General Test Quantitative Reasoning questions from CUET UG 2025.
7^6n - 6^6n, where n is an integer greater than 0, is divisible by
A and B are participating in the same contest, the probability of their winning are $\frac{5}{8}$ and $\frac{1}{4}$ respectively. What is the probability that neither of them will win the contest?
A bag contains 3 red, 2 blue, 5 green and 4 yellow balls. If two balls are picked at random, what is the probability that either both are red or both are blue?
A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct? (A) The probability that both balls are red is $\frac{1}{11}$. (B) The probability that one ball is red, and one ball is blue is $\frac{10}{33}$. (C) The probability that both balls are blue is $\frac{5}{33}$. (D) The probability that both balls are green is $\frac{5}{11}$. Choose the correct answer from the options given below:
A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct? (A) The probability that both balls are red is 1/11. (B) The probability that one ball is red, and one ball is blue is 10/33 (C) The probability that both balls are blue is 5/33. (D) The probability that both balls are green is 5/11. Choose the correct answer from the options given below:
A basket contains 4 red, 5 blue and 3 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?
A basket contains 4 red, 5 blue and 3 green marbles. If three marbles are picked up at random, what is the probability that at least one is blue?
A man and his wife appeared for an interview for the two vacancies. If the probability of husband's selection is $\frac{1}{3}$ and the probability of wife's selection is $\frac{1}{5}$, then the probability that none of them will be selected?
A number when divided by 95 leaves a remainder 43. If the same number is divided by 19, then the remainder will be:
A single card is chosen at random from a standard deck of 52 playing cards. The probability of choosing either a Queen or a Spade (but not both) is:
A speaks the truth in 70% of cases and B lies in 40% of cases. The probability that they will say the same thing while describing a single event (to have occurred or not) will be:
An integer number is chosen at random from the first 100 integers. What is the probability that the chosen number is a perfect cube?
Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?
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:
Consider the Arithmetic Progression: 3,8,13,18..... . What is the 18th term of the given Arithmetic Progression. Choose the correct answer from the options given below:
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?
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:
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:
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:
Determine the unit's digit in the product of consecutive numbers from 86 to 94?
Find the sum of 24 terms of the list of numbers whose n$^{th}$ term is given by: $a_n = 3 + 2n$
Find the value of p for which the lines, $px + 3y + 5 = 0$ and $8x + 2y - 3 = 0$ are parallel.
Five digit numbers formed by using digits 0, 1, 2, 3 and 4 (when repitition of digits are not allowed) are:
For what value of k, the system of equations $3x - ky - 3 = 0$ and $2x - 3y - 4 = 0$ has no solution?
For what value of k, the system of equations $kx + 4y - k + 4 = 0$ and $16x + ky = k$ has an infinite number of solutions?
Four people are chosen at random from a group of 3 men, 2 women and 4 children. The probability that exactly 2 of them are children is:
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.
How many numbers between -13 and 13 are multiples of 3 or 5?
How many pairs of positive integers e, f satisfy 1/e + 4/f = 1/12 where f is an odd integer less than 60?
How many perfect squares lie between 120 and 300?
How many terms of the AP: 24, 21, 18, ............ must be taken so that their sum is 78?
How many times digit 3 appear in the counting from 1 to 1000?
How many times does the digit 3 appear in the counts from 1 to 100?
How many two-digit numbers are divisible by 3?
How many ways can 10 persons shake hands with two persons?
How many ways can a committee of 3 people be chosen out of 7 people?
How many ways, can the letters of the word 'QUANTITATIVE' be arranged, so that all T are together?
If 2x + 3y - 8 = 0 and 3x - 2y - 12 = 0, then $4x^2 + y^2 - 4x$ is equal to:
If 2x + 3y = 26 and y - x = 2, then the value of x + y is:
If : $a + b + c = 14$ and $a^2 + b^2 + c^2 = 96$, then $(ab + bc + ca)$ is
If $2^{(x+y)} = 64$ and $128^{(x-y)} = 2$, then what is the value of x?
If $6x - 10y = 10$ and $\frac{x}{x+y} = \frac{5}{7}$, then (x-y) is equal to:
If each term of a geometric progression (GP) is positive and is the sum of two preceding terms, then the common ratio of the GP is:
If function (x + 296 × 298) is a perfect square, then the value of x is:
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:
If on dividing 26 into two parts, we find that three times the first and seven times the second part together equals to 122. Then, the ratio of first and second part shall be:
If the 5th and 9th terms of an arithmetic progression are 7 and 13, respectively, then the 15th term is:
If the product of n positive numbers is $n^n$, then what is the minimum value of their average for n = 6?
