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Recent questions tagged part-1

If : $\begin{bmatrix}x^2 & 3 & 4\\1 & 9 & 8\end{bmatrix}+\begin{bmatrix}-3x & 1 & -5\\-3 & -2 & -6\end{bmatrix}=\begin{bmatrix}4 & 4 & -1\\-2 & 7 & 2\end{bmatrix}$,find the values of $x$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Evaluate : $\int_0^{\large\frac{\pi}{4}}\normalsize (\tan x+\cot x)^{-1}dx.$

asked Apr 22, 2013 by sreemathi.v

0 answers

Using vectors,show that the perpendiculars from the vertices to the opposite sides of the triangle ABC are concurrent.

asked Apr 22, 2013 by sreemathi.v

0 answers

Simplify : $(1-\omega)(1-{\omega}^2)(1-{\omega}^2)(1-{\omega}^3)$.

asked Apr 22, 2013 by sreemathi.v

0 answers

One number is chosen at random from the numbers 1 to 21.Find the probability that may be a prime number.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $y=\tan^{-1}\bigg(\large\frac{2x}{1-x^2}\bigg)$,prove that $\large\frac{dy}{dx}=\frac{2}{1+x^2}$.

asked Apr 22, 2013 by sreemathi.v

0 answers

Find the cosine of the angle between the planes $x+2y-2z+6=0,2x+2y+z+8=0$.

asked Apr 22, 2013 by sreemathi.v

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The equation $y^2-4y-4x+16=0$ represents a parabola.Find its vertex and focus.

asked Apr 22, 2013 by sreemathi.v

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Find the angle between the straight lines represented by the equation $3x^2-y^2-\sqrt 3x+3y-2=0.$

asked Apr 22, 2013 by sreemathi.v

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Find the middle term in the binomial expansion of $\begin{pmatrix}\large\frac{x^2}{4}-\frac{4}{x^2}\end{pmatrix}^{10}$

asked Apr 19, 2013 by sreemathi.v

0 answers

If $i=\sqrt{-1}$,prove the following : $(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^4+4$

asked Apr 18, 2013 by sreemathi.v

0 answers

Prove that $2(\tan^{-1}1+\tan^{-1}\large\frac{1}{2}\normalsize+\tan^{-1}\large\frac{1}{3}\normalsize)=\pi$

asked Apr 18, 2013 by sreemathi.v

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Integrate : $\int\large\frac{1+\tan^2x}{\sqrt{1+\tan^2x}}\normalsize dx$.

asked Apr 18, 2013 by sreemathi.v

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If the matrix $A=\begin{pmatrix}2 & 3\\5 & -2\end{pmatrix}$,show that $A^{-1}=\large\frac{1}{19}\normalsize A.$

asked Apr 18, 2013 by sreemathi.v

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If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid\overrightarrow{a}\mid $ then show that vector $(2\overrightarrow{a}+\overrightarrow{b})$ is perpendicular to $\overrightarrow{b}$.

asked Apr 18, 2013 by sreemathi.v

0 answers

What is the probability that a leap year has 53 Sundays?

asked Apr 18, 2013 by sreemathi.v

0 answers

Find the angle between the line $\large\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$ and the plane $x+y+2z=0.$

asked Apr 18, 2013 by sreemathi.v

0 answers

If $x^yy^x$=5 show that $\large\frac{dy}{dx}=-\begin{pmatrix}\large\frac{\log y+\Large\frac{y}{x}}{\log x+\Large\frac{x}{y}}\end{pmatrix}$

asked Apr 18, 2013 by sreemathi.v

0 answers

The directrix of a conic section is $3x+4y=1$ and focus is (2,3).Find the equation of the conic section if its eccentricity is $\large\frac{1}{\sqrt 2}$

asked Apr 18, 2013 by sreemathi.v

0 answers

Find the value of 'p' for which the following equation represents a pair of straight lines : $x^2+pxy-2y^2+3gx+3fy=0.$

asked Apr 18, 2013 by sreemathi.v

0 answers

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