Recent questions tagged easy

Show that the relation $R$ defined in the set $A$ of all polygons as $R = \{(P_1, P_2) :\: P_1\ and \;P_2$ have same number of sides$\}$, is an equivalence relation. What is the set of all elements in $A$ related to the right angle triangle $T$ with sides $3, 4$ and $5$?

asked Nov 8, 2012 by vaishali.a

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

asked Nov 8, 2012 by vaishali.a

1 answer

Is the function f defined by $f(x) = \left\{\begin{array}{l l} x, & \quad \text{if $x$ $ \leq $ 1}\\ 5, & \quad \text{if $x$ > 1}\\ \end{array} \right.$ continuous at $(x = 0)$? At $(x = 1)$? At $(x = 2)$?

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Show that each of the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(i) R = \{(a,b) |a-b|$ is a multiple of 4 $\}$ is an equivalence relation. Find the set of all elements related to 1.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in the set $A= \{1,2,3,4,5\} $given by $R = \{(a, b) : |a – b| \,is\, even \} $, is an equivalence relation. Show that all the elements of $\{1, 3, 5\} $ are related to each other and all the elements of $\{2, 4\}$ are related to each other. But no element of $ \{1, 3, 5 \} $ is related to any element of $\{2, 4\}$.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in the set $A$ of all the books in a library of a college, given by ( $R = \{ (x, y) : x\;$ and $\; y\;$ have same number of pages$\}$ ) is an equivalence relation.

asked Nov 7, 2012 by vaishali.a

1 answer

Check whether the relation $R$ in $R$ defined by $R = {(a, b) : a \leq b^3}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in $R$ defined as $R = {(a, b) : a \leq b} $, is reflexive and  transitive but not symmetric.

asked Nov 7, 2012 by vaishali.a

1 answer

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Differentiate the function with respect to x: $cos\;(sin x)$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x: $ \; sin ( x^2 + 5 ) $

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Show that the relation $R$ in the set $R$ of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Examine the following functions for continuity. $f(x) = | \;x - 5\;|$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = x-5$

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by $ f (x) = cos (x^2) $ is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by $ g (x) = x – [x] $ is discontinuous at all integral points. Here $ [x] $ denotes the greatest integer less than or equal to $x$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Is the function defined by $ f (x) = x^2 - \sin\; x + 5 $ continuous at $ x =\pi $ ?

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Prove that the function $ f (x) = x^n $ is continuous at $ x = n $, where n is a positive integer.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer. The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are:

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the shortest distance between lines $\hat{r} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda ( \hat{i} - 2\hat{j} + 2\hat{k} )$ and $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the vector equation of the line passing through $(1, 2, 3)$ and perpendicular to the plane $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the coordinates of the points $A, B, C, D$ be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines $AB$ and $CD$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of a line parallel to x-axis and passing through the origin.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Let $ A\ =\ R–\ {3}$andB=R-{1}.Considerthefunctionoff:A

asked Nov 2, 2012 by vaishali.a

0 answers

If $\theta$ is the angle between any two vectors $ \overrightarrow{a} and \overrightarrow{b} ,$ then $|\overrightarrow{a}.\overrightarrow{b} | = | \overrightarrow{a} \times \overrightarrow{b} | $ when $\theta$ is equal to

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Let \[ F :R->R: f(x) =2x+1 \] and \[ g:R->R:g(x)=x^2 –2 \] find (I) gof (II) fog

asked Nov 2, 2012 by vaishali.a

0 answers

Show that function $ f\: N\ ->N$, given by $ f(x)\ =\ 2x$, is one – one.

asked Nov 2, 2012 by vaishali.a

0 answers

If θ is the angle between two vectors $$\overrightarrow{a} and \overrightarrow{b}$$ when is $$\overrightarrow{a} ⋅ \overrightarrow{b} ≥ 0$$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Prove that $$(\overrightarrow{a} + \overrightarrow{b} ) ⋅ (\overrightarrow{a} + \overrightarrow{b} ) =| \overrightarrow{a} |2 + | \overrightarrow{b} |2$$ if and only if $$\overrightarrow{a} , \overrightarrow{b}$$ are perpendicular, given $$\overrightarrow{a} ≠ 0, \overrightarrow{b} ≠ 0$$

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Given $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c}$$ Find a vector $$\overrightarrow{d}$$ which is perpendicular to both $$\overrightarrow{a} and \overrightarrow{b}, and \overrightarrow{c} ⋅\overrightarrow{d} = 15$$

asked Nov 2, 2012 by anonymous

0 answers

The two adjacent sides of a parallelogram are given. Find the unit vector parallel to its diagonal. Also, find its area.

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Find the position vector of a point tand show that P is the mod point of the line segment

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Show that the points A (1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Find a unit vector parallel to the vector....

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Find the value of x for which $$ x(\hat{i} + \hat{j}+ \hat{k})$$ is a unit vector

asked Nov 2, 2012 by balaji.thirumalai

0 answers

If$$ \overrightarrow {a} = \overrightarrow {b} + \overrightarrow {c} $$ If this is the case, then is it true that $$ |\overrightarrow {a}| = |\overrightarrow {b}| + |\overrightarrow {c}| $$

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Determine the girl’s displacement from her initial point of departure.

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Find the scalar components and magnitude of the vector joining the points $P (x_1, y_1, z_1)$ and $Q (x_2, y_2, z_2)$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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