Recent questions in Relations and Functions

Simplify the boolean expression

asked Apr 16, 2015 by hectordavid1995

1 answer

Evaluate : $\lim \int \limits _0^{\pi} \large\frac{x \tan x }{\sec x . \tan x}$ $dx$

asked Mar 22, 2015 by meena.p

1 answer

If function $f(x) =|x-3| +|x-4|$ , then show that $f(x)$ is not differentiable at $x=3$ and $x=4$

asked Mar 20, 2015 by meena.p

1 answer

Find the inverse of matrix $A=\begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix}$ and hence show that $A^{-1} .A =I$

asked Mar 19, 2015 by meena.p

1 answer

If $a \neq b \neq c$ and $\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end{vmatrix}$ $=0$ , then using properties of determinants, prove that $a+b+c=0$

asked Mar 19, 2015 by meena.p

1 answer

If $\tan ^{-1} x+\tan ^{-1}y+\tan ^{-1} z= \large\frac{\pi}{2}$ $,x,y,z>0$ , then find the value of $xy+yz+zx$

asked Mar 19, 2015 by meena.p

1 answer

There are 3 families A,B and C. The number of men , women and children in these are as under : Dairy expense of men , women and children are $Rs 200, Rs .150$ and $Rs 200$ respectively. Only men and women earn and children or not. using matrix multiplication , calculate the dairy expenses of each family. What impact does more children in the family create on the society ?

asked Mar 19, 2015 by meena.p

1 answer

Write the direction cosines of the normal to the plane $3x+4y+12z=52$

asked Mar 19, 2015 by meena.p

1 answer

Write the value of $\hat i. (\hat j \times \hat k) + \hat j .( \hat k \times \hat i) +\hat k.(\hat i \times \hat j)$ .

asked Mar 19, 2015 by meena.p

1 answer

Write the projection of vector $2 \hat i +3 \hat j - \hat k$ along the vector $\hat i +\hat j$

asked Mar 19, 2015 by meena.p

1 answer

let A = (-1,0,1,2) B=(-4,-2,0,2) and f, g:A->B be functions defined by f(x)=X2-X and g(x)=2| x-1/2 |, -1 x belongs to A. Are f and g equal?

asked Mar 17, 2015 by krishvlk

1 answer

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainer is $\large\frac{8}{9}$ of the curved surface of the whole cone, find the ratio of the line-segment into which the cone’s altitude is divided by the plane.

asked Feb 19, 2015 by meena.p

1 answer

The average of $11,12,13,14$ and x is $13$ . The value of x is

asked Feb 11, 2015 by meena.p

1 answer

Draw a plot showing the variation of photo electric current against the intensity of incident validation on a given photo sensitive surface.

asked Jan 28, 2015 by meena.p

1 answer

The relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q)$ : distance of the point $P$ from the origin is same as the distance of the point $Q$ from the origin $\}$ , is a) Reflexive only b) Symmetry C) both reflexive and symmetry but not transitive d) Is an equivalence relation. Also show that the set of all points related to a point Pis not equal to (0,0) is the circle passing through P with origin as centre.

asked Jun 12, 2014 by balaji.thirumalai

1 answer

Find the equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2x+3y+4z=5$ which is perpendicular to the plane $x-y+z=0$ . Also find the distance of the plane obtained above, from the origin.

asked Mar 25, 2014 by thanvigandhi_1

1 answer

Let $(f:R \to R)$ be defined as $(f(x)=2x+3.)$ Find the function $(g(x):R \to R)$ such that $(g\;o\;f = f\;o\;g = I_R.)$

asked Jan 29, 2014 by balaji

1 answer

If $\ast$ is a binary operation on the set $(\{0, 1, 2, 3, 4, 5\})$ defined 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.$ then draw the composition table for the operation and find the identity element and inverse of $4$ if exists.

asked Jan 27, 2014 by rvidyagovindarajan_1

1 answer

let * be a binaray operation on N given by ab = 1cm (a,b) ,a,b belong to N find 24 and is N,* associative?

asked Oct 4, 2013 by sharon.r.varghese_1

1 answer

If $f:R\rightarrow R$ is defined $f(x)=x^2-3$ then $f^{-1}x$ = ?

asked May 13, 2013 by rvidyagovindarajan_1

1 answer

Let the function $f\;:\;R \rightarrow R$ be defined by $f(x)=\cos x,\forall \;x\;\in R$ . What kind of a function is f?

asked Mar 30, 2013 by balaji.thirumalai

1 answer

Let C be the set of complex numbers. What kind of a mapping defines $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C$ ?

asked Mar 30, 2013 by balaji.thirumalai

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

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.$ Zero is the identity for this operation. True or False?

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$ (iii) Compute $(2 \ast 3) \ast (4 \ast 5)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$ (ii) is $\ast$ commutative?

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Consider a binary operation $\ast$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table (Table 1.2). $\begin{matrix} &1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$ (i) Compute $(23)4$ and $2(3*4)$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statement is true or false. Justify. ii) If $\ast$ is a commutative binary operation on N, then $a \ast (b \ast c) = (c \ast b) \ast a$ .

asked Mar 20, 2013 by balaji.thirumalai

1 answer

State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation $\ast$ on a set N, $a \ast a=a \forall a \in N$

asked Mar 20, 2013 by balaji.thirumalai

1 answer

Find which of the operations given below has identity: $(vi)\;\; a \ast b = ab^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(v)\;\; a \ast b = \large\frac {ab} {4}$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iv)\;\; a \ast b = (a-b)^2$

asked Mar 19, 2013 by meena.p

1 answer