Example $4.30$ Show that the following equations are consistent and solve 1the $x+y+z=3$ $x+2y+3z=4$ $x+4y+9z=6$ (R.G.P.V, Solution. Writing the system in matrix form $:AX=B$ $F\left(x\right)=x^{3}-2x^{2}+2\pi t102\right)$

4. Show that $\dfrac {cos37^{°}+sin37^{°}} {cos370-sin37}=cot8^{°}$ 5. Show that $tan\left(\dfrac {\pi } {4}+θ\right)-tan\left(\dfrac {\pi } {4}-θ\right)=2tan2θ$ $mber\dfrac {4+2i} {1-2i}$ 6. Find the real and imaginary parts of the complex number $s\dfrac {15} {3}and\dfrac {7} {5}$ 7. Find the equation of the straight line making intercepts with the $x-a\times ds$ and y-axis respectively. 8. Find the equation of the point circle with centre $12,-3\right)$ 9. Evaluate Lt $\dfrac {1^{2}+2^{2}+3^{2}+...+n^{2}} {n^{3}}$ 10. Differentiate between $x^{2}+e^{x}secx$ with respect to x. $PART-B$ $10\times 5=50$ Instructions : (1) Answer any five questions. (2) Each question carries ten marks. (3) Answers should be comprehensive and the criterion for valuation is the content but not the length of the answer. 11. (a) $1fA=\left(2$ $2$ 0. 1 1 3 $comP1tC$ $A^{2}-5A+6t$ where I is the unit 1 -1 0 matrix of order 3. (b) Solve the system of equation $x+y+z=$ 3 $x+2y+3z=4$ $x+4y+9z=6$ Gauss-Jordan method. using $1contd$ $14034$ CO.IN WWW.MANARESULTS.

$x+y+z=1$ $2x+2y+3z=6$ $x+4y+9z=3$