Recent questions tagged bookproblem

By using the properties of determinants show that $ (i) \begin{vmatrix} a-b-c&2a&2a \\ 2b&b-c-a&2b \\ 2c&2c&c-a-b \end{vmatrix} = (a+b+c)^3 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

The degree of the differential equation $\bigg(\large\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2$$+\sin\bigg(\large\frac{dy}{dx}\bigg)$$+1=0\; is$

asked Nov 28, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

By using the properties of determinants show that \[\begin{vmatrix} x&x^2&yz \\ y&y^2&zx \\ z&z^2&xy \end{vmatrix} = (x-y)(y-z)(z-x)(xy+yz+zx) \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Determine order and degree (if defined) of differential equation $y''+2y'+\sin y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $y''+(y')^2+2y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $y'+y=e^x$

asked Nov 28, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that $ (i) \quad \begin{vmatrix} 1&a&a^2 \\ 1&b&b^2 \\ 1&c&c^2 \end{vmatrix} = (a-b)(b-c)(c-a) $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 0&a&-b \\ -a&0&-c \\ b&c&0 \end{vmatrix} = 0 \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} b+c&q+r&y+z \\ c+a&r+p&z+x \\ a+b&p+q&x+y \end{vmatrix} = 2 \begin{vmatrix} a&p&x \\ b&q&y \\ c&r&z \end{vmatrix} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 1&bc&a(b+c) \\ 1&ca&b(c+a) \\ 1&ab&c(a+b) \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 2&7&65 \\ 3&8&75 \\ 5&9&86 \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a-b&b-c&c-a \\b-c&c-a&a-b \\c-a&a-b&b-c \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} x&a&x+a \\y&b&y+b \\ z&c&z+c \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

$ \text{If } \begin{vmatrix} x&2 \\ 18&x \end{vmatrix} = \begin{vmatrix} 6&2 \\ 18&6 \end{vmatrix}$, then $x$ is equal to:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the value of $x$, if $ \begin{vmatrix} 2&4 \\ 5&1 \end{vmatrix} = \begin{vmatrix} 2x&4 \\ 6&x \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 1&1&-2\\ 2&1&-3 \\5&4&-9 \end{bmatrix}$, then find $|A|$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant: $\begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&0&1 \\ 0&1&2 \\ 0&0&4 \end{bmatrix}, \text{then show that } |\;3A\;| = 27|\;A\;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&2 \\ 4&2 \end{bmatrix}, \text{then show that } |\;2A\;| = 4|\;A;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant: $\begin{vmatrix} cos\theta &-sin\theta \\ sin\theta & cos\theta \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant:$ \begin{vmatrix} 2&4 \\ -5&-1 \end{vmatrix} $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If $ \sin^{-1} x=y$ then:

asked Nov 28, 2012 by vaishali.a

1 answer

Find the value of the following:\[cos^{-1} \frac {1} {2} +2 sin^{-1}\frac {1} {2} \]

asked Nov 28, 2012 by vaishali.a

2 answers

Find the value of the following: \[ tan^{-1} (1) \;+ \; cos^{-1} \frac {-1} {2} + sin^{-1} \frac {-1} {2} \]

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: <br> $ \mathrm{cosec}^{-1} (-\sqrt 2) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal value of the following: $cos^{-1} \bigg( -\frac {1} {\sqrt 2} \bigg) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following : $\cot^{-1} (\sqrt 3) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: $sec^{-1} \bigg( \frac {2} {\sqrt 3} \bigg) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: $tan^{-1} (-1)$

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: $cos^{-1} \bigg(-\frac {1} {2} \bigg ) $

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: <br>$ tan^{-1} (-\sqrt3)$

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: $cosec^{-1} (2) $

asked Nov 28, 2012 by vaishali.a

1 answer

Find the principal values of the following: <br> $cos^{-1} \bigg(\large\frac { \sqrt 3} {2}\bigg)$

asked Nov 28, 2012 by vaishali.a

2 answers

Find the principal values of the following: <br> $ sin^{-1} \bigg( -\frac {1} {2}\bigg) $

asked Nov 28, 2012 by vaishali.a

2 answers

Determine order and degree (if defined) of differential equation$\bigg(\large\frac{d^2y}{dx^2}\bigg)^2+\normalsize \cos\bigg(\large\frac{dy}{dx}\bigg)=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $\frac{d^2y}{dx^2}=\cos3x+\sin3x$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $\bigg(\frac{ds}{dt}\bigg)^4 +3s\frac{d^2s}{dt^2}=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $\frac{d^4y}{dx^4}+\sin(y''')=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Choose the correct answer in the points on the curve $9y^2 = x^3$, where the normal to the curve makes equal intercepts with the axes are

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the normal to the curve $x^2 = 4y$ passing $(1,2)$ is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the normal at the point $(1,1)$ on the curve $2y + x^2 = 3$ is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the line $y = mx + 1$ is a tangent to the curve $y^2 = 4x$ if the value of $m$ is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the slope of the tangent to the curve $x = t^2 + 3t – 8, y = 2t^2 – 2t – 5$ at the point $(2,– 1)$ is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height $h$ and semi vertical angle $\alpha$ is one-third that of the cone and the greatest volume of cylinder is $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is $\large\frac{2R}{\sqrt 3}$ . Also find the maximum volume.

asked Nov 28, 2012 by thanvigandhi_1

2 answers

Let $f$ be a function defined on $[a, b]$ such that $f' (x) > 0$, for all $x \: \in (a, b)$. Then prove that $f$ is an increasing function on $(a, b).$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius $r$ is $ \large\frac{4r}{3}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

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