Recent questions tagged 2012

If $ y=e^{\large a \: cos^{-1}\: x} ; -1 \: \leq \: x \leq \: 1$, show that $ (1+x^2) \large\frac{d^2y}{dx^2}-x\frac{dy}{dx}-$$a^2y=0.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

If $ x \sqrt {1+y} + y \sqrt{1+x}=0 \: for \: -1 < x < 1$ Prove that : $\large \frac{dy}{dx}=\frac{1}{(1+x)^2} $

asked Jan 11, 2013 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 Jan 11, 2013 by thanvigandhi_1

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At what point will the tangent to the curve $ y=2x^3-15x^2+36x-21$ be parallel to x - axis? Also, find the equations of tangents to the curve at these points ?

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \sin x \sqrt {1+\cos2x} dx.$

asked Jan 11, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{x^2+x+1}{(x+2)(x+1)^2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{dx}{x[6(log \: x)^2]+7( log \: x)+2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

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Evaluate : $ \int \tan^{-1} \sqrt{ \large\frac{1-sinx}{1+sinx}}dx. $

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation $ x(1+y^2)dx-y(1+x^2)dy=0 $ given that $ y=0, \: when \: x=1$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation $\large\frac{dy}{dx}$$+\sec x.y = \tan \: x. $

asked Jan 11, 2013 by thanvigandhi_1

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Find the magnitude of two vectors $ \overrightarrow a \: and \overrightarrow b $ having the same magnitude and such that the angle between them is $ 60^{\circ} $ and their scalar product is $\large\frac{1}{2}$.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A man is known to speak the truth 3 out of 5 times. He throws a dice and reports that it is 1. Find the probability that it is actually 1.

asked Jan 11, 2013 by thanvigandhi_1

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Two bags A and B contain 2 white, 4 red and 3 white, 3 red balls respectively. One of the bags is selected at random and a ball is drawn from it. If the selected ball is of white colour, find the probability that it is drawn from bag A.

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Let A = R-{3} and B = R-{1}. Consider the function$ f:A \rightarrow B$ defined by $ f(x)=\large\frac{x-2}{x-3}$. Is f one-one and onto? Justify your answer.

asked Jan 11, 2013 by thanvigandhi_1

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Solve, using matrices : $ 2x-y+3z=5;3x+2y-z=7 ; 4x+5y-5z = 9$

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the largest possible area of the right-angled triangle whose hypotenuse is 5 cm.

asked Jan 11, 2013 by thanvigandhi_1

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Prove that the radius of the right circular cylinder of the greatest curved surface that can be inscribed in a given cone is half of the radius of the cone.

asked Jan 11, 2013 by thanvigandhi_1

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Find the region included between the parabola $ y^2=x $ & the line $ x+y=2.$

asked Jan 11, 2013 by thanvigandhi_1

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Find the shortest distance between the lines : $\overrightarrow r = (1+2\lambda ) \hat i + (2+3\lambda)\hat j + (3+4\lambda)\hat k $ and $ \overrightarrow r = (2+3\mu ) \hat i + 4(1+\mu)\hat j + 5(1+\mu)\hat k $

asked Jan 11, 2013 by thanvigandhi_1

0 answers