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Recent questions in Objective type Questions and Answers
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TN XII Math
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Objective type Questions and Answers
The curve $y^{2}(x-2)=x^{2}(1+x)$ has
tnstate
class12
bookproblem
p234
objective
q48
modelpaper
oct-2008
oct-2009
asked
May 21, 2013
by
poojasapani_1
1
answer
Identify the true statements in the following:
tnstate
class12
bookproblem
p234
objective
q50
asked
May 20, 2013
by
poojasapani_1
1
answer
If $x=r\cos\theta,y=r\sin\theta,$ then $\large\frac{\partial r}{\partial x}$ is equal to
tnstate
class12
bookproblem
p234
objective
q49
modelpaper
jun-2009
asked
May 20, 2013
by
poojasapani_1
1
answer
If $u=\large\frac{1}{\sqrt{x^{2}+y^{2}}},$ then $x\large\frac{\partial u}{\partial x}$$+y\large\frac{\partial u}{\partial y}$ is equal to
tnstate
class12
bookproblem
p233
objective
q47
modelpaper
mar-2008
jun-2009
asked
May 20, 2013
by
poojasapani_1
1
answer
If $u=\sin^{-1}\begin{pmatrix}\large\frac{x^{4}+y^{4}}{x^{2}+y^{2}}\end{pmatrix}$ and $f=\sin u$ then $f$ is a homogeneous function of degree
tnstate
class12
bookproblem
p233
objective
q46
asked
May 20, 2013
by
poojasapani_1
1
answer
If $u=x^{y}$ then$\large\frac{\partial u}{\partial x}$ is equal to
tnstate
class12
bookproblem
p233
objective
q45
modelpaper
oct-2008
asked
May 20, 2013
by
poojasapani_1
1
answer
The curve $y=ax^{3}+bx^{2}+cx+d$ has a point of inflexion at $x=1$ then
tnstate
class12
bookproblem
p233
objective
q44
modelpaper
jun-2006
asked
May 20, 2013
by
poojasapani_1
1
answer
The point of inflexion of the curve $y=x^{4} $ is at
tnstate
class12
bookproblem
p233
objective
q43
asked
May 20, 2013
by
poojasapani_1
1
answer
Which of the following curves is concave down ?
tnstate
class12
bookproblem
p233
objective
q42
modelpaper
mar-2008
jun-2009
asked
May 20, 2013
by
poojasapani_1
1
answer
The curve $y=e^{-x} $ is
tnstate
class12
bookproblem
p233
objective
q41
asked
May 20, 2013
by
poojasapani_1
1
answer
If $f(x)=x^{2}-4x+5$ on $[0 ,3 ]$ then the absolute maximum value is
tnstate
class12
bookproblem
p233
objective
q40
asked
May 18, 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
In a semi circle of diameter $4$cm a rectangle is to be inscribed . The maximum area of the rectangle is
tnstate
class12
bookproblem
p233
objective
q38
modelpaper
mar-2006
asked
May 18, 2013
by
poojasapani_1
1
answer
The function $y=\tan x-x $ is
tnstate
class12
bookproblem
p233
objective
q37
asked
May 18, 2013
by
poojasapani_1
1
answer
The function $f(x)=x^{2}$ is decreasing in
tnstate
class12
bookproblem
p232
objective
q36
modelpaper
jun-2009
asked
May 18, 2013
by
poojasapani_1
1
answer
The function $f(x)=x^{2}-5x+4$ is increasing in
tnstate
class12
bookproblem
p232
objective
q35
asked
May 18, 2013
by
poojasapani_1
1
answer
Which of the following function is increasing in $(0 , \infty)$
tnstate
class12
bookproblem
p232
objective
q34
modelpaper
oct-2006
asked
May 18, 2013
by
poojasapani_1
1
answer
If$f(a)=2;f '(a)=1;(g)=(a)=-1;g '(a)=2$ then the value of $\;\lim \limits_{x \to 2}\Large\frac{g(x)f(a)-g(a)f(x)}{x-a}$ is
tnstate
class12
bookproblem
p232
objective
q33
modelpaper
jun-2008
asked
May 18, 2013
by
poojasapani_1
1
answer
$\;\lim \limits_{x \to 0}\Large\frac{a^{x}-b^{x}}{c^{x}-d^{x}}$ is
