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CBSE XII
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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
Find all the points of discontinuity of $f$ defined by $f (x) = | x | – | x + 1 |.$
cbse
class12
bookproblem
ch5
sec1
q34
p160
sec-c
medium
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Examine that sin | x | is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q33
p160
sec-b
medium
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Show that the function defined by f (x) = | cos x | is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q32
p160
sec-b
medium
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
Discuss the continuity of the cosine, cosecant, secant and cotangent functions.
cbse
class12
bookproblem
ch5
sec1
q22
p160
sec-c
difficult
math
asked
Nov 5, 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
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below: \[\] \begin{array}{cccc} \textbf{Types} & \textbf{Machine I} & \textbf{Machine II}& \textbf{Machine III}\\ A&12&18&6 \\ B&6&0&9 \end{array} \[\] Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, Formulate the L.P.P and solve to find the maximum profit.
cbse
class12
bookproblem
ch12
misc
q4
p526
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below: \[\]$\begin{array}{cccc} \textbf{Food} & \textbf{Vitamin A} & \textbf{Vitamin B}& \textbf{Vitamin C}\\ X & 1 & 2 &3 \\ Y & 2 & 2 &1 \end{array}$\[\] One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?
cbse
class12
bookproblem
ch12
misc
q3
p526
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Read the details below and Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag? A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
cbse
class12
bookproblem
ch12
misc
q2
p526
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Refer to Example 9 in book ( page 521 - copied below ). (Diet problem) A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A?How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?
cbse
class12
bookproblem
ch12
misc
q1
p525
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
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
Choose the correct answer in the distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is
cbse
class12
bookproblem
ch11
misc
p499
q22
sec-b
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the vector equation of the line passing through (1, 2, -4) and perpendicular to the two lines $\frac{\large x-8}{\large 3} = \frac{\large y+19}{\large -16} = \frac{\large z-10}{\large 7}$ and $\frac{\large x-15}{\large 3} = \frac{\large y-29}{\large 8} = \frac{\large z-5}{\large -5}$
cbse
class12
bookproblem
ch11
misc
p499
q20
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the vector equation of the line passing through $(1, 2, 3)$ and parallel to the planes $\hat{r}. (\hat{i} - \hat{j} + 2\hat{k}) = 5$ and $\hat{r} (3\hat{i} + \hat{j} + \hat{k} ) = 6$
cbse
class12
bookproblem
ch11
misc
p499
q19
sec-c
difficult
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the distance of the point (-1, -5, -10) from the point of intersection of the line $\hat{r} = 2\hat{i} - \hat{j} + 2\hat{k} + \lambda (3\hat{i} + 4\hat{j} + 2\hat{k}) $ and the plane $\hat{r} . (\hat{ i} -\hat{ j} + \hat{k} ) = 5$
cbse
class12
bookproblem
ch11
misc
p499
q18
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If O be the origin and the coordinates of P be $(1, 2, – 3)$, then find the equation of the plane passing through P and perpendicular to OP.
cbse
class12
bookproblem
ch11
misc
p499
q16
sec-b
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the equation of the plane which contains the line of intersection of the planes $\hat{r} . (\hat{i} + 2\hat{j} +3\hat{k}) - 4 = 0$ and $\hat{r} . (2\hat{i} + \hat{j} - \hat{k}) + 5 = 0$ and which is perpendicular to the plane $\hat{r} . (5\hat{i} + 3\hat{j} -6\hat{k}) +8 = 0$
cbse
class12
bookproblem
ch11
misc
p499
q17
sec-b
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If the points $( 1, 1 , p)$ and $(– 3 , 0, 1)$ be equidistant from the plane $\hat{r} . (3\hat{i} +4\hat{j} -12\hat{k} +13) = 0$ then find the value of $p$.
cbse
class12
bookproblem
ch11
misc
p498
q14
sec-c
difficult
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the equation of the plane passing through the point $( -1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.
cbse
class12
bookproblem
ch11
misc
p498
q13
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the coordinates of the point where the line through $(3, – 4, – 5)$ and $(2, – 3, 1)$ crosses the plane $2x + y + z = 7.$
cbse
class12
bookproblem
ch11
misc
p498
q12
sec-b
medium
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 YZ-plane.
cbse
class12
bookproblem
ch11
misc
p498
q10
sec-b
medium
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
If $ l_1, m_1, n_1$ and $l _2, m_2, n_2 $ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are $m_1n_2-m_2n_1$, $n_1l_2-n_2l_1$, $l_1m_2-l_2m_1$
cbse
class12
bookproblem
ch11
misc
p497
q2
difficult
sec-b
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
What is the value of $$\hat{i} (\hat{j}. \hat{k}) \hat{j} (\hat{i}. \hat{k}) \hat{k} (\hat{j}. \hat{i})?$$
cbse
class12
bookproblem
sec-a
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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
If $$\overrightarrow{a} ,\overrightarrow{b} , \overrightarrow{c}$$ are mutually perpendicular vectors of equal magnitudes, show that the vector $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}$$ is equally inclined to $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c} $$.
cbse
class12
ch10
sec-b
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
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $1 / \sqrt{3}, 1 / \sqrt{3}$ and $1 / \sqrt{3} $
cbse
class12
bookproblem
sec-a
math
asked
Nov 2, 2012
by
balaji.thirumalai
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
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