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Recent questions tagged oct-2007
Questions
Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.
tnstate
class12
bookproblem
ch3
exercise3-5
q5
p166
oct-2007
mar-2008
modelpaper
asked
Jun 13, 2013
by
sreemathi.v
1
answer
The marks secured by $400$ students in a Mathematics test were normally distributed with mean $65$. If $120$ students got more marks above $85$, the number of students securing marks between $45$ nd $65$ is
tnstate
class12
bookproblem
p244
objective
q150
modelpaper
oct-2007
asked
Jun 3, 2013
by
poojasapani_1
1
answer
If in a poisson distribution $P(X=0)=k$ then the variance is
tnstate
class12
bookproblem
p243
objective
q142
modelpaper
oct-2007
mar-2007
oct-2008
mar-2009
asked
May 30, 2013
by
poojasapani_1
1
answer
Given $E(X+c)=8$ and $E(X-c)=12$ then the value of $c$ is
tnstate
class12
bookproblem
p242
objective
q131
modelpaper
oct-2006
oct-2007
jun-2009
asked
May 28, 2013
by
poojasapani_1
1
answer
Which of the following is correct?
tnstate
class12
bookproblem
p241
objective
q121
modelpaper
oct-2007
asked
May 27, 2013
by
poojasapani_1
1
answer
The order of $[7]$ in $(Z_{9},+_{9})$ is
tnstate
class12
bookproblem
p240
objective
q117
modelpaper
oct-2006
oct-2007
jun-2008
mar-2009
asked
May 24, 2013
by
poojasapani_1
1
answer
Which of the following is not a binary operation on $R$
tnstate
class12
bookproblem
p240
objective
q113
modelpaper
oct-2007
jun-2008
jun-2009
mar-2010
asked
May 24, 2013
by
poojasapani_1
1
answer
If $\;p\;$ is $T$ and $\;q$ is $F$, then which of the following have the truth value$T$? \[\begin{array}{1 1}(1)p \vee q&(2)\sim p\vee q\\(3)p \vee \sim q&(4)p \wedge\sim q\end{array}\]
tnstate
class12
bookproblem
p240
objective
q107
modelpaper
oct-2007
mar-2010
asked
May 24, 2013
by
poojasapani_1
1
answer
If $f '(x)=\sqrt{x}$ and $f(1)=2$ then $f(x)$ is
tnstate
class12
bookproblem
p239
objective
q100
modelpaper
oct-2007
asked
May 24, 2013
by
poojasapani_1
1
answer
The amount present in a radio active element disintegrates at a rate proportional to its amount .The differential equation corresponding to the above statement is ($k$ is negative)
tnstate
class12
bookproblem
p238
objective
q94
modelpaper
oct-2007
asked
May 23, 2013
by
poojasapani_1
1
answer
The differential equation of the family of lines $y=mx$ is
tnstate
class12
bookproblem
p238
objective
q91
modelpaper
oct-2007
asked
May 23, 2013
by
poojasapani_1
1
answer
The volume generated by rotating the triangle with vertices at $(0,0),(3,0)$ and $(3,3) $ about $x$-axis is
tnstate
class12
bookproblem
p236
objective
q75
modelpaper
oct-2006
oct-2007
jun-2009
asked
May 22, 2013
by
poojasapani_1
1
answer
The area of the region bounded by the graph of $y=\sin x$ and $y=\cos x $ between $x=0$ and $x=\large\frac{\pi}{4}$ is
tnstate
class12
bookproblem
p236
objective
q68
modelpaper
jun-2006
oct-2007
mar-2010
asked
May 22, 2013
by
poojasapani_1
1
answer
The value of $\int\limits_{-\pi/2}^{\pi/2}\large\left(\frac{\sin x}{2+\cos x}\right)$$dx$ is
tnstate
class12
bookproblem
p235
objective
q63
jun-2007
oct-2007
asked
May 21, 2013
by
poojasapani_1
1
answer
The curve $a^{2}y^{2}=x^{2}(a^{2}-x^{2})$ has
tnstate
class12
bookproblem
p234
objective
q53
modelpaper
mar-2007
oct-2007
oct-2009
mar-2010
asked
May 21, 2013
by
poojasapani_1
1
answer
If $u=\log\begin{pmatrix}\large\frac{x^{2}+y^{2}}{xy}\end{pmatrix}$ then $x\large\frac{\partial u}{\partial x}+$$y\large\frac{\partial u}{\partial y}$ is
tnstate
class12
bookproblem
p234
objective
q51
modelpaper
jun-2006
mar-2007
oct-2007
mar-2010
asked
May 21, 2013
by
poojasapani_1
1
answer
The least possible perimeter of a rectangle of area $100m^{2}$ is
tnstate
class12
bookproblem
p233
objective
q39