tnstate
class12
bookproblem
p232
objective
q32
modelpaper
mar-2007
oct-2009
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
The value of$'c'$ of Lagranges Mean Value Theorem for $f(x)=\sqrt{x}$ when $a=1$ and $b=4$ is
tnstate
class12
bookproblem
p232
objective
q30
asked
May 17, 2013
by
poojasapani_1
1
answer
The value of $c$ in Rolle's Theorem for the function $f(x)=\cos\large\frac{x}{2}$ on $[\pi,3]$ is
tnstate
class12
bookproblem
p232
objective
q29
modelpaper
mar-2006
mar-2008
asked
May 17, 2013
by
poojasapani_1
1
answer
The $'c'$ of Lagranges Mean Value Theorem for the function $f(x)=x^{2}+2x-1;a=0,b=1$ is
tnstate
class12
bookproblem
p232
objective
q28
modelpaper
mar-2009
asked
May 17, 2013
by
poojasapani_1
1
answer
The Rolle's constant for the function $y=x^{2}$ on $[-2,2] $ is
tnstate
class12
bookproblem
p231
objective
q27
asked
May 16, 2013
by
poojasapani_1
1
answer
If the velocity of a particle moving along a straight line is directly proportional to the square of its distance from a fixed point on the line. Then its acceleration is proportional to
tnstate
class12
bookproblem
p231
objective
q26
sec-a
medium
asked
May 16, 2013
by
poojasapani_1
1
answer
If $s=r^{3}-4t^{2}+7,$ the velocity when the acceleration is zero is
tnstate
class12
bookproblem
p231
objective
q25
sec-a
easy
modelpaper
oct-2006
mar-2007
oct-2009
asked
May 16, 2013
by
poojasapani_1
1
answer
The value of $'a'$ so that the curves $y=3e^{x}$ and $y=\large\frac{a}{3}e^{x}$ intersect orthogonally is
tnstate
class12
bookproblem
p231
objective
q24
sec-a
medium
asked
May 16, 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
For the curve $x=e^{t}\cos t: y=e^{t}\sin t$ the tangent line is parallel to the $x$-axis when $t$ is equal to
tnstate
class12
bookproblem
p231
objective
q22
sec-a
medium
asked
May 16, 2013
by
poojasapani_1
1
answer
The gradient of the tangent to the curve $y=8+4x-2x^{2}$ at the point where the curve cuts the $y$-axis is
tnstate
class12
bookproblem
p231
objective
q20
sec-a
easy
asked
May 16, 2013
by
poojasapani_1
1
answer
The Angle between the parabolas $y^{2}=x$ and $x^{2}=y$ at the origin is
tnstate
class12
bookproblem
p231
objective
q21
sec-a
medium
asked
May 16, 2013
by
poojasapani_1
1
answer
If the volume of an expanding cube is increasing at the rate of $4cm^{3}/sec $ then the rate of change of surface area when the volume of the cube is $8$ cubic cm is
tnstate
class12
bookproblem
p231
objective
q19
sec-a
medium
asked
May 16, 2013
by
poojasapani_1
1
answer
If $y=6x-x^{3}$ and $x$ increases at the rate of $5$ units per second, the rate of change of slope when $x=3 $ is
tnstate
class12
bookproblem
p231
objective
q18
sec-a
easy
asked
May 16, 2013
by
poojasapani_1
1
answer
The radius of a cylinder is increasing at the rate of $2$ cm/sec and its altitude is decreasing at the rate of $3$cm/sec . The rate of change of volume when the radius is $3$cm and the altitude is $5$cm is
tnstate
class12
bookproblem
p230
objective
q17
modelpaper
jun-2007
asked
May 15, 2013
by
poojasapani_1
1
answer
For what values of $x$ is the rate of increase of $x^{3}-2x^{2}+3x+8$ is twice the rate of increase of $x$
tnstate
class12
bookproblem
p230
objective
q16
asked
May 15, 2013
by
poojasapani_1
1
answer
What is the surface area of a sphere when the volume is increasing at the same rate as its radius?
