CUET General Test Quantitative Reasoning > Number System PYQs

Which of the following numbers is divisible by 11?

In number system √2 is:

Match the LIST-I with LIST-II | LIST-I (Number) | LIST-II (Unit digit of the number) | |---|---| | A. $4^{425}$ | I. 6 | | B. $4^{1024}$ | II. 4 | | C. $133^{63} \times 4^{49}$ | III. 3 | | D. $3^{81}$ | IV. 8 | Choose the *correct* answer from the options given below:

If $7^{126}$ is divided by 48, find the remainder.

Consider the following statements: I. If a and b are composite numbers, then a + b is always composite. II. Zero is a natural number but not a whole number. Which of the above statements is/are correct from the options given below:

Find the sum of the first n positive integers.

Which of the numbers given below is divisible by 15?

Find the number which is nearest to 3105 and is exactly divisible by 21.

In a number system $\sqrt{3}$ is:

The sum of the perfect squares between 120 and 300 is .

Which of the following statements is/are correct about irrational numbers? (A) The sum of two rational numbers is always irrational. (B) $\pi$ is an irrational number. (C) The value of $\sqrt{49}$ is an irrational number. (D) The value of $\sqrt{5}$ is an irrational number. Choose the correct answer from the options given below:

Match **List-I** with **List-II** | List-I (Statements/Expressions etc.) | List-II (Values, etc.) | |---|---| | (A) Find the sum of the first 20 odd natural numbers. | (I) 285 | | (B) How many prime numbers are there between 100 and 200? | (II) 0 | | (C) Find the sum of the squares of the digits from 1 to 9. | (III) 400 | | (D) Find the unit's digit in the product $81 \times 82 \times 83 \times ... ... ... \times 89$? | (IV) 21 | Choose the **correct** answer from the options given below:

Find the missing number: <img src="https://balti.afterboards.in/VkBGHBFhffAu03o" width="400px"/>

In number system 3√2, is?

Select the number which when added to itself 13 times, gives 112.

How many numbers between 11 and 90 are divisible by 7 ?

If I write down all the numbers from 1 to 100, then how many times I have written the digit 3 ?

Match the LIST-I with LIST-II | LIST-I (For given Euclidean Algorithm, a = bq + r, Where a & b are real) | LIST-II Values of q and r | |---|---| | A. a = -112, b = -7 | I. q = -13, r = 1 | | B. a = 118, b = -9 | II. q = 14, r = 3 | | C. a = -109, b = 6 | III. q = -19, r = 5 | | D. a = 115, b = 8 | IV. q = 16, r = 0 | Choose the *correct* answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The number $\pi$ is a/an | (I) whole number | | (B) 0 is a/an | (II) complex number | | (C) $\sqrt{-1}$ is a/an | (III) composite number | | (D) 6 is a/an | (IV) irrational number | Choose the **correct** answer from the options given below:

Which one of the following statements is/are true? A. 48713280 is divisible by 11 B. 59761543 is not divisible by 3 C. 342221319 is divisible by 99 D. 10050432 is not divisible by 8 Choose the correct answer from the options given below:

Consider the following statements: I. If x and y are composite numbers, then x+y is always composite. II. There does not exist a natural number which is neither prime nor composite. Which of the above statements is/are correct?

Which one of the following statements is/are false? A. Every whole number is a natural number. B. Every integer is a rational number. C. Every rational number is an integer D. Every integer is a whole number. Choose the correct answer from the options given below:

Which of the following numbers is both a perfect square and a perfect cube?

The difference between the two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the reminder is 15. Find the smallest number?

Which one is correct A. $\sqrt{3}$ is irrational B. Sum of two irrational number is always irrational C. $\sqrt{p}$, where $p$ is prime, is irrational D. Every composite number can be expressed as a product of primes Choose the **correct** answer from the options given below:

Select the missing number from given options. | 12 | 7 | 95 | |---|---|---| | 14 | 8 | 132 | | 16 | 9 | ? |

Which of the following lists of numbers is/are an Arithmetic Progression? (A) 2, 8, 14, 20,........ (B) 0, 4, 8, 12,........ (C) 6, 12, 18, 24,........ (D) 21, 17,15,........ Choose the correct answer from the options given below:

The sum of the natural numbers which are divisors of 100, is:

