Question 2 :
Check whether the following is a quadratic equation: $(x – 3)(2x +1) = x(x + 5)$

Question 3 :
State True or False: Every quadratic equation has at least one real root.

Question 4 :
What are the roots of the quadratic equation $2x^2-\sqrt{5}x-2=0$ using the quadratic formula.

Question 5 :
Check whether the following is quadratic equation : $(x+2)^3 = 2x (x^2 - 1)$

Question 6 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$

Question 7 :
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Write an equation to find out the number of toys produced on that day.

Question 9 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$

Question 10 :
Find two consecutive positive integers, sum of whose squares is 365.

Question 11 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Question 12 :
The prime factorisation of a ___________ is unique, except for the order of its factors.

Question 13 :
Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion.

Question 14 :
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Question 15 :
Can $12^n$ end with the digit 0 or 5 for any natural number n?

Question 16 :
Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 19 :
Given that HCF (306, 657) = 9, What is LCM (306, 657)?