26 questions found · showing 20
What is the remainder when 9² + 9⁴ + 9⁶ + ... + 9¹⁰⁰ is divided by 6?
P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?
A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct?
I. The minimum number of cuts is 9.
II. The number of smaller pieces which are not painted on any face is 6.
Select the correct answer using the code given below:
PQRST is a 5-digit number (all distinct digits) such that T = 0, P is thrice S, S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
If N² = 12345678987654321, then how many digits does the number N have?
If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Is (p + q)² − 4pq positive, where p, q are natural numbers?
Statement I: p < q.
Statement II: p > q.
Which one of the following is correct in respect of the above Question and the Statements?
How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1; where p, q and r are natural numbers (not necessarily distinct)?
A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?
The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?
What is the 489th digit in the number 123456789101112...?
If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4?
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
Consider the following statements:
I. There exists a natural number which when increased by 50% can have its number of factors unchanged.
II. There exists a natural number which when increased by 150% can have its number of factors unchanged.
Which of the statements given above is/are correct?
The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?
Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?
Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)?
Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by team X?
What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999?
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
