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Recent questions tagged easy
Questions
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 \(5\)?
cbse
class12
bookproblem
ch1
sec1
q13
p6
easy
sec-a
math
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
cbse
class12
bookproblem
ch1
sec1
q11
p6
easy
sec-a
math
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 $(x = 2)$?
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q5
math
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.
cbse
class12
bookproblem
ch1
ex1-1
q9
p6
easy
sec-a
modelpaper
2012
q13
math
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 \(\{2, 4\}\).
cbse
class12
bookproblem
sec1
ch1
q8
p9
easy
sec-b
math
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.
cbse
class12
bookproblem
ch1
sec1
q7
p6
easy
sec-a
math
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.
cbse
class12
bookproblem
ch1
sec1
q5
p6
easy
sec-a
math
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.
cbse
class12
bookproblem
ch1
sec1
q4
p5
sec-a
easy
math
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.
cbse
class12
math
bookproblem
ch1
sec1
q3
p5
easy
sec-a
asked
Nov 7, 2012
by
vaishali.a
1
answer
Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q4
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the function with respect to x: $cos\;(sin x)$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $ \; sin ( x^2 + 5 ) $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q-1
sec-a
easy
math
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.
cbse
class12
bookproblem
ch1
sec1
q2
p5
easy
sec-a
math
asked
Nov 7, 2012
by
vaishali.a
1
answer
Examine the following functions for continuity. $f(x) = | \;x - 5\;|$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-4
math
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$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-3
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity. $f(x) = x-5$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-1
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Show that the function defined by \( f (x) = cos (x^2) \) is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q31
p160
sec-b
easy
math
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 $x$.
cbse
class12
bookproblem
ch5
sec1
q19
p160
sec-b
easy
math
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 $ ?
cbse
class12
bookproblem
ch5
sec1
q20
p160
sec-b
easy
math
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.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q4
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q2
sec-a
easy
math
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 $x=5$.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q1
sec-a
easy
math
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:
cbse
class12
additionalproblem
easy
sec-a
math
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.
cbse
class12
bookproblem
ch11
misc
p498
q11
sec-b
easy
math
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 $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$
cbse
class12
bookproblem
ch11
misc
p498
q9
sec-b
easy
math
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 $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$
cbse
class12
bookproblem
ch11
misc
p498
q7
sec-a
easy
math
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 $k$.
cbse
class12
bookproblem
ch11
misc
p498
q6
sec-a
easy
math
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 $CD$.
cbse
class12
bookproblem
ch11
misc
p498
q5
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the equation of a line parallel to x-axis and passing through the origin.
cbse
class12
bookproblem
ch11
misc
p498
q4
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$
cbse
class12
bookproblem
ch11
misc
p498
q3
sec-a
easy
math
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).
cbse
class12
bookproblem
ch11
misc
p497
q1
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Let \( A\ =\ R–\ {3}\)andB=R-{1}.Considerthefunctionoff:A
additionalproblem
cbse
class12
sec-a
easy
math
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
bookproblem
class12
cbse
sec-a
easy
math
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
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
Show that function \( f\: N\ ->N\), given by \( f(x)\ =\ 2x\), is one – one.
cbse
class12
additionalproblem
ch1
sec-a
easy
math
asked
Nov 2, 2012
by
vaishali.a
0
answers
If θ is the angle between two vectors $$\overrightarrow{a} and \overrightarrow{b}$$ when is $$\overrightarrow{a} ⋅ \overrightarrow{b} ≥ 0$$
cbse
class12
bookproblem
sec-a
easy
math
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 $$\overrightarrow{a} ≠ 0, \overrightarrow{b} ≠ 0$$
cbse
class12
bookproblem
sec-a
easy
math
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 $$\overrightarrow{a} and \overrightarrow{b}, and \overrightarrow{c} ⋅\overrightarrow{d} = 15$$
bookproblem
cbse
class12
sec-a
easy
ch10
math
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.
cbse
class12
bookproblem
sec-a
easy
math
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
cbse
class12
bookproblem
sec-a
easy
math
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.
cbse
class12
bookproblem
sec-b
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a unit vector parallel to the vector....
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
cbse
class12
bookproblem
sec-a
easy
math
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
cbse
class12
bookproblem
sec-a
easy
math
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 $$ |\overrightarrow {a}| = |\overrightarrow {b}| + |\overrightarrow {c}| $$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Determine the girl’s displacement from her initial point of departure.
cbse
class12
bookproblem
sec-a
easy
math
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 $Q (x_2, y_2, z_2)$.
cbse
class12
bookproblem
sec-a
easy
ch10
math
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.
cbse
class12
bookproblem
ch10
concepts
toolbox
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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