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Recent questions tagged 2008-1

Find the equation of the plane passing through the points $(3,4,1)$ and $(0,1,0)$ and parallel to the line $\large\frac{x+3}{2}=\frac{y-3}{7}=\frac{z-2}{5}$

asked Jul 15, 2013 by sreemathi.v

1 answer

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is \( \large\frac{1}{3} \) h.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the point on the line \( \large\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2} \) at a distance \( 3 \sqrt 2 \) from the point (1, 2, 3)

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If \( \overrightarrow a + \overrightarrow b + \overrightarrow c = 0\) and \( | \overrightarrow a | = 3, | \overrightarrow b | = 5\) and \( |\overrightarrow c | = 7\), show that the angle between \( \overrightarrow a\: and \: \overrightarrow b \) is equal to \( 60^{\circ}\)

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Solve the following differential equation : $ \large\frac{dy}{dx} = \large\frac{x(2y-x)}{x(2y+x)} $ if \( y = 1 \) when \( x = 1 \)

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If $ A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & 2 \\[0.3em] 2 & 2 & 1 \end{bmatrix}$ what is $ A^2-4A-5I=0$

asked Dec 29, 2012 by thanvigandhi_1

1 answer

If \( f(x) = x + 7\) and \( g(x) = x - 7, x \in \: R \) , find ( fog ) (7)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

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

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the value of $x$ and $y$ if : $ 2\begin{bmatrix} 1 & 3 \\[0.3em] 0 & x \\[0.3em] \end{bmatrix} + \begin{bmatrix} y & 0 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix} = \begin{bmatrix} 5 & 6 \\[0.3em] 1 & 8 \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

1 answer

Evaluate : $\begin{bmatrix} a+ib & c+id \\[0.3em] -c+id & a-ib \\[0.3em] \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the co-factor of \(a_{12} \) in the following : $ \begin{bmatrix} 2 & -3 & 5 \\[0.3em] 6 & 0 & 4 \\[0.3em] 1 & 5 & -7 \end{bmatrix}$

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Evaluate : $\int \mathrm \: \large\frac{x^2}{1+x^3} $$dx $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Evaluate : $\int_0^1 \mathrm \: \large\frac{dx}{1+x^2} $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find a unit vector in the direction of \( \overrightarrow a = 3\hat i - 2\hat j + 6\hat k \)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the angle between the vectors : \( \overrightarrow a = \hat i - \hat j + \hat k \) and \( \overrightarrow b = \hat i + \hat j - \hat k \)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

For what value of \( \lambda\) are the vectors \( \overrightarrow a = 2\hat i + \lambda\hat j + \hat k \) and \( \overrightarrow b = \hat i - 2\hat j + 3\hat k \) perpendicular to each other?

asked Dec 20, 2012 by thanvigandhi_1

0 answers

(i) Is the binary operation * , defined on set N, given by \(ab =\large \frac{a+b}{2}\) for all \( a,b \in\: N\), commutative? \[ \] (ii) Is the above binary operation associative?

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Prove the following : $ \tan^{-1}\large\frac{1}{3}$$ + \tan^{-1}\large\frac{1}{5}$$+ \tan^{-1}\large\frac{1}{7}$$+\tan^{-1}\large\frac{1}{8} = \frac{\pi}{4} $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Let $ A = \begin{bmatrix} 3 & 2 & 5 \\[0.3em] 4 & 1 & 3 \\[0.3em] 0 & 6 & 7 \end{bmatrix}$ Express $A$ as sum of two matrices such that one is symmetric and the other is skew symmetric.

asked Dec 20, 2012 by thanvigandhi_1

1 answer

For what value of \(k\) is the following function continuous at \( x=2\)? $ f(x) = \left\{ \begin{array}{l l} 2x+1\: \: \: ; & \quad \text{ $x$ < 2}\\ k\: \: \: \: \: \: \: \: \: \:\: \: \: \: ; & \quad \text{ $x$ =2}\\ 3x-1\: \: \: ; & \quad \text{ $x$ >2} \end{array} \right.$

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Differentiate the following with respect to \( x \) : $\tan^-1 \bigg(\large \frac{\sqrt {1+x} - \sqrt {1-x}}{\sqrt {1+x} + \sqrt {1-x}}\bigg) $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the equation of tangent to the curve \( x = \sin 3t, y = \cos 2t, at\: t = \large\frac{\pi}{4} \)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^\pi \mathrm \:\large\frac{x\sin x}{1+\cos^2x}$$ dx $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Solve the following differential equation : $ (x^2-y^2) dx +2 \: xy \: dy = 0 $ given that \( y = 1 \) when \( x = 1 \)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

solve the following differential equation : $ cos^2x\:\large \frac{dy}{dx} $$+ y = tan \: x $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

If \( \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k \) find a vector \( \overrightarrow c \) such that \( \overrightarrow a\) x \( \overrightarrow c = \overrightarrow b \) and \( \overrightarrow a . \overrightarrow c = 3\)

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the shortest distance between the following lines : \[ \frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1} \: and \: \frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1} \]

asked Dec 19, 2012 by thanvigandhi_1

0 answers

A pair of dice is thrown four times. If getting a doublet is considered a success, find the probability distribution of number of successes.

asked Dec 19, 2012 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} \alpha & \beta & \gamma \\[0.3em] \alpha^2 & \beta^2 & \gamma^2 \\[0.3em] \beta + \gamma & \gamma + \alpha & \alpha + \beta \end{bmatrix} = ( \alpha - \beta ) (\beta - \gamma) (\gamma - \alpha) ( \alpha + \beta + \gamma ) $

asked Dec 19, 2012 by thanvigandhi_1

0 answers

Show that the rectangle of maximum area that can be inscribed in a circle is a square

asked Dec 19, 2012 by thanvigandhi_1

0 answers

Using integration find the area of the region bounded by the parabola \( y^2 = 4x \) and the circle \( 4x^2 + 4y^2 = 9 \).

asked Dec 19, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_{-a}^a \: \sqrt {\large\frac{a-x}{a+x}} dx $

asked Dec 19, 2012 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point ( -1, -1, 2 ) and perpendicular to each of the following planes : $2x + 3y - 3z = 2 \: and \: 5x - 4y + z = 6 $

asked Dec 19, 2012 by thanvigandhi_1

0 answers

A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are listed below. He has maximum area of 9000 \( m^2 \) available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximise the daily output.

asked Dec 19, 2012 by thanvigandhi_1

0 answers

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truckare 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.

asked Dec 19, 2012 by thanvigandhi_1

0 answers

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