modelpaper
oct-2007
oct-2008
asked
May 18, 2013
by
poojasapani_1
1
answer
$\;\lim \limits_{x \to \infty}\large\frac{x^{2}}{e^{x}}$ is
tnstate
class12
bookproblem
p232
objective
q31
modelpaper
oct-2007
oct-2008
asked
May 18, 2013
by
poojasapani_1
1
answer
If a normal makes an angle $\theta$ with positive $x$-axis then the slope of the curve at the point where the normal is drawn is
tnstate
class12
bookproblem
p231
objective
q23
sec-a
medium
modelpaper
oct-2007
asked
May 16, 2013
by
poojasapani_1
1
answer
The eccentricity of the hyperbola with asymptotes $x+2y-5=0 ,2x-y+5=0 $ is
tnstate
class12
bookproblem
p276
objective
q114
modelpaper
oct-2006
oct-2007
asked
May 14, 2013
by
poojasapani_1
1
answer
If $\large\frac{1-i}{1+i}$ is a root of the equation $ax^{2}+bx+1=0$ where $a ,b $ are real then $(a , b) $is
tnstate
class12
bookproblem
p273
objective
q79
modelpaper
oct-2007
asked
May 13, 2013
by
poojasapani_1
1
answer
The quadratic equation whose roots are $\pm\;i\sqrt{7} $is
tnstate
class12
bookproblem
p273
objective
q77
modelpaper
oct-2007
asked
May 13, 2013
by
poojasapani_1
1
answer
$z_{1}=4+5i,z_{2}=-3+2i$ then $\large\frac{z_{1}}{z_{2}}$is
tnstate
class12
bookproblem
p272
objective
q73
modelpaper
oct-2006
oct-2007
asked
May 12, 2013
by
poojasapani_1
1
answer
The polar form of the complex number $(i^{25})^{3}$ is
tnstate
class12
bookproblem
p271
objective
q66
modelpaper
mar-2006
oct-2006
mar-2007
oct-2007
jun-2009
asked
May 12, 2013
by
poojasapani_1
1
answer
The shortest distance between the parallel lines $ \large\frac{x-3}{4}=\frac{y-1}{2}=\frac{z-5}{-3} $ and $\large\frac{x-1}{4}=\frac{y-2}{2}=\frac{z-3}{3}$ is
tnstate
class12
bookproblem
p270
objective
q52
modelpaper
oct-2007
asked
May 11, 2013
by
poojasapani_1
1
answer
The point of intersection of the lines $\large\frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} $ and $\large\frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2}$ is
tnstate
class12
bookproblem
p269
objective
q49
modelpaper
oct-2007
jun-2009
asked
May 11, 2013
by
poojasapani_1
1
answer
If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \;\overrightarrow{QS}=-\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow {2k},$ then the area of the quadrilateral $PQRS$ is
tnstate
class12
bookproblem
p266
objective
q30
modelpaper
oct-2006
oct-2007
asked
May 9, 2013
by
poojasapani_1
0
answers
If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if
tnstate
class12
bookproblem
p265
objective
q21
modelpaper
oct-2006
oct-2007
mar-2008
oct-2009
asked
May 8, 2013
by
poojasapani_1
1
answer
Inverse of $\begin{bmatrix}2& -1 \\-5 & 3 \end{bmatrix}$ is
tnstate
class12
bookproblem
p264
objective
q15
modelpaper
mar-2006
oct-2007
oct-2008
oct-2009
asked
May 7, 2013
by
poojasapani_1
1
answer
If $A$ and $B$ are any two matrices such that $AB=O$ and $A$ is non-singular, then
tnstate
class12
bookproblem
p264
objective
q13
modelpaper
mar-2007
oct-2007
mar-2008
mar-2009
asked
May 7, 2013
by
poojasapani_1
1
answer
If $A$ is a matrix of order $3$, then det($kA$)
tnstate
class12
bookproblem
p264
objective
q11
modelpaper
oct-2006
oct-2007
jun-2009
asked
May 7, 2013
by
poojasapani_1
1
answer
If $A$ is a scalar matrix with scalar $k \neq 0$ of order $3$ than $A^{-1}$ is
tnstate
class12
bookproblem
p263
objective
q6
modelpaper
oct-2007
mar-2008
jun-2008
oct-2008
mar-2010
asked
May 7, 2013
by
poojasapani_1
1
answer
Evaluate the limit for the following if exists. $\;\lim \limits_{x \to 1 } x^{\large\frac{1}{x-1}}$
tnstate
class12
bookproblem
ch5
sec-1
exercise5-6
p34
q1
q1-10
modelpaper
oct-2006
oct-2007
jun-2009
asked
May 6, 2013
by
poojasapani_1
1
answer
Let $P$ be a point on the curve $y=x^{3}$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.
