Recent questions tagged 2012

If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4. Find$ (i)\: P(A \cap B ) (ii)\: P(A/B) (iii)\: P(A \cup B). $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and $ P(E \cap F)$. = 0.2. Find P(E/F) and P(F/E).

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Show that the relation R in the set A = {1, 2, 3, 4, 5} is given by R = {(a, b) : |a-b|is even }, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $\begin{bmatrix} 1+a^2-b^2 & 2ab & -2b \\ 2ab & 1-a^2+b^2 & 2a \\ 2b & -2a & 1-a^2=b^2 \end{bmatrix} = (1 + a^2 + b^2)^3. $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} 3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{bmatrix} = 3(a + b + c)(ab+bc+ca) $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

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

asked Jan 4, 2013 by thanvigandhi_1

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If $ ( cos \: x )^y = (sin\: y)^y$ find $ \large\frac{dy}{dx} $

asked Jan 4, 2013 by thanvigandhi_1

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Prove that : $\large \frac{d}{dx}$$(log_ex)=\large\frac{1}{x}. $

asked Jan 4, 2013 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 change of (a) the perimeter, (b) the area of the rectangle.

asked Jan 4, 2013 by thanvigandhi_1

1 answer

Find the intervals in which the function f given by $ f(x) =\sin x + \cos x, 0 \leq x \leq 2\pi $ is strictly increasing or strictly decreasing.

asked Jan 4, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{(x-4)e^x}{(x-2)^3}$$dx$

asked Jan 4, 2013 by thanvigandhi_1

0 answers

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

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int x^2\cot^{-1}xdx $

asked Jan 4, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{1}{b^2sin^2x+a^2cos^2x}$$dx $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $ x^2 \large\frac{dy}{dx} $$= y^2+ 2xy $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $ (x^2+1)\large \frac{dy}{dx}$$+2xy = \sqrt {x^2+4} $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Find the direction cosines of the vector joining the points A(1, 2, -3 ) and B ( -1, -2, 1 ), directed from A to B.

asked Jan 4, 2013 by thanvigandhi_1

0 answers

In a factory, which manufactures nuts, machines A, B and C manufacture respectively 25%, 35% and 40% of nuts. Of their outputs 5, 4 and 2 percent respectively are defective nuts. A nut is drawn at random from the product and is found to be defective. Find the probability that it is manufactured by machine B.

asked Jan 4, 2013 by thanvigandhi_1

0 answers