Recent questions in Model Papers

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

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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

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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

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(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

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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

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^4\mid x-1\mid dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

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