Practice No. System Questions and Answers

• Twin prime numbers are the prime numbers whose difference is always equal to 2. The number of twin primes between 35 and 100 is:
• Find the unit digit of the product 127 × 137 × 413 × 291 × 342 × 533 × 342.
• What is the digit in the units place of the number (1624)24 ?
• Find the unit digit in (257)45 × (248)73.
• Find the number of factors in 1750.
• If a number 'a' is divisible by 18 and another number 'b' is divisible by 12, then (a2 – b2) is divisible by:
• Solve the following equation: 48 ÷ [35 – {30 – (31 – 26 ÷ 2 × 4)}]
• A six-digit number 4c68d2 is divisible by 12. Find the sum of all possible values of 'c' for the largest possible value of 'd'.
• 'M' is the largest three-digit number that leaves 3 as a remainder when divided by 9, 12 and 5, Find the sum of digits of 'M'.
• Sandeep can solve 20 questions in 1 hour. If he decreased his efficiency by 20%, then how much time would he take to solve the same number of questions?
• Find the remainder when the number (289n + 147) is divided by 17.
• Find the largest three-digit number that leaves '3', '4' and '5' as remainder when it is divided by '7', '8' and '9', respectively.
• What is the number of divisors of 360?
• What is the place value of 3 in 3678921410. 1. 3 ×104 2. 3 ×107 3. 3 ×105 4. 3 ×109
• The scores of KL Rahul in a T20 series were 78, 34, 56, 90, and 45. While the scores of Rishabh Pant in the same series were 22, 87, 43, 100, and 60, respe...
• One-seventh of a 2-digit number is 10 less than half of the number. What is the sum of the digits of the 2-digit number?
• Determine the following number which is divisible by 3?
• 240 students need to be arranged to sit in 12 rows. If the number of rows increases by 25%, then find the number of students who will now be sitting in eac...
• Find the mean proportion of 2.56 and 0.0324.
• Find the fourth proportional of 12, 24, and 30.
• What is the smallest four-digit number that can be evenly divided by 20, 24, and 36?
• For which range of 'p' does the expression 19p - 2p²- 35 have a positive value??
• The mean of three distinct numbers is 30. If the third number is to the combined total of the first two numbers in the ratio 16:29, what is the sum of the ...
• What is the largest three-digit number that, when divided by either 13 or 17, results in a remainder of 2?
• In an examination, five students—A, B, C, D, and E—participated. The overall average score for these students was 58. Specifically, students A, C, and ...
• How many whole numbers between 100 and 750 are multiples of both 18 and 24?
• In a particular examination, Cheenu achieved 48% of the total marks and fell short by 72 marks to pass. On the other hand, Meenu obtained 68% of the total ...
• The average marks scored by boys and girls in a class are 48 and 32, respectively. The total marks obtained by the entire class is 1680, with 40 students i...
• In a certain pond, there are 60 more crabs than fish. Unfortunately, 20% of the crabs have perished. Additionally, the pond has welcomed 80 new fish. As a ...
• When a number is reduced by 25%, the resulting value is 36 more than 60% of the number's initial value. What is the original number?
• The mean of 12 numbers is 15. When two additional numbers, x and y , are included, the average increases by 1. Given that the difference between x and y is...
• In an examination, Ajay earned 28% of the total marks, falling short of the passing mark by 42 marks. On the other hand, Vijay achieved 41% of the total ma...
• A school organizes a picnic for students. The cost of transportation is ₹8,000, and the food cost is ₹5,000. If there are 50 students attending the pic...
• Two friends, P and Q, each have the same amount saved. Q manages to save one-fourth of his income, while P saves one-third of his. Given that P spends Rs. ...
• Consider a three-digit number where the middle digit (tens place) is 3. If the digits in the hundreds and ones places are swapped, the new number becomes 1...
• Consider a set of 11 distinct positive integers whose average is 20. If the average of the initial six integers in this set is 14, and the average of the f...
• If p and q are real numbers such that p2 + (p - 2q - 1)2 = - 4q(p + q), then the value p - 2q is
• Suppose, (√(5a+9) )+ (√(5a-9)) = 3(2+√2), then √(10a+9) will be equal to?
• Consider two natural numbers, 'a' and 'b', which are in the ratio of 17:20. If we increase 'a' by 18 and decrease 'b' by 20, the new ratio of 'a' to 'b' be...