Recent questions tagged modelpaper

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

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

asked Dec 18, 2012 by thanvigandhi_1

1 answer

Sketch the graph of y=| x+3 | and evaluate$\Large \int\limits_{-6}^0\normalsize| x+3 |dx$

asked Dec 17, 2012 by sreemathi.v

1 answer

Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( \hat i + 2\hat j + 3\hat k) + \lambda ( \hat i - 3\hat j + 2\hat k )$ and $ \overrightarrow r = 4 \hat i + 5\hat j + 6\hat k + \mu (2\hat i + 3\hat j + \hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

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

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines $ \overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $ \overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the line of intersection of the planes $\overrightarrow r. (\hat i + \hat j + \hat k)=1$ and $ \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0$ and parallel to $x$ - axis.

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the integral $\large \int \frac{\sec^2x}{\large cosec^2x}$$dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function$\frac{(\large log \; x)^2}{\large x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\Large \frac{\large e^{\tan^{-1}x}}{\large 1+x^2}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $\frac{(1+log\: x)^2}{x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the area of the region ${(x, y) : y^2\: \leq \: 4x, 4x^2 + 4y^2\: \leq\: 9}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

By using the properties of definite integrals, evaluate the integral $\int\limits_0^\frac{\Large \pi}{\Large 2}(2 \log \sin x-\log \sin 2x)\;dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals: $\int\limits_1^4 [\; |x-1|+|x-2|+|x-3|\;]dx$

asked Dec 2, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the direction cosines of a line which makes equal angles with the coordinate axes.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]

asked Nov 29, 2012 by vaishali.a

1 answer

Find the particular solution of the differential equation $(1+e^{2x})dy + (1+y^2)e^xdx$ = 0, given that $y = 1$ when $x = 0$

asked Nov 29, 2012 by sreemathi.v

1 answer