Recent questions tagged q2

Find the real and imaginary parts of the following complex numbers: $\large\frac{1}{1+i}$

asked Apr 1, 2013 by geethradh

1 answer

Solve the following non-homogeneous system of linear equation by determinant method: $2x+3y=5\;,4x+6y=12 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 6 & 12 & 6 \\1 & 2 & 1 \\4 & 8 & 4 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;7x\;+\;3y\;=\;-1\;,\;2x\;+\;y\;=\;0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the adjoint of the matrix A =$\begin{bmatrix} 1 & 2 \\3 & -5 \end{bmatrix}$ and verify the result $ A\;(adj\; A)=(adj\;A)\;A=$|$A$|$.I$

asked Mar 28, 2013 by poojasapani_1

1 answer

If $A_{ij}$ is the cofactor of the element $a_{ij}$ of the determinant $\begin{vmatrix}2 & -3 & 5\\6 & 0 & 4\\1 & 5 & -7\end{vmatrix}$,then write the value of $a_{32}.A_{32}$.

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the differential equation representing the family of curves y=mx,where m is an arbitrary constant.

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the value of $\tan^{-1}\begin{bmatrix}2\sin\bigg(2\cos^{-1}\frac{\sqrt 3}{2}\bigg)\end{bmatrix}$

asked Mar 20, 2013 by sreemathi.v

1 answer

For each operation $\ast$ defined below, determine whether $\ast$ is binary, commutative or associative: On $Z$, define $a \ast b = a-b$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Let $f,\, g\, and\, h$ be functions from $R\, to\, R.$ Show that \[ (f . g) oh = (foh) . (goh)\]

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Check the injectivity and surjectivity of the following functions: (i) $f : N\to N\; given\; by\; f(x)\; = x^2 $

asked Mar 14, 2013 by meena.p

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (ii) \quad \begin{vmatrix} 1&0&4 \\ 3&5&-1 \\ 0&1&2 \end{vmatrix} $

asked Mar 6, 2013 by sreemathi.v

1 answer

$ \text{Evaluate the determinants: } \text{(ii): } \begin{vmatrix} x^2-x+1&x-1\\x+1&x+1 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Check the injectivity and surjectivity of the following functions: $f : Z\to Z$ given by $f(x)\; = x^3$

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions:(iv) $f : N\to N\; given\; by\; f(x)\; = x^3 $

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: $f : R\to R $ given by $ f(x)\; = x^2 $

asked Mar 5, 2013 by meena.p

1 answer

Check the injectivity and surjectivity of the following functions: $f : Z\to Z \;given\; by\; f(x)\; = x^2 $

asked Mar 5, 2013 by meena.p

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'$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$, write the elements $a_{23}$, $a_{31}$, $a_{12}$

asked Mar 4, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix} write:(ii) Element\; of \;the\; matrices.$

asked Mar 4, 2013 by sreemathi.v

1 answer

Evaluate $cos\bigg(cos^{-1}\bigg(\frac{-\sqrt{3}}{2}\bigg)+\frac{\pi}{6}\bigg)$

asked Feb 19, 2013 by sreemathi.v

1 answer

Write a unit vector in the direction of $ \overrightarrow a = 2\hat i - 6\hat j + 3\hat k.$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve for x : \[ tan^{-1}\frac{1-x}{1+x}=\frac{1}{2}tan^{-1}x:x > 0.\]

asked Feb 15, 2013 by thanvigandhi_1

0 answers

Evaluate ; \[ sin \bigg[ \frac{\pi}{3}-sin^{-1} \bigg( -\frac{1}{2} \bigg) \bigg] \]

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the principal value of $ tan^{-1} \sqrt 3 - sec^{-1}(-2) $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Using the principal values, evaluate the following \[ tan^{-1}\frac{1}{\sqrt{3}}+sin^{-1} \bigg( -\frac{1}{2} \bigg) \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find principal value of the expression $ cos^{-1}(cos(-680^{\circ})).$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Write the principal value of $ cot^{-1} \{ cot \bigg( -\frac{\pi}{4} \bigg) \} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

What is the principal value of $ \cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg). $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large\frac{\cos \sqrt x}{\sqrt x}$$dx $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the principal value of $ \tan^{-1}(-1) $.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Write the angle between two vectors $ \overrightarrow a \: and \: \overrightarrow b$ with magnitudes $ \sqrt 3 $ and 2 respectively having $ \overrightarrow a.\overrightarrow b=\sqrt 6 $.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

A die is thrown 120 times and getting 1 or 5 is considered success. Find the mean, variance of number of successes.

asked Feb 5, 2013 by meena.p

0 answers

What is the principal value of $\cos^{-1} \bigg( \cos\large\frac{2\pi}{3} \bigg) $$+ \sin^{-1} \bigg( \sin\large\frac{2\pi}{3} \bigg) $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A, while each packet of the same quality of food Q contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and almost 300 units of cholesterol. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A?

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,4,-2) and parallel to the plane -2x+y-3z=7

asked Feb 5, 2013 by meena.p

0 answers

If $\bar{\alpha}=3\bar{i}-\bar{j}\;and\;\bar{\beta}=2\bar{i}+\bar{j}-\bar{k}.$ Express $ \bar{\beta}$ as a sum of two vectors $ \bar{\beta_1}\;and\;\bar{\beta_2},\;where \; \bar{\beta_1}$ is parallel to $ \bar{\alpha}\;and\; \bar{\beta_2}$ is prependicular to $ \bar{\alpha}$

asked Feb 4, 2013 by meena.p

1 answer

Write the value of $\int \large\frac{2-3sin \: x}{cos^2x}$$dx $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Form the differential equation of the family of curves represented by the equation $ (x+a)^2-2y^2=a^2$

asked Feb 4, 2013 by meena.p

0 answers

Find the area bounded by the x-axis part of the curve $ y=1+\Large\frac{8}{x^2}$ and the ordinates x = 2 and x = 4 If the ordinate at x = a divides the area into two equal parts find 'a'

asked Feb 4, 2013 by meena.p

1 answer

Write the value of $ \sin\bigg[ \large\frac{\pi}{3}$$-sin^{-1} \bigg( -\large\frac{1}{2} \bigg) \bigg]. $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the range of one branch of $ \sin^{-1} x$ other than the pricipal branch.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the range of the principal branch of $ \sec^{-1}(x)$ defined on the domain R-(-1,1).

asked Feb 3, 2013 by thanvigandhi_1

1 answer

If $ \sin\: \{ \sin^{-1}\large\frac{1}{5}$$+\cos^{-1}x \} = 1 $, then find the value of x.

asked Feb 3, 2013 by thanvigandhi_1

1 answer

If a matrix has 12 elements, what are the possible order it can have?

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Prove that $ \tan^{-1}\large\frac{1}{3}$$+\tan^{-1}\large\frac{1}{2}=\frac{\pi}{4} $

asked Jan 31, 2013 by thanvigandhi_1

1 answer

$\Large\int \frac {\tan (log)x} {x} dx=$\[(a)\;log\cos (log x) \qquad (b)\;log\sec (log x)\qquad(c)\;log\sin (log x) \qquad(d)\;-log\cos (log x)\]

asked Jan 30, 2013 by meena.p

0 answers

Evaluate : $ \sin \bigg[ \large\frac{\pi}{3}$$-\sin^{-1} \bigg( -\large\frac{1}{2} \bigg) \bigg]. $

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Find the value of $ tan^{-1}\sqrt 3 - sec^{-1}(-2). $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

The function $y=\tan^{-1}x-x $ decreases in the interval of \[(a)\;(1,\infty)\qquad(b)\;(-1,\infty)\qquad(c)\;(-\infty,\infty)\qquad(d)\;(0,\infty)\]

asked Jan 28, 2013 by meena.p

0 answers

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