tnstate
class12
bookproblem
ch5
sec-1
exercise5-2
p18
q7
modelpaper
oct-2007
mar-2010
asked
May 3, 2013
by
poojasapani_1
1
answer
Find the area of the region bounded by the ellipse $\large\frac{x^{2}}{9}+\frac{y^{2}}{5}$$=1$ between the two latus rectums.
tnstate
class12
bookproblem
ch7
sec-1
exercise7-4
p117
q7
modelpaper
oct-2007
asked
Apr 27, 2013
by
poojasapani_1
1
answer
Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{\pi}{6}}^{\large\frac{\pi}{3}}\large\frac{dx}{1+\sqrt{\tan x}}$
tnstate
class12
bookproblem
ch7
sec-1
exercise7-2
p98
q10
modelpaper
oct-2007
asked
Apr 27, 2013
by
poojasapani_1
1
answer
Trace the curve $y$=$x^{3}$ Discuss the following curves for extence,symmetry,Asymptotes and loops
tnstate
class12
bookproblem
ch6
sec-1
exercise6-2
p78
q1
modelpaper
oct-2006
jun-2007
oct-2007
jun-2008
oct-2008
asked
Apr 24, 2013
by
poojasapani_1
1
answer
The overall percentage of passes in a certain examination is $80$.If $6$ candidates appear in the examination what is the probability that atleast $5$ pass the examination.
tnstate
class12
bookproblem
ch10
sec-1
exercise10-3
p215
q5
modelpaper
oct-2007
asked
Apr 21, 2013
by
poojasapani_1
1
answer
Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-2
p211
q7
q7-3
modelpaper
mar-2006
oct-2007
mar-2008
asked
Apr 20, 2013
by
poojasapani_1
1
answer
Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$
tnstate
class12
bookproblem
ch3
exercise3-4
q4
q4-1
p157
oct-2007
may-2008
may-2010
modelpaper
asked
Apr 16, 2013
by
geethradh
1
answer
Solve the following $(x^{2}+y^{2})dx+3xy dy$=$0$
tnstate
class12
bookproblem
ch8
sec-1
exercise8-3
p137
q5
modelpaper
oct-2007
asked
Apr 15, 2013
by
poojasapani_1
1
answer
Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a tringle of constant area.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q7
modelpaper
mar-2006
oct-2007
asked
Apr 14, 2013
by
poojasapani_1
1
answer
A cable of a suspension bridge is in the form of a parabola whose span is $40mts$ . The road way is $5mts$ below the lowest point of the cable . if an extra support is provided across the cable $30mts$ above the ground level, Find the length of the support if the height of the pillars are $55mts$.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-1
p193
q5
jun-2006
oct-2007
modelpaper
asked
Apr 9, 2013
by
poojasapani_1
1
answer
Find the vector and cartesian equations of the plane through the points $(1 , 2 , 3 )$and $(2 , 3 , 1 )$ perpendicular to the plane $ 3x-2y+4z-5=0$
modelpaper
tnstate
class12
bookproblem
ch2
sec-1
exercise2-8
p111
q11
mar-2006
oct-2006
oct-2007
jun-2008
asked
Apr 8, 2013
by
poojasapani_1
1
answer
Prove that sin $(A - B)$= sin $ A$ cos $B$ - cos $A$ sin $B$.
tnstate
class12
bookproblem
ch2
sec-1
exercise2-4
p78
q7
jun-2007
oct-2007
modelpaper
asked
Apr 5, 2013
by
poojasapani_1
1
answer
Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-5
p45
q1
q1-3
oct-2007
mar-2010
modelpaper
sec-b
easy
asked
Mar 30, 2013
by
poojasapani_1
1
answer
A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p36
q10
oct-2007
modelpaper
sec-c
medium
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the adjoint of the following matrices $\begin{bmatrix} 3 & -1 \\2 & -4& \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q1
q1-1
oct-2007
modelpaper
sec-a
easy
asked
Mar 27, 2013
by
poojasapani_1
1
answer
Show that the set G of all positive rationals forms a group under the composition $*$ defined by $a * b = (\large\frac{ab}{3})$ for all $a, b \in G.$
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q5
modelpaper
mar-2006
jun-2006
oct-2007
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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