Recent questions tagged modelpaper

Find $ \large\frac{dy}{dx},$$ if \: y=\sin^{-1} \bigg[ x \sqrt{1-x}-\sqrt x \sqrt{1-x^2} \bigg] $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If $ y=\sqrt{x^2-1}-\log \bigg( \large\frac{1}{x}+\sqrt{1+\frac{1}{x^2}} \bigg) $ find $\large\frac{dy}{dx} $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi-vertical angle is $ \tan^{-1} \bigg(\large\frac{1}{2} \bigg) $. Water is poured into it at a constant rate of 5 cubic meter per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10 m.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\pi}\large\frac{x\: dx}{a^2\cos^2x+b^2\sin^2x}$$a,b>0 $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Show that the differential equation $ 2y.e^{\large\frac{x}{y}}dx+(y-2xe^{\large\frac{x}{y}})dy=0. $ is homogeneous and find its particular solution given that x = 0 when y = 1.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the particular solution of the differential equation : $ \large\frac{dy}{dx}+y\cot x=2x+x^2\cot x, x \neq 0$ given that y = 0 when $ x=\large\frac{\pi}{2}.$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Form a differential equation of the family of ellipse having foci on y - axis and centre at origin.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

The scalar product of the vector $ \hat i + 2\hat j + 4\hat k $ with a unit vector along the sum of vectors $ \hat i + 2\hat j + 3\hat k $ and $ \lambda \hat i + 4\hat j - 5\hat k $ is equal to one. Find the value of $ \lambda $.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find a vector in the direction of vectors $ 5\hat i - \hat j + 2\hat k$ which has magnitude 8 units.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the value of p so that the lines $ \large\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $\large\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5} $ are right angles.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

A foot ball match may be either won, drawn or lost by the host country's team. So there are three ways of forecasting the result of any one match. One correct and two incorrect. Find the probability of forecasting at least three correct result for four matches.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If a,b,c are positive and unequal, show that the following determinant is negative. $ \Delta = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

using matrices, solve the following system of equations $ x+2y-3z=-4;2x+3y+2z=2 ; 3x-3y-4z=11 $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle $ \alpha $ is $ \large\frac{4}{27}\pi h^3\tan^2 \alpha $.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate the following $ \int_{-1}^{\large\frac{3}{2}} |x\sin \: \pi \: x |dx $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Sketch the graph of $ f(x) = \left\{ \begin{array}{l l}|x-2|+2, & \quad { x \leq 2} \\ x^2-2, & \quad { x > 2} \end{array} \right. $ Evaluate $ \int_0^4 f(x) dx $ What does the value of this integral represent on the graph?

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point P(1,1,1) and containing the line $ \overrightarrow r = (-3\hat i + \hat j + 5\hat k)+ \lambda (3\hat i - \hat j - 5\hat k).$. Also show that the plane contains the line $ \overrightarrow r = (-\hat i + 2\hat j + 5\hat k)+ H (\hat i - 2\hat j - 5\hat k).$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Two bags A and B contain 4 white and 3 black balls and 2 white,2 black balls respectively. From bag A, two balls are transferred to bag B. Find the probability of drawing (a) 2 white balls from Bag B? (b) 2 black balls from bag B? (c) 1 white and 1 black ball from bag B?

asked Feb 4, 2013 by thanvigandhi_1

1 answer