Number System & Series PYQs — UPSC CSAT

All 152 Number System & Series Previous Year Questions for UPSC CSAT, with answers and explanations. Click any question for the full solution.

202523

What is the unit digit in the multiplication of 1 x 3 x 5 x 7 x 9 x ... x 999?
Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR – PS = PPT . If Q = 3 and T < 6, then what is the number of possible values of (R, S) ?
What is the 489th digit in the number 123456789101112...?
The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible ?
A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N ?
What is the maximum value of n such that 7 x 343 × 385 × 1000 × 2401 × 77777 is divisible by 35^n?
If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4 ?
Consider the following statements : 1. There exists a natural number which when increased by 50% can have its number of factors unchanged. 2. 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?
What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + . . . + 9¹⁰⁰ is divided by 6?
The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?
If N² = 12345678987654321, then how many digits does the number N have?
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)?
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 – 4 pq, where p, q are natural numbers, positive ? 1. p < q. 2. p > q. Which one of the following is correct in respect of the above Question and the Statements ?
Let p + q = 10, where p, q are integers. 1. Value-I = Maximum value of p x q when p, q are positive integers. 2. Value-II = Maximum value of p x q when p ≥ − 6, q ≥ − 4. Which one of the following is correct?
Consider a set of 11 numbers: 1. Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ − 5. 2. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?
There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
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) ?
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
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?
Let x be a real number between 0 and 1. 1. x² > x³. 2. x > √x. Which of the following statements is/are correct? Select the correct answer using the code given below:

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202321

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202019

201910

20186

20179

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20145

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