$f(x) = \dfrac{x^2+2x-15}{x^2-7x-18}$ is negative if and only if

The number of integers $n$ that satisfy the inequalities $|n - 60| < |n - 100| < |n - 20|$ is

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

If $5 - \log_{10}\sqrt{1+x} + 4\log_{10}\sqrt{1-x} = \log_{10}\sqrt{11-x^2}$, then $100x$ equals

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

If $r$ is a constant such that $|x^2 - 4x - 13| = r$ has exactly three distinct real roots, then the value of $r$ is

Amal purchases some pens at ₹8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹12 each. If the remaining pens are sold at ₹11 each, then he makes a net profit of ₹300, while he makes a net loss of ₹300 if the remaining pens are sold at ₹9 each. The wage of the employee, in INR, is

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹806.25 and ₹866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to