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Questions >> TN XII Math

TN XII Math

Applications of Matrices and Determinants

Complex Numbers

Analytical Geometry

Differential Calculus Applications - I

Differential Calculus Applications - II

Integral Calculus and its applications

Differential Equations

Discrete Mathematics

Probability Distribution

Objective type Questions and Answers

If $f(x)=x^{2}-4x+5$ on $[0 ,3 ]$ then the absolute maximum value is

asked May 18, 2013 by poojasapani_1

1 answer

The least possible perimeter of a rectangle of area $100m^{2}$ is

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

asked May 18, 2013 by poojasapani_1

1 answer

The function $y=\tan x-x$ is

asked May 18, 2013 by poojasapani_1

1 answer

The function $f(x)=x^{2}$ is decreasing in

asked May 18, 2013 by poojasapani_1

1 answer

The function $f(x)=x^{2}-5x+4$ is increasing in

asked May 18, 2013 by poojasapani_1

1 answer

Which of the following function is increasing in $(0 , \infty)$

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

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

asked May 18, 2013 by poojasapani_1

1 answer

$\;\lim \limits_{x \to \infty}\large\frac{x^{2}}{e^{x}}$ is

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

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

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

asked May 17, 2013 by poojasapani_1

1 answer

The Rolle's constant for the function $y=x^{2}$ on $[-2,2]$ is

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

asked May 16, 2013 by poojasapani_1

1 answer

If $s=r^{3}-4t^{2}+7,$ the velocity when the acceleration is zero is

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

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

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

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

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

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

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

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

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 $x$

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?

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?

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

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

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

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

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

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

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

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

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

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

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

asked May 15, 2013 by poojasapani_1

1 answer

The rate of change of area $A$ of circle of a radius $r$ is

asked May 15, 2013 by poojasapani_1

1 answer

The gradient of the curve $y=-2x^{3}+3x+5$ at $x=2$ is

asked May 15, 2013 by poojasapani_1

1 answer

The normal to the rectangular hyperbola $xy=9$ at $(6,\frac{3}{2})$ meets the curve again at

asked May 14, 2013 by poojasapani_1

1 answer

The area of the triangle formed by the tangent at any point on the rectangular hyperbola $xy=72$ and its asymptotes is

asked May 14, 2013 by poojasapani_1

1 answer

The length of the latus rectum of the rectangular hyperbola $xy=32$ is

asked May 14, 2013 by poojasapani_1

1 answer

One of the foci of the rectangular hyperbola $xy=18$ is

asked May 14, 2013 by poojasapani_1

1 answer

The co-ordinate of the vertices of the rectangular hyperbola $xy=16$ are

asked May 14, 2013 by poojasapani_1

1 answer

The asymptotes of the rectangular hyperbola $xy=c^{2}$ are

asked May 14, 2013 by poojasapani_1

1 answer

Length of the semi-transverse axis of the rectangular hyperbola $xy=8$ is

asked May 14, 2013 by poojasapani_1

1 answer

The eccentricity of the hyperbola with asymptotes $x+2y-5=0 ,2x-y+5=0$ is

asked May 14, 2013 by poojasapani_1

1 answer

The locus of the point of intersection of perpendicular tangents to the hyperbola $\large\frac{x^{2}}{16}-\frac{y^{2}}{9}$ = $1$ is

asked May 14, 2013 by poojasapani_1

1 answer

The product of the perpendiculars drawn from the point $(8 ,0)$ on the hyperbola to its asymptotes is $\large\frac{x^{2}}{64}-\frac{y^{2}}{36}=$ $1$ is

asked May 14, 2013 by poojasapani_1

1 answer

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