\(\text { Solve } 4 x-2 y+3 z=1, x+3 y-4 z=-7,3 x+y+2 z=5\)

\(\text { Solve } x=3 z-5,2 x+2 z=y+16,7 x-5 z=3 y+19\)

Sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares

Two water taps together can fill a tank in \(9 \frac{3}{8}\) hours. The tap of lager diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

\(\text { If } \mathbf{A}=\left[\begin{array}{cc} 1 & -1 \\ 2 & 3 \end{array}\right], B=\left[\begin{array}{ll} 2 & 1 \\ 1 & 0 \end{array}\right], \text { verify that } (A+B)^{2} \neq A^{2}+2 A B+B^{2}\)

\(\text { If } A=\left[\begin{array}{rr} 1 & 0 \\ -1 & 7 \end{array}\right] \text { and } I=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right], \text { then prove }\text { that } \mathrm{A}^{2}-8 \mathrm{~A}+7 \mathrm{I}=0\)

\(\text { Given } \mathbf{A}=\left[\begin{array}{ccc} 1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2 \end{array}\right], B=\left[\begin{array}{ll} 1 & 3 \\ 0 & 2 \\ 1 & 4 \end{array}\right] \text { and }C=\left[\begin{array}{cccc} 1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1 \end{array}\right], \text { show that }(A B) C=A BC.\)

\(\text { Solve }: 2 x+y+4 z=15, x-2 y+3 z=13,3 x+y-z=2\)

Find the values of a and b if \(16 x^{4}-24 x^{3}+(a-1) x^{2}+(b+1) x+49 \text { is a perfect square. }\)

solve the equation \(\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}, \text { where }x+1 \neq 0, x+2 \neq 0 \text { and } x+4 \neq 0 \text { using quadratic formula.}\)

Simplify : \(\frac{a^{2}-16}{a^{3}-8} \times \frac{2 a^{2}-3 a-2}{2 a^{2}+9 a+4} \div \frac{3 a^{2}-11 a-4}{a^{2}-2 a+4}\)

A train covered a certain distance at a uniform speed. If the train would have been 10 km/hr faster it would have taken 2 hour less than the scheduled time and if the train were slower by 10 km/hr, it would have taken 3 hour more than the scheduled time. Find the distance covered by the train.

A car left 30 minutes later than the scheduled time. In order to reach its destination 150 km away in time, it has to increase its speed by 25 km/br from its usual speed. Find its usual speed

A garment shop announces a 50% discount on every purchase of items for their customers. Draw the graph for the relation between the Marked Price and the Discount. Hence find
(i) the marked price when a customer gets a discount of Rs.3250  (from graph)
(ii) the discount when the marked price is Rs.2500.