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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 $I$ is the unit matrix of order $n$ . Where $K\neq 0$ is a constsnt , then adj (KI)=

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a matrix of order $3$ , then det( $kA$ )

asked May 7, 2013 by poojasapani_1

1 answer

The inverse of the matrix $\begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a square matrix of order $n$ then |adj $A$ | is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ = $\begin{bmatrix} 2 & 1 \\3 & 4 \end{bmatrix}$ , than (adj $A)A$ =

asked May 7, 2013 by poojasapani_1

1 answer

If the matrix $\begin{bmatrix} -1 & 3 & 2 \\1 & k & -3 \\1 & 4 & 5 \end{bmatrix}$ has an inverse than the value of $k$

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

asked May 7, 2013 by poojasapani_1

1 answer

If the rank of the matrix $\begin{bmatrix} \lambda & -1 & 0 \\0 & \lambda & -1 \\-1 & 0 & \lambda \end{bmatrix}$ is $2$ , than $\lambda$ is

asked May 7, 2013 by poojasapani_1

1 answer

If A= $\begin{bmatrix} 2& 0& 1 \end{bmatrix}$ than the rank of $AA^{T}$ is

asked May 6, 2013 by poojasapani_1

1 answer

If A= $\begin{bmatrix} 1\\ 2 \\ 3 \end{bmatrix}$ than the rank of $AA^{T}$ is

asked May 6, 2013 by poojasapani_1

1 answer

The rank of the diagonal matrix $\begin{bmatrix} -1 & & \\ & -2 & \\ & & 0\\& & &-4\\ & & & &0 \end{bmatrix}$

asked May 6, 2013 by poojasapani_1

1 answer

The rank of the matrix $\begin{bmatrix} 1 & -1 & 2 \\2 & -2 & 4 \\4 & -4 & 8 \end{bmatrix}$ is

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0}(\cos x)^{\large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0 +} x^{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \large\frac{\pi}{2}\;-} (\tan x)^{\cos x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim \limits_{x \to 1 } x^{\large\frac{1}{x-1}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0+} x^{2}\log_{e}x.$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\cot x}{\cot 2x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\log _{e}x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\frac{1}{x^{2}}-\large 2\tan^{-1}(\frac{1}{x})}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty}\large\frac{\sin\frac{2}{x}}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 2}\large\frac{x^{n}-2^{n}}{x-2}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0}\large\frac{\sin ^{-1} x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\tan x-x}{x- \sin x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x\to 2} \large\frac{\sin \pi x}{2 - x}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $y=12x^{2}-2x^{3}-x^{4}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(\theta)=\sin 2\theta$ in $(0 , \pi )$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{4}-6x^{2}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=2x^{3}+5x^{2}-4x$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{2}-x$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=(x-1)^{1/3}$

asked May 6, 2013 by poojasapani_1

0 answers

Resistance to motion, $F$ , of a moving vehicle is given by, $F=\large\frac{5}{x}$ $+100x.$ Determine the minimum value of resistance.

asked May 6, 2013 by poojasapani_1

1 answer

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius $r$ .

asked May 6, 2013 by poojasapani_1

1 answer

Show that of all the rectangles with a given perimeter the one with the greatest area is a square.

asked May 5, 2013 by poojasapani_1

1 answer

Show that of all the rectangles with a given area the one with smallest perimeter is a square.

asked May 5, 2013 by poojasapani_1

1 answer

Find two positive numbers whose product is $100$ and whose sum is minimum.

asked May 5, 2013 by poojasapani_1

1 answer

Find two numbers whose sum is $100$ and whose product is a maximum.

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $t+ \cos t$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $\sin^{2} \theta , [0 ,\pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $(x^{2}-1)^{3}$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $x^{4}-6x^{2}$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $2x^{3}+5x^{2}-4x$

asked May 5, 2013 by poojasapani_1

1 answer

Find the local maximum and minimum values of the following: $x^{3}-x$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x-2\cos x , [-\pi ,\pi ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sin x +\cos x ,[0 ,\large\frac {\pi}{3}]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\large\frac{x}{x+1},$ $[1 , 2 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=\sqrt{9-x^{2}} ,[-1 , 2]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{3}-12x+1 ,[-3 , 5]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=1-2x-x^{2}, [-4 , 1 ]$

asked May 5, 2013 by poojasapani_1

1 answer

Find the absolute maximum and absolute minimum values of $f$ on the given interval: $\;f(x)=x^{2}-2x+2 , [0 , 3 ]$

asked May 5, 2013 by poojasapani_1

1 answer

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