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Recent questions tagged q2-a

1.8g of glucose (molar mass =180) are dissolved in 60g of water.Calculate the molality

asked Aug 6, 2014 by sreemathi.v

1 answer

Prove by the method of mathematical induction that $\large\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+....+\frac{1}{(3n+1)(3n+4)}=\frac{n}{4(3n+4)}$,for all $n\in N$.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $x\neq y\neq z$ and $\begin{vmatrix}x& x^2 & 1+x^3\\y & y & 1+y^3\\z & z^2 & 1+z^3\end{vmatrix}=0$.Then show that $xyz=-1$.

asked Apr 18, 2013 by sreemathi.v

0 answers

Using properties of determinants,show that $\begin{vmatrix}a^2+1 & ab & ac\\ba & b^2+1 & bc\\ca & cb & c^2+1\end{vmatrix}=a^2+b^2+c^2+1$

asked Apr 17, 2013 by sreemathi.v

0 answers

Show that : $\begin{vmatrix}1 & 1 & 1\\{\alpha}^2 &{\beta}^2 &{\gamma}^2\\{\alpha}^3 &{\beta}^3 &{\gamma}^3\end{vmatrix}=(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)(\alpha\beta+\beta\gamma+\alpha\gamma)$.

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

Prove that :$ \begin{vmatrix}a & b & ax+by\\b & c & bx+cy\\ax+by & bx+cy & 0\end{vmatrix}=(b^2-ac)(ax^2+2bxy+cy^2).$

asked Apr 15, 2013 by sreemathi.v

0 answers

By using properties of determinants ,prove that :$\begin{vmatrix}1+\sin^2x& \cos ^2x&4\sin 2x\\\sin^2x & 1+cos^2 x& 4\sin 2x\\\sin^2 x& \cos ^2x &1+4\sin 2x\end{vmatrix}=2+4\sin 2x$.

asked Apr 12, 2013 by sreemathi.v

0 answers

By using properties of determinants,prove that the determinant $\begin{vmatrix}a & \sin x& \cos x\\-\sin x & -a & 1\\\cos x & 1 & a\end{vmatrix}$ is independent of x.

asked Apr 11, 2013 by sreemathi.v

0 answers

Using properties of determinants,show that $P\alpha^2+2q\alpha+r=0$,given that :p,q and r are not in G.P and $\begin{vmatrix}1 & \large\frac{q}{p} & \alpha+\large\frac{q}{p}\\1 & \large\frac{r}{q} & \alpha+\large\frac{r}{q}\\p\alpha+q &q\alpha+r &0\end{vmatrix}=0$.

asked Apr 11, 2013 by sreemathi.v

2 answers

Using properties of determinants,prove that : $\begin{vmatrix}a & a+b & a+b+c\\2a & 3a+2b & 4a+3b+2c\\3a & 6a+3b & 10a+6b+3c\end{vmatrix}=a^3$

asked Apr 10, 2013 by sreemathi.v

0 answers

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