Recent questions tagged modelpaper

Show that the function f given by $ f (x) = tan^{–1} (sinx + cosx), x > 0$ is always an strictly increasing function in $ \bigg(0,\frac{\pi}{4} \bigg) $

asked Dec 22, 2012 by thanvigandhi_1

0 answers

Find the area of the region enclosed between the two circles $x^2+ y^2 = 4$ and $(x – 2)^2 + y^2 = 4$.

asked Dec 22, 2012 by thanvigandhi_1

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A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol, and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. How many packets of each food should be used to minimize the amount of vitamin A in the diet? What is the minimum amount of vitamin A?

asked Dec 22, 2012 by thanvigandhi_1

0 answers

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

asked Dec 21, 2012 by balaji.thirumalai

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A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by any other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10} $ and $ \frac{2}{5} $ . The probabilities that he will be late are $ \frac{1}{4}, \frac{1}{3} $ and $ \frac{1}{12} $ if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train.

asked Dec 21, 2012 by thanvigandhi_1

1 answer

Find the distance between the point P (6, 5, 9) and the plane determined by points A (3, –1, 2), B (5, 2, 4) and C (–1, –1, 6).

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Let * be a binary operation on N given by a * b = HCF (a, b) , a, b $ \in $ N. Write the value of 22 * 4.

asked Dec 21, 2012 by thanvigandhi_1

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Evaluate : $ \int_0^{\Large\frac{1}{\sqrt 2}} \mathrm \: \frac{\large 1}{\large \sqrt{1-x^2}} dx $

asked Dec 21, 2012 by thanvigandhi_1

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Evaluate : $ \int \mathrm \: \frac{\large \cos \sqrt x}{\large \sqrt x} dx $

asked Dec 21, 2012 by thanvigandhi_1

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Write the principal value of $ \cos^{-1} \bigg(\cos \frac{\large 7\pi}{\large 6} \bigg). $

asked Dec 21, 2012 by thanvigandhi_1

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Write the value of the following determinant : $ \begin {vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end {vmatrix} $

asked Dec 21, 2012 by thanvigandhi_1

1 answer

Find the value of x from the following : $\begin {bmatrix} x & 4 \\ 2 & 2x \end {bmatrix} = 0 $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Find the value of p if $ ( 2\hat i + 6\hat j + 27\hat k )$ x $ ( \hat i + 3\hat j + p\hat k ) = \overrightarrow 0. $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Write the direction cosines of a line equally inclined to the three coordinate axes.

asked Dec 21, 2012 by thanvigandhi_1

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If $ \overrightarrow P $ is a unit vector and $ ( \overrightarrow x - \overrightarrow p ). ( \overrightarrow x + \overrightarrow p ) = 80$, then find $ | \overrightarrow x | $.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When $ x = 8 cm $ and $ y = 6 cm $ , find the rate of a change of (a) the perimeter, (b) the area of the rectangle.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

If $ \sin\: y = x\sin (a+y)$, prove that $ \large\frac{dy}{dx} = \frac{\large \sin^2(a+y)}{\large \sin a}. $

asked Dec 21, 2012 by thanvigandhi_1

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Let f : N $ \rightarrow $ N be defined by : $ f(n) = \left\{ \begin{array}{l l} \large\frac{n+1}{2} & \quad \text{if $n$ is odd}\\ \large\frac{n}{2} & \quad \text{ if $n$ is even} \end{array} for \: all\: n\: \in \: N. \right.$ Find whether the function f is bijective.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int \mathrm \: \large\frac{dx}{ \sqrt{5-4x-2x^2}} $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

If $ y = \frac{\large sin^{-1}x}{\large \sqrt {1-x^2}} $, show that $ (1 - x^2) \large\frac{d^2y}{dx^2} - 3x \large\frac{dy}{dx} $$- y = 0 $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

On a multiple choice examination with three possible answers ( out of which only one is correct ) for each of the five questions, what is the probability that the candidate would get four or more correct answers just by guessing?

asked Dec 21, 2012 by thanvigandhi_1

0 answers