Mathematical Ab...

The number of terms in the expansion of (1 + 3x + 3x² + x³)⁶ is:

Equation of the circle having diameter 8 and diameters y + 2x - 5 = 0 and 2y + 3x - 8 = 0 is?

Three pipes A, B, and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B, and C discharge chemical solutions P, Q, and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

Evaluate 2(sec⁡ A − cos ⁡A)² + 2(cosec A − sin ⁡A)² − 2(cot⁡ A − tan⁡ A)² − 2.

A can do a piece of work in 5 days and B can do the same work in 5 days. In how many days working together will they do the same work?

60% of the employees of a company are college graduates. Of these, 10% are in sales. Of the employees who did not graduate from college, 80% are in sales. The probability that an employee selected at random is in sales is:

Shakeel started a software business by investing Rs. 20000. After six months, Neel joined him with a capital of Rs. 30000. After 3 years, they earned a profit of Rs. 13950. What was Shakeel’s share in the profit?

Find the coefficients of the term independent of x in the expansion of 

Lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular, if:

A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get ₹ 5 more. The difference in the cost price of the two bicycles was: