(gof)(x)=\cos^3x,$ find the functions f and g.

asked Jan 23, 2013 by meena.p

0 answers

Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.

asked Jan 23, 2013 by meena.p

1 answer

Prove that the inverse of an equivalence relation is an equivalence relation.

asked Jan 23, 2013 by meena.p

0 answers

Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.

asked Jan 23, 2013 by meena.p

1 answer

Let a relation R on the set R of real numbers defined as $(x,y)\; \varepsilon\;R \Leftrightarrow x^24xy+3y^2\;=\;0.$Show that R is reflexive but neither symmetric nor transitive.

asked Jan 23, 2013 by meena.p

0 answers

Let a relation R on the set R of real numbers be defined as $ (a,b) \varepsilon R \Leftrightarrow 1+ ab > 0 for\; all\; a, b\; \varepsilon\; R.$show that R is reflexive and symmetric but not transitive.

asked Jan 23, 2013 by meena.p

0 answers

If the function $ f\;:\;R \rightarrow A $ given by $f(x)=\frac{x^2}{x^2+1}$is surjection, find the set A.

asked Jan 23, 2013 by meena.p

0 answers

Show that the relation "congruence modulo 2" on the set Z (set of integers) is an equivalence relation. Also find the equivalence class of 1.

asked Jan 23, 2013 by meena.p

0 answers

Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$

asked Jan 23, 2013 by meena.p

1 answer

If R is a relation on a set $A(A \neq \phi),$ prove that R is symmetric iff $R^{-1} = R$

asked Jan 23, 2013 by meena.p

0 answers

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

Let f, g be two functions defined by \[f(x)=\frac{x}{x+1},g(x)=\frac{x}{1-x},\;then\;find\;(fog)^{-1}(x)\]

asked Jan 23, 2013 by meena.p

0 answers

If $f(x)=\frac{1+x}{1-x},$show that $f[f(\tan\theta)]= - cot\theta$

asked Jan 23, 2013 by meena.p

0 answers

If $f(x)=\frac{5x+3}{4x-5}\big(x\neq\frac{5}{4}\big),$find g(x) such that $gof(x) = x$

asked Jan 23, 2013 by meena.p

0 answers

Let $f :R \rightarrow R $ defined by $f(x) = (ax^2+b)^3$ find the function $g :R \rightarrow R $ such that $f(g(x)) = g(f(x))$

asked Jan 23, 2013 by meena.p

0 answers

Let $ \int : {R\; \rightarrow \;R}$ be a function defined by $ f(x) = x^2-3x+4,$ for all $x \in R ,$ find the value of $f^{-1}(2)$.

asked Jan 23, 2013 by meena.p

0 answers

Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.

asked Jan 22, 2013 by meena.p

1 answer

If $f(x)=\sin^2x+\sin^2\big(x+\frac{\pi}{3}\big)+\cos x.cos\big(x+\frac{\pi}{3}\big)\;and\;g\big(\frac{5}{4}\big)=1$, then find the value of gof(x)=x.

asked Jan 22, 2013 by meena.p

0 answers

If $f(x)=\frac{x-1}{x+1},(x \neq 1,-1),$ show that $fof^{-1}$ is an identity function.

asked Jan 22, 2013 by meena.p

0 answers

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$show that $\overrightarrow{a} \times \overrightarrow{b}=\overrightarrow{b} \times \overrightarrow{c} =\overrightarrow{c} \times \overrightarrow{a}$.Interpret the result geometrically?

asked Jan 17, 2013 by sreemathi.v

1 answer

Evaluate the following\[\int\frac{(\cos 5x+\cos 4x)}{1-2\cos 3x}dx\]

asked Jan 14, 2013 by sreemathi.v

0 answers

Evaluate the following $\int\frac{dt}{\sqrt {3t-2t^2}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

If the straight line $x\cos\alpha+y\sin\alpha=p$ touches the curve $\Large\frac{x^2}{a^2}\;\;\frac{y^2}{b^2}=\normalsize 1$,then prove that $a^2\cos^2\alpha+b^2\sin^2\alpha=p^2$.

asked Jan 11, 2013 by sreemathi.v

0 answers

A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs300/- per subscriber per year.The company proposes to increase the annual subscription and it is believed that for every increase of Re1/- one subscriber will discontinue the service.Find what increase will bring maximum profit?

asked Jan 11, 2013 by sreemathi.v

0 answers

There are two bags,one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls.A die is thrown.If it shows up 1 or 3,a ball is taken from the 1st bag,but it shows up any other number,a ball is chosen from the second bag.Find the probability of choosing a black ball.

asked Jan 9, 2013 by sreemathi.v

1 answer

A letter is known to have come either from TATA NAGAR or from CALCUTTA.On the envelope,just two consecutive letter TA are visible.What is the probability that the letter came from TATA NAGAR.

asked Jan 9, 2013 by sreemathi.v

2 answers