Recent questions tagged sec-b

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

0 answers

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

In a class, having 60% boys, 5% of the boys and 10% of the girls have an I.Q. of more than 150. A student is selected at random and found to have an I.Q. of more than 150. Find the probability that the selected student is a boy.

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Find the distance of a point(2,4,-1) from the line $\large \frac{x-5}{1}\;=\frac{y-3}{4}\;=\frac{z-6}{-9}$

asked Jan 3, 2013 by sreemathi.v

1 answer

Two systems of rectangular axis have the same origin.If a plane cuts them at distances a,b,c and a',b',c',respectively,from the origin,prove that\[\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{{a'}^2}+\frac{1}{{b'}^2}+\frac{1}{{c'}^2}\]

asked Jan 3, 2013 by sreemathi.v

1 answer

O is the origin and A is (a,b,c).Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the angle between the lines whose direction cosines are given by the equations $l+m+n=0,l^2+m^2-n^2=0$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equations of the two lines through the origin which intersect the line $\;\large\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at angles of $\large \frac{\pi}{3}$ each.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the points (2,1,0),(3,-2,-2) and (3,1,7).

asked Jan 3, 2013 by sreemathi.v

1 answer

If the line drawn from the point $(-2,-1,-3)$ meets a plane at right angle at the point $(1,-3,3)$ find the equation of the plane.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which is at a distance $3\sqrt 3$ units from origin and the normal to which is equally inclined to coordinate axis.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

asked Jan 3, 2013 by sreemathi.v

1 answer

Prove that the lines $x=py+q;z=ry+s$ and $x=p'y+q';z=r'y+s'$ are perpendicular if $pp'+rr'+1=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the angle between the lines $r=(3\hat i+2\hat j+6\hat k) +\lambda(2\hat i+\hat j+2\hat k) \;and\; r=(2\hat i-5\hat k)+\mu(6\hat i+3\hat j+2\hat k)$

asked Jan 3, 2013 by sreemathi.v

1 answer