tnstate
class12
bookproblem
p230
objective
q15
modelpaper
mar-2010
asked
May 15, 2013
by
poojasapani_1
1
answer
If the length of the diagonal of a square is increasing at the rate of $0.1 cm/sec.$ What is the rate of increase of its area when the side is $\large\frac{15}{\sqrt{2}} $cm?
tnstate
class12
bookproblem
p230
objective
q14
asked
May 15, 2013
by
poojasapani_1
1
answer
If the normal to the curve $x^{2/3}+y^{2/3}=a^{2/3}$ makes an angle $\theta$ with the $x$-axis then the slope of the normal is
tnstate
class12
bookproblem
p230
objective
q13
asked
May 15, 2013
by
poojasapani_1
1
answer
The parametric equations of the curve $x^{2/3}+y^{2/3}=a^{2/3}$ are
tnstate
class12
bookproblem
objective
p230
q12
asked
May 15, 2013
by
poojasapani_1
1
answer
The angle between the curve $y=e^{mx}$ and $y=e^{-mx}$ for $m>1 $ is
tnstate
class12
bookproblem
p230
objective
q11
asked
May 15, 2013
by
poojasapani_1
1
answer
The angle between the curves $\large\frac{x^{2}}{25}+\frac{y^{2}}{9}=$$1$ and $\large\frac{x^{2}}{8}-\frac{y^{2}}{8}=$$1$ is
tnstate
class12
bookproblem
p230
objective
q10
modelpaper
jun-2007
mar-2009
asked
May 15, 2013
by
poojasapani_1
1
answer
The equation of the normal to the curve $\theta =\large\frac{1}{t}$ at the point $(-3 , -1/3)$ is
tnstate
class12
bookproblem
p229
objective
q9
asked
May 15, 2013
by
poojasapani_1
1
answer
The equation of the tangent to the curve $y=\large\frac{x^{3}}{5}$ at the point $(-1,-1/5)$ is
tnstate
class12
bookproblem
p229
objective
q8
modelpaper
mar-2008
asked
May 15, 2013
by
poojasapani_1
1
answer
The point on the curve $y=3x^{2}-6x-4$ at which the tangent is parallel to the $x$ -axis is
tnstate
class12
bookproblem
p229
objective
q7
asked
May 15, 2013
by
poojasapani_1
1
answer
The slope of the tangent to the curve $y=3x^{2}+3\sin x $ at $x=0 $ is
tnstate
class12
bookproblem
p229
objective
q5
modelpaper
mar-2007
jun-2008
jun-2009
asked
May 15, 2013
by
poojasapani_1
1
answer
The slope of the normal to the curve $y=3x^{2}$ at the point whose $x$ coordinate is $2$ is
tnstate
class12
bookproblem
p229
objective
q6
modelpaper
mar-2006
oct-2006
jun-2007
oct-2009
asked
May 15, 2013
by
poojasapani_1
1
answer
A spherical snowball is melting in such a way that its volume is decreasing at a rate of $1 cm^{3}/min.$ The rate at which the diameter is decreasing when the diameter is $10 cms$ is
tnstate
class12
bookproblem
p229
objective
q4
modelpaper
mar-2010
asked
May 15, 2013
by
poojasapani_1
1
answer
The velocity $v$ of a particle moving along a straight line when at a distance $x$ from the origin is given by $a+by^{2}=x^{2}$ where $a$ and $b$ are constants. Then the acceleration is
tnstate
class12
bookproblem
p229
objective
q3
modelpaper
mar-2009
asked
May 15, 2013
by
poojasapani_1
1
answer
The rate of change of area $A$ of circle of a radius $r$ is
tnstate
class12
bookproblem
p229
objective
q2
modelpaper
oct-2008
asked
May 15, 2013
by
poojasapani_1
1
answer
The gradient of the curve $y=-2x^{3}+3x+5$ at $x=2$ is
tnstate
class12
bookproblem
p229
objective
q1
asked
May 15, 2013
by
poojasapani_1
1
answer
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