If a and b are positive real numbers. Match List-I with List-II | List-I | List-II | |---|---| | Identities | Relation | | (A) $(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})$ | (I) $=a-b$ | | (B) $(a+\sqrt{b})(a-\sqrt{b})$ | (II) $=a^2-b$ | | (C) $(\sqrt{a}+\sqrt{b})^2$ | (III) $=a-b^2$ | | (D) $(\sqrt{a})^2-(\sqrt{b})^4$ | (IV) $=a+2\sqrt{ab}+b$ | Choose the correct answer from the options given below:

If a - b = 4, b - c = 6 and a - c = 10, then the value of $a^2 + b^2 + c^2 - ab - bc - ca$ is:

7^6n - 6^6n, where n is an integer greater than 0, is divisible by

How many pairs of positive integers e, f satisfy 1/e + 4/f = 1/12 where f is an odd integer less than 60?

Which one of the following is/are correct? (A) Every irrational number is a real number. (B) Every real number is an irrational number. (C) The sum or difference of a rational number and an irrational number is an irrational number. (D) The product or quotient of a non-zero rational number with an irrational number is an irrational number. Choose the correct answer from the options given below:

Match List-I with List-II [a, b as given in the Euclidean algorithm, quotient (q), Remainder (r)] Remainder (r) $a = bq + r$ | List-I | List-II | |---|---| | (A) a = 112, b = 7 | (I) r = 1 | | (B) a = 118, b = 9 | (II) r = 3 | | (C) a = 119, b = 6 | (III) r = 5 | | (D) a = 115, b = 8 | (IV) r = 0 | Choose the correct answer from the options given below:

How many numbers between -13 and 13 are multiples of 3 or 5?

The sum of the perfect squares between 150 and 250 is:

Determine the unit's digit in the product of consecutive numbers from 86 to 94?

Consider the following statements: (A) The unit's digit in the product of (5236 x 6231) is 1. (B) The digit in the unit's place for the product 31 x 32 x 33 x 34 x ....x 49 is 0. (C) The sum of the face values of 7 and 4 in 8175349 is 11. (D) The sum of the place values of 3 in 3935 is 6. Choose the correct answer from the options given below:

Two numbers are in ratio 2:7 and their L.C.M. is 182. The greater number is

Consider the following statements (A) 141 is a prime number. (B) 2984234 is divisible by 11 (C) 39552 is divisible by 18. (D) The sum of the face values of 3 and 5 in 36251 is 8. Choose the correct answer from the options given below:

Consider the following statements (A) Square of an odd number is of the form 4n + 1. (B) 1 is a prime number. (C) 83356768 is divisible by 11. Which of the statement(s) given above is/are incorrect?

The difference between the squares of two consecutive even integers will always be divisible by which of the following? (A) 2 (B) 3 (C) 4 (D) 5 Choose the correct answer from the options given below:

Six bells ring at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. Once, when they start ringing simultaneously for the first time, then determine how many times they will ring together in a continuous span of 30 minutes?

A number when divided by 95 leaves a remainder 43. If the same number is divided by 19, then the remainder will be:

Match List-I with List-II | List-I | List-II | |---|---| | (A) Remainder when $17^{35234}$ is divided by 8 | (I) 0 | | (B) Remainder when 4444 is divided by 9 | (II) 1 | | (C) Unit's digit of $(34)^{15} + (34)^{16}$ | (III) 2 | | (D) Unit digit of $7^4 - 9^3$ | (IV) 7 | Choose the correct answer from the options given below:

The nearest integer to 6650 which is exactly divisible by 429 is

The sum of the digits of a 4-digit number is subtracted from the number. The resulting number is always

Arrange the fractions in decreasing order: (A) $\frac{4}{5}$ (B) $\frac{7}{8}$ (C) $\frac{3}{7}$ (D) $\frac{5}{9}$ Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (A) Unit's digit of $(257)^{153} \times (346)^{72}$ | (I) 3 | | (B) Unit's place of the product $61 \times 62 \times 63 \times 64 \times ... \times 69$ is | (II) 4 | | (C) 121012 is divided by 12, the remainder is | (III) 0 | | (D) Unit's digit of $(257)^{153} + (346)^{72}$ | (IV) 2 | Choose the correct answer from the options given below:

Given below are two statements: Statement (I): 2469385422 is divisible by 18. Statement (II): 3475824638 is divisible by 11. In light of the above statements, choose the most appropriate answer from the options given below.