If the sum of n terms of an A.P. is $nP + \frac{1}{2}n(n - 1)Q$, where P and Q are constants, find the common difference.
If the third and ninth terms of an A.P. are 1 and 19 respectively, then the 23rd term will be:
If $\log_8 x = 2/3$, then the value of X is:
If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is:
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:
In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 1.5 minutes after he starts playing. What is the probability that the music will stop within the first 15 seconds after starting?
In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:
In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 8?
In a team every player shakes his hand with other player only once. If total number of handshakes is 120, then the number of players is:
In an A.P, if $m^{th}$ term is n and the $n^{th}$ term is m, where $m \neq n$, find the $p^{th}$ term.
In an arithmetic progression, if 6 is the third term, the ninth term exceeds the seventh term by 3, then 12 is which term?
In an examination, a student scores 3 marks for every correct answer and looses 1 marks for every wrong answer. A student attempted all the 120 questions and scored 320 marks. Find the number of questions, he answered incorrectly.
In an examination which had 200 questions, students score 4 marks for every correct answer and lose 1 mark for every wrong answer. A student attempted all the 200 questions and scored 200 marks. The number of questions, student answered correctly in the examination, is:
In arithmetic progression(A.P.), the first term is 7 and the 6th term is 22. The sum of the first 10 terms of A.P. is:
In how many different ways can the letters of the word 'DELETE' be arranged?
In how many different ways can the letters of the word 'DELETE' be arranged?
In how many different ways can the letters of the word 'RUMOUR' be arranged?
In how many different ways can the letters of the word OPERATE be arranged?
In how many different ways can the letters of the word GOODNESS be arranged?
In how many different ways, can the letters of the word ASSOCIATION be arranged, so that the vowels always come together?
In how many different ways can the letters of the word 'OFFICE' be arranged so that the vowels never come together?
In how many different ways can the word "DAUGHTER" be arranged so that the vowels always come together?
In how many ways are the letters of the word DOCUMENT arranged so that all the vowels always come together?
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
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:
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:
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:
Match List-I with List-II | List-I | List-II | |---|---| | (A) The number of different words that can be formed with CUSTOM with the condition that the word should begin with M is ______. | (I) 70 | | (B) The number of different ways in which the letters of the word EXTRA can be arranged so that the vowels are never together is ______. | (II) 45 | | (C) There are 10 points in a plane. No three of these points are in a straight line. The total number of straight line that can be formed by joining the two points is _______. | (III) 72 | | (D) The number of ways a committee of 4 people be chosen out of 8 people is _______. | (IV) 120 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (A) $^{75}P_2 - ^{75}C_2$ | (I) 504 | | (B) $^{5}P_5 - ^{10}C_3$ | (II) 6 | | (C) $^{16}C_{13} - ^{8}C_3$ | (III) 2775 | | (D) $^nP_4 = 360$, then find n | (IV) 0 | 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:
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:
Match List-I with List-II | List-I | List-II | |---|---| | (A) $^8P_3 - ^{10}C_3$ | (I) 6 | | (B) $^8P_5$ | (II) 21 | | (C) $^nP_4 = 360$, then find n. | (III) 216 | | (D) $^nC_2 = 210$, find n. | (IV) 6720 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (A) $^n{C_{r-1}} + ^n{C_r}$ | (I) $^n{C_{n-r}}$ | | (B) $^n{C_r}$ | (II) $n + ^1{C_r}$ | | (C) $^{50}{C_r} = ^{50}{C_{r+2}}$, then r = | (III) 24 | | (D) $^n{P_3} = 9240$, n=? | (IV) 22 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (Expression) | (Value) | | (A) $\frac{12!}{10!(2!)}$ | (I) 110 | | (B) $^nC_2 = 210$, find n. | (II) 136 | | (C) $^6P_3 - ^5C_2$ | (III) 66 | | (D) If $^nC_9 = ^nC_8$, find $^nC_{15}$ | (IV) 21 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (Expressions) | (Values) | | (A) 1/6! + 1/7! = x/8! Find x | (I) 1 | | (B) Evaluate: $\frac{n!}{(n-r)!}$, n = 6, r = 2 | (II) 100 | | (C) If ⁿC₉ = ⁿC₈, find ⁿC₁₇. | (III) 64 | | (D) ⁶P₃ - ⁵P₂ | (IV) 30 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (Expressions) | (Values) | | (A) $^nP_4 = 360$, then find n | (I) 1155 | | (B) If $^{13}C_{3r} = ^{15}C_{r+3}$, then find r | (II) 56 | | (C) Find $^{15}C_{11} - ^{15}C_4$ | (III) 6 | | (D) Find $^8P_2$ | (IV) 3 | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (Statements/Expressions, etc.) | (Value/Expressions, etc.) | | (A) P(E) | (I) 1 | | (B) The probability of an impossible event | (II) P(A). P(B) | | (C) For exhaustive events E₁ and E₂, P(E₁ ∪ E₂)= | (III) 1-P(Ē) | | (D) For independent events A and B, P(A ∩ B)= | (IV) 0 | Choose the correct answer from the options given below:
One card is drawn from a well-shuffled deck of 52 cards. Find the probability that the card be an ace.
