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Recent questions tagged 2007

Verify Lagrange's mean value theorem for the function $f(x)=3x^2-5x+1$ defined in interval $[2,5].$

asked Apr 16, 2013 by sreemathi.v

0 answers

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

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that : $2\tan^{-1}\bigg(\large\frac{1}{3}\bigg)\normalsize +\cot ^{-1}(4)=\tan^{-1}\bigg(\large\frac{16}{13}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that the bisectors of the angles between the pair of straight lines $11x^2-16xy-y^2=0$ are parallel and perpendicular to $x+2y+5=0.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the value of 'k' so that the second degree equation $12x^2-10xy+ky^2+14x-5y+2=0$ may represent a pair of straight lines.For this value of 'k' find the angle between the lines represented by the above equation.

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the following system of equations using matrices : $x+y+z=6,x-y+z=2,2x+y-z=1$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Using the properties of determinants ,show that $\begin{vmatrix}x-y-z & 2x & 2x\\2y & y-z-x & 2y\\2z & 2z & z-x-y\end{vmatrix}=(x+y+z)^3$

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the differential equation $\tan y dx+\sec^2y\tan x dy=0$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the modulus and amplitude of the complex number $\large\frac{2+3i}{3+2i}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Five students scored marks as follows : 8,10,15,20,22.

asked Apr 16, 2013 by sreemathi.v

0 answers

Kamal and Monika appear for an interview for two vacancies.The probability of Kamal's selection is $\large\frac{1}{3}$ and that of Monika's selection is $\large\frac{1}{5}$.Find the probability that only one of them will be selected.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the ellipse whose minor axis is 4 and which has a distance of 6 units between its foci.

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve $\int\large\frac{1}{x\cos^2(1+\log x)}\normalsize dx$.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $e^{x+y}=xy,$show that $\large\frac{dy}{dx}\normalsize=\large\frac{y(1-x)}{x(y-1)}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the parabola having focus at (3,-4) and directrix as $x+y=2.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the line passing through the intersection of the straight lines $2x+3y=1$ and $3x+4y=6$ and perpendicular to the line $5x-2y=7$.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $A\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$,show that $A^2-3I=2A$.

asked Apr 16, 2013 by sreemathi.v

0 answers

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