If x and y are negative integers, then which of the following statements is/are always true? (A) x + y is positive integer. (B) xy is positive integer. (C) x-y is positive integer. Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The least number that must be subtracted from 2025 to get a number exactly divisible by 17 | (I) 5 | | (B) The least number that must be added to $1057^5$ to get a number exactly divisible by 23. | (II) 2 | | (C) Unit digit of $6^{15} - 7^4$ | (III) 0 | | (D) The product of any number and the 1st whole number is: | (IV) 1 | Choose the correct answer from the options given below:

The sum of first 10 prime numbers is:

Which of the following pair of numbers is relatively prime to each other?

How many two-digit numbers are divisible by 3?

The remainder when $(15^{23} + 23^{23})$ is divided by 19, is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The least number that must be subtracted from 2025 to get a number exactly divisible by 17 | (I) 5 | | (B) The least number that must be added to $1057^{5}$ to get a number exactly divisible by 23 | (II) 2 | | (C) Unit digit of $6^{15}-7^4$ | (III) 0 | | (D) Find the product of any number and the 1st whole number | (IV) 1 | Choose the correct answer from the options given below:

Which one of the following statement(s) is/are correct? (A) Every whole number is a natural number. (B) Every natural number is a whole number. (C) Every integer is a whole number. (D) Every rational number is a whole number Choose the correct answer from the options given below:

How many perfect squares lie between 120 and 300?

The sum of all prime numbers less than 20 is:

If function (x + 296 × 298) is a perfect square, then the value of x is:

$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{10} =$

How many times does the digit 3 appear in the counts from 1 to 100?

If m and n are distinct natural numbers, then which of the following is/are integer(s)? (A) $m/n + n/m$ (B) $mn(m/n+n/m)(m^2 + n^2)^{-1}$ (C) $mn/(m^2 + n^2)$ Choose the correct answer from the options given below:

How many times digit 3 appear in the counting from 1 to 1000?

Which of the following is/are prime numbers? (A) 241 (B) 337 (C) 391 (D) 571 Choose the correct answer from the options given below:

Consider the following statements (A) To obtain prime numbers less than 121, we have to reject all the multiples of 2, 3, 5 and 7. (B) Every composite number less than 121 is divisible by a prime number less than 11. (C) 173 is not a prime number. (D) 7710312401 is divisible by 11. Which of the statement(s) given above is/are correct? Choose the correct answer from the options given below:

Consider the following statements (A) The difference between the place values of 9 and 5 in the number 639457 is 4. (B) The number π is an irrational number. (C) The sum of all the prime numbers from 1 to 20 is 67. (D) The difference between the face values of 5 and 3 in number 475839 is 2. Choose the correct answer from the options given below:

What is the remainder when the number $(44)^2$ is divided by 9?

The unit place digit of the number $(37)^2$ is:

Simplify $24 ÷ 4 × 2 + 8 - 4 =$ ?

The difference of the greatest and the smallest of the fractions $\frac{1}{2}$, $\frac{8}{11}$, $\frac{7}{8}$, $\frac{7}{9}$, $\frac{5}{6}$ is:

The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is:

The unit digit in the product $(784 \times 618 \times 917 \times 463)$ is :

Which one of the following numbers is not a prime number?

Which fraction among $\frac{2}{3}$, $\frac{4}{5}$, $\frac{7}{11}$, $\frac{1}{3}$ is largest?

The smallest five digit number which is exactly divisible by 12, 15 and 18 is:

If 7-digit number 485A64B is divisible by 8 and 9, then find the greatest value of A + B.

Simplify : $2 \times [4 - \{2 - (2-3) - (2+3)\} - 1] - 5 \times [-3 - (3-2)]$

Find the length of the longest rod which can be used to measure exactly the lengths 5 m 13 cm, 11 m 34 cm and 12 m 15 cm.

Which of the following is correct for divisibility? (1) A number is divisible by 6 if it is divisible by 3 or 2. (2) A number is divisible by 5 if its unit digit is 0 or 5. (3) A number is divisible by 3 if its unit digit is divisible by 3. (4) A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Choose the correct answer from the options given below:

The ascending order of the numbers 0.8, 0.88, 0.808, 0.08 is

Find the value of $\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \ldots}}}}$.

