Recent questions tagged easy

Find the value of $k$ if area of triangle is $4\; sq. units$ and vertices are: $(k, 0), (4, 0), (0, 2)$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find area of the triangle with vertices at the point given in (1, 0), (6, 0), (4, 3)

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Which of the following is correct:

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Let $A$ be a square matrix of order $3 \times 3$, then $ |kA|$ is equal to:

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

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 \[ \begin{vmatrix} 0&a&-b \\ -a&0&-c \\ b&c&0 \end{vmatrix} = 0 \]

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: \[ tan^{-1} (1) \;+ \; cos^{-1} \frac {-1} {2} + sin^{-1} \frac {-1} {2} \]

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 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

Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the points at which the function $f$ given by $f (x) = (x – 2)^4 (x + 1)^3$ has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

The sum of the perimeter of a circle and square is $k$, where $k$ is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the function $f$ given by $f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0$ is $(i) \;increasing\qquad (ii) \;decreasing.$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the normal at any point $\theta$ to the curve $ x = a \cos\theta + a \: \theta \sin\: \theta, y = a\sin\theta - a\theta \cos\theta$ is at a constant distance from the origin.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the equation of the normal to curve $y^2 = 4x$ which passes through the point $(1, 2).$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following: $(33)^{-\large\frac{1}{5}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following: $ \left(\large\frac{17}{81}\right)^{\frac{1}{4}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Determine order and degree (if defined) of differential equation $y'+5y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $(y''')^2+(y'')^3+(y')^4+y^5=0$

asked Nov 27, 2012 by sreemathi.v

1 answer

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

asked Nov 27, 2012 by sreemathi.v

1 answer

The maximum value of $ [ x(x-1) +1]^{\frac{1}{3}}, 0 \leq \: x \leq$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

For all real values of $x$, the minimum value of $ \large\frac{1-x+x^2}{1+x+x^2}$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the point on the curve $ x^2 = 2y$ which is nearest to the point $(0, 5)$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

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