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Recent questions tagged p30

Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find $F^{-1}$ of the following functions \(F\) from \(S\) to \(T\), if it exists - - $(ii)\;\; F=\{(a,2), (b,1), (c,1)\}$

asked Mar 13, 2013 by sreemathi.v

1 answer

Evaluate:\[\int \limits _{\pi/6}^{\pi/3} \frac{dx}{1+\sqrt {\tan x}}\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int \limits _0 ^ \pi \Large\frac{e^{\cos x}}{[e^{\cos x}+e^{-\cos x}]}dx\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int\limits_0^1 \sqrt{\frac{1-x}{1+x}}dx\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int\limits_0^{\pi/2} \frac {\sqrt {\tan x}}{1+\sqrt {\tan x}}dx\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int\limits_0^{16} \frac{x^{1/4}}{1+x^{1/2}}dx\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int_{-\pi}^\pi (\sin ^{-1}x+x^{295})\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int \limits_0^{\pi /2} \frac{1}{\cos (x-\pi/3) \cos (x-\pi/6)}\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int\limits_0^1 x\sqrt{\large\frac{1-x^2}{1+x^2}}$$dx$

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\large\int\limits_{-\pi}^\pi \frac {2x(1+\sin x)}{1+\cos ^2x}$

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int \limits_0^{\pi/2} log (\cos \theta) d\theta$

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int \limits _0^{\pi/2} \frac{1}{2\cos x+4 \sin x}dx$

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:\[\int_{-1}^1 log \bigg(\large\frac{4-x}{4+x}\bigg)dx\]

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int \limits_3^9 \frac {\sqrt {12-x}}{\sqrt x+\sqrt {12-x}}dx$

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int \limits_{-\pi}^{\pi} x^{20} \sin ^9x dx $

asked Feb 4, 2013 by meena.p

1 answer

Evaluate:$\int \limits_1^4 [\; \left |x-1 \right|+\left |x-2 \right |+\left| x-3\right |\;]\;dx$

asked Feb 4, 2013 by meena.p

1 answer

Let $A = \{1, 2, 3\}$. Then number of equivalence relations containing $(1, 2)$ is

asked Nov 27, 2012 by vaishali.a

1 answer

Let $ A = \{1, 2, 3\}$. Then number of relations containing $(1, 2)\;$ and $\;(1, 3)$ which are reflexive and symmetric but not transitive is

asked Nov 27, 2012 by vaishali.a

1 answer

Let $A=\{\text{-1,0,1,2}\}$ and $B=\{\text{-4,-2,0,2}\} and $f,g: A $\rightarrow B$ be functions defined by $f(x)=x^2-x, \;x \in A$ and $g(x)=2 |x- \frac {1} {2} | -1,\; x \in A$. Are $f$ and $g$ equal?

asked Nov 26, 2012 by vaishali.a

1 answer

Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Show that zero is the identity for this operation and each element $a\neq0$ of the set is invertible with $6-a$ being the inverse of $a$.

asked Nov 22, 2012 by vaishali.a

1 answer

Given a non-empty set \( X,\) let \(\ast :\; P(X)\; \times\; P(X) \to P(X) \) be defined as \(A \ast B = \; ( A-B)\; \cup \; (B-A),\; \forall A, B \in \; P(X).\). Show that the empty set \(\emptyset \) is the identity for the operation $\ast$ and all the elemnets \(A\) of \( P(X) \) are invertible with \( A^{-1} \;= A\).

asked Nov 22, 2012 by vaishali.a

1 answer

Consider the binary operation $\ast :\; R \times R \rightarrow R$ and $o :\; R \times R \rightarrow R$ defined as $a \ast b = | a \text{-b}|$ and \(\;a\;o\;b=a, \forall a,\;b \in R.\) Show that \(\ast\) is commutative but not associative, \(o\) is associative but not commutative. Further, show that \(\forall\; a,\; b,\; c \in R,\; a\; \ast\; (b\; o\; c) = (a \ast b) \;o\; (a \ast c)\). [If it is so, we say that the operation $\ast$ distributes over $o$]. Does $o$ distribute over? Justify your answer.

asked Nov 22, 2012 by vaishali.a

1 answer

Find the number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself.

asked Nov 22, 2012 by vaishali.a

1 answer

Given a non-empty set \(X\), consider the binary operation \(\ast : P(X) × P(X) \to P(X)\) given by \(A \ast B=A \cap B\; \forall A, \) \( B \;in\; P(X),\) where \(P(X)\) is the power set of \(X\). Show that \(X\) is the identity element for this operation and \(X\) is the only invertible element in \(P(X)\) with respect to the operation \(\ast\).

asked Nov 22, 2012 by vaishali.a

1 answer

Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find the inverse of the following function \(F\) from \(S\) to \(T\), if it exists - \[\;\; F=\{(a,3), (b,2), (c,1)\}\]

asked Nov 22, 2012 by vaishali.a

1 answer

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