The ratio of two numbers is 2:3 and their HCF is 4. Their LCM is :

Given below are two statements: Statement (I): All natural numbers are rational numbers. Statement (II): 1 is the smallest prime number. In the light of the above statements, choose the most appropriate answer from the options given below:

The value of $(625)^{-3/4}$ is:

What is the smallest square number which is divisible by 4, 6 and 32?

Find the value of $(25)^3 + (-29)^3 + (4)^3$

The value of $\frac{(2 \cdot 7)^3 - (2 \cdot 2)^3}{(2 \cdot 7)^2 + 2 \cdot 7 \times 2 \cdot 2 + (2 \cdot 2)^2}$ is

Let A be the greatest number that will divide 505, 555 and 605, leaving the same remainder in each case. Then sum of the digits in a is:

Find the value of $\sqrt[3]{117649}$ =

The value of $\left(\frac{8}{125}\right)^{\frac{-4}{3}}$ is __________

$\frac{1}{0.004}$ is equal to:

Simplify $2\frac{3}{4} \div 2\frac{2}{3} \div 1\frac{1}{12} = ?$

Simplify $786 \times 237 + 786 \times 763 = ?$

Find the missing number in place of ? from the following given options. <img src="https://balti.afterboards.in/IA47PtxGnJBqf9I" width="300px"/>

Find the greatest number that will divide 38, 88 and 163 so as to leave the same remainder in each case

Find the value of $\frac{5^{\frac{2}{3}} \times \sqrt[3]{5^7}}{\sqrt[3]{5^6}}$

The value of $13.7 \times 12.7 \times 0.8$ is ______

The sum of greatest five digits and lowest/smallest four digits number is:

If $\sqrt[3]{x} = 2y$. Then, the value of $\frac{y^3}{x}$ is ______

The value of $\sqrt{.01} \times \sqrt[3]{.027} - 0.3$ is

The value of $\frac{(793 + 232)^2 - (793 - 232)^2}{(793 \times 232)}$ is

The greatest length of the scale that can measure exactly 20 cm, 90 cm, 1 m 25 cm and 1 m 30 cm length is:

Match List I with List II: | List I | List II | | --- | --- | | A. Sum of first 5 primes | I. 15 | | B. Average of first 5 primes | II. 28 | | C. Sum of first 5 natural numbers | III. 3 | | D. Average of first 5 natural numbers | IV. 5.6 | Choose the correct answer from the options given below:

Consider the series: 2, 3, 5, 7, 11, 13, 17, 19, 21, 23, 29 Find the number which is different from other similar numbers.

Find the value of $\left(\sqrt[3]{\frac{125}{27}} - \sqrt[3]{\frac{512}{729}}\right) \div \sqrt[3]{\frac{64}{5832}}$ is

What is the smallest number of five digits formed by using the digits 2, 4, 0, 3, 5 ?

$296 \times 296 - 204 \times 204 = ?$

$-224 + (-314) \times 9 = ?$

$-\sqrt{8} + \sqrt{128} - \sqrt{32}$ is equal to

If P consumes 1500 ml of milk every day. How many liters of milk will be consumed in 4 weeks ?

Find the smallest among the following ? $\sqrt[4]{6}, \sqrt{2}, \sqrt[3]{4}$ and $\sqrt{3}$

The ratio of two numbers is 5 : 6 and their HCF is 8. What is the LCM of these numbers?

The value of $2 \div 2 - 2$

The value of $\frac{(8.9)^2 - (2.1)^2}{8.9 - 2.1}$

The value of $\left(\frac{x}{y}\right)^{2a-3b} \times \left(\frac{x}{y}\right)^{3b-4c} \times \left(\frac{x}{y}\right)^{4c-2a}$

Find the LCM of $\frac{3}{5}$, $\frac{4}{9}$ and $\frac{5}{8}$ is

If $(a+b)^2 = 5 + 2\sqrt{6}$, what can be the possible value of 'b' from the following?

Distance of A to B is <img src="https://balti.afterboards.in/O7TQ9VBjENCFo6S" width="400px"/>

Given set is (2, 17, 31) is set of: (a) Prime numbers (b) Whole numbers (c) Odd numbers (d) Even numbers Choose the correct answer from the options given below:

Ratio $5^{8.14} : 5^{5.14}$ is equal to:

The LCM and HCF of two numbers are 35 and 15 respectively. The product of these numbers is ________.

The value of $3 - 3 \div 3$:

The value of $x^{a-b} \times x^{b-c} \times x^{c-a}$ is: