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Recent questions tagged sec3
Questions
Find the least positive integer $\mathit{n}$ such that $\left ( \large\frac{1+\mathit{i}}{1-\mathit{i}} \right )^{\mathit{n}}$$ = 1$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q3
p130
asked
Apr 1, 2013
by
geethradh
1
answer
Find the real and imaginary parts of the following complex numbers: $\left ( 2+i \right )\left ( 3-2i \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
q2
q2-3
p130
asked
Apr 1, 2013
by
geethradh
1
answer
Find the real and imaginary parts of the following complex numbers: $\large\frac{2+5i}{4-3i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q2
q2-2
asked
Apr 1, 2013
by
geethradh
1
answer
Find the real and imaginary parts of the following complex numbers: $\large\frac{1}{1+i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q2
q2-1
asked
Apr 1, 2013
by
geethradh
1
answer
Express the following in the standard form $a + ib$: $\large\frac{i^{4}+i^{9}+i^{16}}{3-2i^{8}-i^{10}-i^{15}}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-4
asked
Apr 1, 2013
by
geethradh
1
answer
Express the following in the standard form $a + ib$: $\left ( -3+i \right )\left ( 4-2i \right )$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-3
asked
Apr 1, 2013
by
geethradh
1
answer
Express the following in the standard form $a+ib$: $\large\frac{\left ( 1+i \right )\left ( 1-2i \right )}{1+3i}$
tnstate
class12
bookproblem
ch3
sec3
exercise3-1
p130
q1
q1-2
asked
Apr 1, 2013
by
geethradh
1
answer
Express the following in the standard form $a + ib$: $\large\frac{2\left ( i-3 \right )}{\left ( 1+i \right )^{2}}$
tnstate
class12
bookproblem
ch3
sec3
q1
q1-1
p130
exercise3-1
asked
Apr 1, 2013
by
geethradh
1
answer
Express the following in the standard form $a + ib$: $\frac{2(i-3)}{(1+i)^2}$
class12
tnstate
bookproblem
ch3
sec3
ex3-1
q1
q1-1
p130
asked
Apr 1, 2013
by
balaji.thirumalai
0
answers
State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)
cbse
class12
ch1
sec3
p18
sec-a
bookproblem
q5
q5-2
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)
class12
cbse
ch1
sec3
q5
q5-1
easy
sec-a
p18
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f . g) oh = (foh) . (goh)\]
cbse
class12
ch1
sec3
bookproblem
easy
sec-a
q2
q2-2
math
asked
Mar 19, 2013
by
balaji.thirumalai
1
answer
Find $ gof$ and $fog$, if $f(x) = 8x^3$ and $g(x)=x^\frac{1}{3}$
cbse
class12
bookproblem
ch1
sec3
q3
q3-2
p18
sec-a
easy
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Find \( gof\) and \(fog\), if (ii) \( f(x) = 8x^3\) and \( g(x) = x ^ \frac { 1} {3} \)
cbse
class12
bookproblem
ch1
sec3
q3
q3-2
p18
math
asked
Mar 7, 2013
by
meena.p
1
answer
Find $ gof$ and $fog$, if $ f(x) = |\;x\;|$ , and $ g(x) = |\;5x-2\;| $
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
sec-a
easy
math
asked
Mar 7, 2013
by
meena.p
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iv) \begin{bmatrix} 1 & 5 \\ -1 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-4
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $(iii) \begin{bmatrix} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-3
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ (ii) \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec3
q10
p89
medium
sec-b
q10-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $(ii) (A - A') $ is a skew symmetric matrix.
cbse
class12
bookproblem
ch3
sec3
q8
p89
easy
sec-b
q8-1
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
$ (ii)$ Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix. $
cbse
class12
bookproblem
ch3
sec3
q7
p89
medium
sec-b
q7-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
$(ii) If A = \begin{bmatrix} sin\alpha & cos\alpha \\ -cos\alpha & sin\alpha \end{bmatrix}$ then verify that $A'A = I $
cbse
class12
bookproblem
ch3
sec3
q6
p89
easy
sec-b
q6-2
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix} $$
cbse
class12
bookproblem
ch3
sec3
q5
p88
easy
q5-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix}$, then verify that $ (ii) ( A - B )' = A' - B' $
cbse
class12
bookproblem
ch3
sec3
q3
p88
easy
shortanswer
q3-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
If $A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} $then verify that $ (ii) (A-B)' = A' - B'$
cbse
class12
bookproblem
ch3
sec3
q2
p88
easy
q2-2
sec-b
math
asked
Mar 5, 2013
by
balaji.thirumalai
1
answer
(iii) Find the transpose of the matrix \begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix}
cbse
class12
bookproblem
ch3
sec3
q1
q1-3
p88
easy
sec-a
math
asked
Mar 1, 2013
by
sharmaaparna1
1
answer
Find the transpose of the following matrices: $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$
cbse
class12
bookproblem
ch3
sec3
q1
q1-2
p88
easy
sec-a
math
asked
Mar 1, 2013
by
balaji.thirumalai
1
answer
Find area of the triangle with vertices at the point given in each of the following (-2, -3), (3, 2), (-1, -8)
cbse
class12
bookproblem
ch4
sec3
q1
p122
qp3
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find area of the triangle with vertices at the point given in each of the following (2, 7), (1, 1), (10, 8)
cbse
class12
bookproblem
ch4
sec3
q1
p122
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find equation of line joining (3, 1) and (9, 3) using determinants.
cbse
class12
bookproblem
ch4
sec3
q4
p123
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
Find values of $k$ if area of triangle is $4\; sq. units$ and vertices are $(-2, 0), (0, 4), (0, k)$
cbse
class12
bookproblem
ch4
sec3
q3
p123
qp2
easy
sec-a
math
asked
Feb 23, 2013
by
pady_1
1
answer
A lot of 100 watches is known to have 10 defective watches.If 8 watches are selected(one by one with replacement) at random,what is the probability that there will be at least one defective watch?
cbse
class12
ch13
sec3
q23
p273
short-answer
exercise9-4
math
sec-a
asked
Jan 9, 2013
by
sreemathi.v
1
answer
There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?
cbse
class12
bookproblem
ch13
sec3
q6
p556
sec-b
easy
modelpaper
2012
q24
math
jeemain
probability
asked
Dec 18, 2012
by
thanvigandhi_1
1
answer
In each of the following cases,determine the direction cosines of the normal to the plane and the distance from the origin. $(a)\; z = 2 $
cbse
class12
bookproblem
ch11
sec3
q1
q1-a
p493
easy
sec-a
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector \(3\hat i + 5\hat j - 6 \hat k.\)
cbse
class12
bookproblem
ch11
sec3
q2
p493
medium
sec-b
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the Cartesian equation of the plane $\;(a)\; \overrightarrow r. (\hat i + \hat j - \hat k) = 2$
cbse
class12
bookproblem
ch11
sec3
q3
q3-a
p493
easy
sec-a
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(a)\; 2x + 3y + 4z -12 = 0$
cbse
class12
bookproblem
ch11
sec3
q4
q4-a
p493
sec-a
easy
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the vector and cartesian equations of the planes that passes through the point $(1, 0, -2)$ and the normal to the plane is $ \hat i+\hat j - \hat k $
cbse
class12
bookproblem
ch11
sec3
q5
q5-a
p493
sec-a
easy
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the equations of the planes that passes through three points. $(1, 1, -1), (6, 4, -5), (-4, -2, 3) $
cbse
class12
bookproblem
ch11
sec3
q6
q6-a
p493
sec-a
easy
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the intercepts cut off by the plane $2x + y -z = 5.$
cbse
class12
bookproblem
ch11
sec3
q7
p493
sec-a
easy
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the equation of the plane with intercept 3 on the y - axis and parallel to ZOX plane.
cbse
class12
bookproblem
ch11
sec3
q8
p493
easy
sec-a
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the equation of the plane through the intersection of the planes $3x -y + 2z -4 = 0$ and $x + y + z -2 = 0$ and the point $(2, 2, 1).$
cbse
class12
bookproblem
ch11
sec3
q9
p493
medium
sec-b
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the vector equation of the plane passing through the intersection of the planes $ \overrightarrow r .(2\hat i + 2 \hat j - 3\hat k) = 7, \overrightarrow r .(2\hat i + 5\hat j + 3\hat k ) = 9$ and through the point $(2, 1, 3).$
cbse
class12
bookproblem
ch11
sec3
q10
p493
sec-b
medium
math
asked
Dec 15, 2012
by
thanvigandhi_1
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$x -y + z = 0.$
cbse
class12
bookproblem
ch11
sec3
q11
p493
sec-b
medium
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the angle between the planes whose vector equations are $ \overrightarrow r. ( 2\hat i + 2\hat j - 3\hat k ) = 5 \: and\: \overrightarrow r. ( 3\hat i - 3\hat j + 5\hat k ) = 3. $
cbse
class12
bookproblem
ch11
sec3
q12
p494
sec-b
easy
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(a)\; 7x + 5y + 6z + 30 = 0 \: and \: 3x -y -10z + 4 = 0 $
cbse
class12
bookproblem
ch11
sec3
q13
q13-a
p494
easy
sec-a
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
In the following cases,find the distance of each of the given points from the corresponding given plane (a)Point(0,0,0),Plane $3x-4y+12z-3=0$
cbse
class12
bookproblem
ch11
sec3
q14
q14-a
p494
sec-a
easy
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the angle between two vectors \( \overrightarrow a\) and \( \overrightarrow b\) with magnitudes \( \sqrt 3\) and \(2\) , respectively having \( \overrightarrow a . \overrightarrow b = \sqrt 6.\)
cbse
class12
bookproblem
ch10
sec3
q1
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the angle between the vectors $\hat i - 2\hat j + 3\hat k$ and $ 3\hat i - 2\hat j + \hat k$
cbse
class12
bookproblem
ch10
sec3
q2
p477
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the projection of the vector $ \hat i − \hat j$ on the vector $ \hat i + \hat j $.
cbse
class12
bookproblem
ch10
sec3
q3
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the projection of the vector $ \hat i + 3\hat j + 7\hat k$ on the vector $7\hat i − \hat j + 8\hat k$.
cbse
class12
bookproblem
ch10
sec3
q4
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
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