Recent questions tagged medium

Using properties of definite integrals, evaluate the following : $ \int_0^{\pi}\large\frac{x\: sin\: x}{1+cos^2x}$$dx $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Three cards are drawn successively with replacement from a well shuffled deck of 52 playing cards. If getting a card of spade is considered a success, find the probability distribution of the number of success.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the area of the origin enclosed between the two curves $ (x-6)^2+y^2=36\: and \: x^2+y^2=36$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Using integration find the area of the region bounded by the triangle whose vertices are (1,3)(2,5) and (3,4).

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the perpendicular distance of the points (2,3,4) from the line $ \large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$, Also, find the coordinates of the foot of the perpendicular.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Prove that $ tan^{-1}\sqrt x = \frac{1}{2}cos^{-1} \bigg(\frac{1-x}{1+x} \bigg), x \in [0,1].$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve the equation $ sin^{-1}6x+sin^{-1}6\sqrt 3 x = -\frac{\pi}{2}. $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

For what value of k, is the following function continuous at x = 0 ? $ f(x) = \left\{ \begin{array}{l l}\large\frac{1-\cos4x}{8x^2}, & \quad if { x \neq 0 } \\ k, & \quad if { x = 0 } \end{array} \right. $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ y=tan^{-1}\left \{\large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right \} $,find $\large\frac{dy}{dx}.$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the angle of intersection of the curve $( y^2=x \: and \: x^2=y)$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve : $ (x^2+xy)dy=(x^2+y^2)dx $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve : $\large \frac{dy}{dx}+\frac{y}{x}=e^x$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve the differential equation $ x.\cos\bigg(\large\frac{y}{x} \bigg).\frac{dy}{dx}$$=y\cos \bigg( \large\frac{y}{x} \bigg) $$+x $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

An open box with a square base is to be made out of a given quantity of cardboard of area $ c^2$ square units. Show that the maximum volume of the box is $\large\frac{c^3}{6\sqrt 3}$ cubic units.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Evaluate : $\int_0^{\Large\frac{\pi}{4}} \large\frac{\sin\: x.\cos\: x}{\cos^4x+sin^4x}$$dx $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the point (1,1,-1) and perpendicular to the planes $(x+2y+3x-7=0 \: and \: 2x-3y+4z=0.)$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the values of x which satisfy the equation \[ sin^{-1}x+sin^{-1}(1-x)=cos^{-1}x.\]

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove that $ 2sin^{-1}\frac{3}{5}-tan^{-1}\frac{17}{31}=\frac{\pi}{4} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find $\large \frac{dy}{dx}$ if $ x=\large\frac{1+\log\:t}{t^2}$$,y= \large\frac{3+2log\: t}{t} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large\frac{dx}{2\sin^2x+5\cos^2x} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find $ \int_2^8 \large\frac{\sqrt{10-x}}{\sqrt x+\sqrt{10-x}}$$dx $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Obtain the inverse of the following matrix using elementary operation $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Solve the differential equation $ y.e^{\large\frac{x}{y}} dx=(x.e^{\large\frac{x}{y}}+y^2)dy ; y \neq 0$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the image of the point (1,6,3) in the line $ \large\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer