Quantitative Ap...

In the above figure, PT and RS are 2 parallel lines which are tangents to the circle with centre O. PQ is also a tangent to the circle ∠ PSO = 30^º and PT = 6 units. What is the value of the area of PTOQ?

How many positive integral pairs (x, y) exists such that 4 < ∣x − 5∣ × ∣y − 7∣ < 7

How many non-zero integer values of x satisfy the equation given below such that x <= 10.

Cost of 1 pen, 3 pencils and 5 markers is Rs 100. Cost of 18 pencils, 2markers and 6 pens is Rs 320. What is the minimum possible cost of 1 marker, 1 pen and 1 pencils if it is given that the cost of each of the items is a natural number?

If t satisfies the following equation:

log₃ ​78 + t − 6 = log₃ ​(1 − 3^t−5)

What is the value of |t|

An entrepreneur borrows an amount of Rs 20 lakhs from a local bank for a duration of 3 years at a 20% interest rate, compounded annually. At the end of each of these 3 years, he returns a certain amount of money to the bank. The amount returned at the end of each of these 3 years is the same. At the end of 3 years, the bank additionally demanded a cheque of Rs. 1.8 lakhs to settle the loan. What was the amount he used to pay at the end of each year?

A milk merchant buys milk at Rs 50 per litre, but while selling, he marks up the price by 20% and also mixes water to the milk such that the milk-water mixture he sells has 80% milk and 20% water. Assuming that the water has zero cost price, what discount percentage should he give to the mixture such that by selling it, he earns a 10% profit?

Ram was asked to calculate the sum of an arithmetic progression whose first term was 2 and common difference was 7. The total number of terms was 30. He wrote down all the 30 terms in ascending order and then started adding from smallest number. After calculating the sum of first x terms correctly, Ram started taking common difference as 14 instead of 7 and ended up with sum of 3210. How many factors does x − 4 has?

What is the number of common terms between the following series

A₁: 4,10,16,22,28,..........,610

A₂ ​: 2,9,16,23,............... 632

X = Highest power of 144 in 25!

Y = Highest power of 96 in 50!

How many of the following sentences are correct about the value Y - X?

1. It is a perfect square

2. It is a perfect cube

3. It is prime

4. It is even