Class 10 Formulas

Which of the following statement is incorrect?

• $LCM\ \left(a,\ b\right)\times\ HCF\left(a,\ b\right)\ =\ a\times b$

• $LCM\ \left(a,\ b\right)=\ \frac{a\ \times b}{HCF\left(a,\ b\right)}$

• $HCF\left(a,\ b\right)=\frac{a\ \times b}{LCM\left(a,\ b\right)}$

• $LCM\ \left(a,\ b\right)\times a=HCF\left(a,\ b\right)\times b$

 $If\ \alpha\ and\ \beta\ are\ the\ zeros\ of\$   $p\left(x\right)\ =ax^2\ +\ bx\ +\ c\ =\ 0\$  then

•  $\alpha\ +\ \beta\ =\frac{-b}{a}\ and\ \alpha\beta\ =\frac{-c}{a}$  

•  $\alpha\ +\ \beta\ =\frac{b}{a}\ and\ \alpha\beta\ =\frac{-c}{a}$  

•  $\alpha\ +\ \beta\ =\frac{-b}{a}\ and\ \alpha\beta\ =\frac{c}{a}$  

•  $\alpha\ +\ \beta\ =\frac{b}{a}\ and\ \alpha\beta\ =\frac{c}{a}$  

If a pair of linear equations unique solution then

• $\frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ =\frac{c_1}{c_2}$

• $\frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2}$

• $\frac{a_1}{a_2}\ \ne\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2}$

• $\frac{a_1}{a_2}\ \ne\frac{b_1}{b_2}\$

In a pair of linear equations $\frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ =\frac{c_1}{c_2}$  then they are 

• coincident lines, infinitely many solutions

• intersecting lines, exactly one solution

• parallel lines, no solutions

• none of these

In a pair of linear equations $\frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2}$  then they are 

• coincident lines, infinitely many solutions

• intersecting lines, exactly one solution

• parallel lines, no solutions

• none of these

A quadratic equation $ax^2\ +bx\ +\ c\ =\ 0$  

 has two equal roots, if

•  $b^2\ -\ 4ac\ >\ 0$  

•  $b^2\ -\ 4ac\ <\ 0$  

•  $b^2\ -\ 4ac\ =0$  

•  $b^2\ -\ 4ac\ \ge\ 0$  

In an AP last term

• $a_{n\ }=a\ +\left(n-1\right)d$

• $a_{n\ }=d\ +\left(n-1\right)a$

• $a_{n\ }=a\ +\left(n+1\right)d$

• $a_{n\ }=d\ +\left(n+1\right)a$

A quadratic equation $ax^2\ +bx\ +\ c\ =\ 0$  

 has .......................roots, if  $b^2\ -\ 4ac\ >\ 0$  

• two equal real roots

• two distinct real roots

• no real roots

• none of these

A quadratic equation $ax^2\ +bx\ +\ c\ =\ 0$ then  x = ............

•  $\frac{-b\ \pm\sqrt{b^2\ -\ 4ac}}{2a}$  
  

•  $\frac{-b\ \pm\sqrt{b^2\ +\ 4ac}}{2a}$  

•  $\frac{b\ \pm\sqrt{b^2\ -\ 4ac}}{2a}$  

•  $\frac{-b\ \pm\sqrt{b^2\ -\ 4ac}}{2c}$  
  

The sum of the first n-term of an AP is

• $s\ =\left(2a\ +\ \left(n-1\right)d\right)$

• $s\ =\frac{n}{2}\left(a\ +\ \left(n-1\right)d\right)$

• $s\ =\frac{n}{2}\left(2a\ +\ \left(n+1\right)d\right)$

• $s\ =\frac{n}{2}\left(2a\ +\ \left(n-1\right)d\right)$