5PS ADD MATHS

Given the function $g\ :\ x\ \rightarrow\ \left|5-3x\right|,$  find the objects with image 10.

•  $1\ \frac{2}{3}\ and\ 3$  

•  $1\ \frac{2}{5}\ and\ -3$  

•  $-1\ \frac{2}{3}\ and\ 5$  

•  $-1\ \frac{2}{5}\ and\ 3$  

Given $f:\ x\rightarrow3x-5\ and\ g\ :\ x\ \rightarrow\ x^2+4$  

, find the value of  $fg\left(3\right)\ and\ gf\left(3\right)$  

•  $fg\left(3\right)=43\ and\ gf\left(3\right)=\ 2$  

•  $fg\left(3\right)=34\ and\ gf\left(3\right)=20$  

•  $fg\left(3\right)=3\ and\ gf\left(3\right)=2$  

•  $fg\left(3\right)=34\ and\ gf\left(3\right)=-20$  

Given $\alpha\ and\ \beta\$  are the roots of the quadratic equation  $x^2-4x+3=0.$  Form the quadratic equation with roots  $\alpha+\frac{1}{\beta}\ and\ \beta+\frac{1}{\alpha}.$  

•  $3x^2+x+1=0$  

•  $x^2+16x-16=0$  

•  $3x^2-16x-16=0$  

•  $3x^2-16x+16=0$  

The straight line $y=mx-5\$  does  not intersect the curve  $y^2-4y+x^2=21.$  Find the range of values of m.

•  $m>-\frac{\sqrt{24}}{5}\ and\ m>\frac{\sqrt{24}}{5}$  

•  $m<\frac{\sqrt{24}}{5}\ and\ m<-\frac{\sqrt{24}}{5}$  

•  $-\frac{\sqrt{24}}{5}<m<\frac{\sqrt{24}}{5}$  

•  $\frac{\sqrt{24}}{5}<m<-\frac{\sqrt{24}}{5}$  

Solve the simultaneous equations $x+4y=18$   and  $x^2+y^2+6x-2y-7=0.$  

•  $x=-2\ and\ y=5$  

•  $x=-2\ and\ y=-5$  

•  $x=2\ and\ y\ =5$  

•  $x=2\ and\ y=-5$  

•  $x=\frac{1}{2}\ and\ y\ =\frac{1}{5}$  

Given $2^{5x-1}+16=2^{5x}$  , find the value of x that satisfies the equation.

•  $-2$  

•  $-1$  

•  $0$  

•  $1$  

•  $2$  

 $\frac{\sqrt{6}-\sqrt{2}}{\sqrt{8+2\sqrt{12}}}=A-\sqrt{B},\$  find the value of  $2B-A.$  

•  $-\frac{324}{81}$  

•  $\frac{384}{96}$  

•  $\frac{896}{128}$  

•  $-\frac{448}{28}$  

Find the value of  $\log_349\ \times\log_7\sqrt{81}.$ 

• 2

• 3

• 4

• 5

A cinema has 20 seats in the first row, 22 seats in the second row and thereafter each of the rows increase by 2 seats for a total of 30 rows. Find the total number of seats from the 7th to the 16th row in the cinema.

• 560

• 640

• 410

• 380

 $12,\ 6,\ 3,\ ...,\ \frac{3}{32}.$  

Find the sum of all the terms of the geometric progression

• 23.90625

• 23.96025

• 23.25609

• 23.60925