Question 1 :
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced.

Question 2 :
Find the roots of the quadratic equation (by using the quadratic formula): $-3x^2+5x+12=0$

Question 5 :
A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, original average speed of the train is?

Question 6 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x+4\right)^2-8x=0$

Question 7 :
Find the roots of the quadratic equation (by using the quadratic formula): $\frac{1}{2}x^2-\sqrt{11}x+1=0$

Question 8 :
State True or False whether the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$

Question 9 :
Justify why the following quadratic equation has two distinct real roots: $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+\frac{1}{\sqrt{2}}=0$