Out of 6 men and 4 women, a committee of 5 members is to be formed so that it has 2 women and 3 men. In how many different ways can it be done:
$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{10} =$
Read the information given below carefully and answer the question that follows: (A) The different ways in which the alphabets of the word BAKERY can be arranged is 720 (B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576 Choose the correct answer from the options given below:
Read the information given below carefully and answer the question that follows: Aditi, a salesgirl is appointed at a basic salary of ₹ 1200 per month. The condition of employment further stated that for every sale of ₹ 10000 or above she does, she will get 50 % of basic salary and 10 % of the sales as special incentive. However, this incentive scheme shall not work on the first ₹ 10000 of sales made. What should be the value of sales if Aditi wants to earn ₹ 7600 in a particular month?
Read the information given below carefully and answer the question that follows: **Question: How much does Ajay pay to his driver every month as Salary?** **Statements:** i. Rakesh pays 20% more per month, to his driver than Ajay as Rakesh's driver has a 15 year experience. Moreover, Ajay pays 30% more per month than Karan as Karan's driver has mere 5 years of experience. ii. As Karan would avail 10% discount on drivers's salary by paying for 6 months in advance, Karan paid his driver Rs 54000 for 6 months in advance. Determine which of the following is True in order to solve the asked question?
Reena is twice as old as Sunita. Three years ago, Reena was three times as old as Sunita. What is present age of Reena?
Rita purchased 9 pens and 7 pencils for ₹ 66. Megha also bought 5 pens and 11 pencils of the same kind for ₹ 58. What is the cost of 3 pencils?
Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables is:
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?
Solve the given equation by replacing the question mark "?" with the most appropriate option: $16^2 + 8^2 - 16 * 8 = \ ?$
Suppose we throw a dice once. Then, which one of the following is/are correct? (A) The probability of getting a number greater than 4 is $\frac{1}{3}$ (B) The probability of getting a number greater than or equal to 4 is $\frac{1}{3}$ (C) The probability of getting a number less than or equal to 3 is $\frac{1}{2}$ (D) The probability of getting a number less than or equal to 6 is 1. Choose the correct answer from the options given below:
The 21st and 33rd terms of an arithmetic progression are 91 and 145 respectively. What is the 29th term?
The 7th and 9th terms of an arithmetic progression are 10 and 11, respectively. Find the 15th term.
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:
The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have
The first and the last terms of an arithmetic progression are 25 and 180, respectively. If the sum of all the terms is 1025, how many terms are there?
The graphs of ax+by = c and dx+ey = f will be: (A) parallel, if the system has no solution. (B) coincident, if the system has finite numbers of solutions. (C) intersecting, if the system has only one solution. Which of the above statements is/ are correct? Choose the correct answer from the options given below:
The graphs of px + qy = r, mx + ny = s will be (A) intersecting, if the system has only one solution. (B) overlapping, if the system has a finite number of solutions. (C) parallel, if the system has infinite solutions Which of the statements below is/are incorrect?
The intersection point on the Y- axis of $5x - 3y = 9$ is
The middle term of the series 4 + 6 + 8 + ..................... + 196 is
The nearest integer to 6650 which is exactly divisible by 429 is
The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _________ .
The pair of linear equations $kx + 3y + 1 = 0$ and $2x + y + 3 = 0$ intersect each other, if
The pair of linear equations mx + 2y + 3 = 0 and 3x + 6y + 2 = 0 intersect each other, if
The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:
The present ratio of ages of P and Q is 2:7. Six years ago, this ratio was 1:5. Determine the present age of P?
The probability that a card drawn from a pack of 52 cards will be a red card or an ace (including the chance of any red ace), is:
The remainder when $(15^{23} + 23^{23})$ is divided by 19, is:
The sum of all prime numbers less than 20 is:
The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:
The sum of first 10 prime numbers is:
The sum of n terms of the series $1 + \frac{3}{2} + 2 + \frac{5}{2} + 3 + \frac{7}{2} + ...$
The sum of n terms of the series $1 + 1.5 + 2 + 2.5 + 3 + ...$ is?
The sum of the digits of a 4-digit number is subtracted from the number. The resulting number is always
The sum of the perfect squares between 150 and 250 is:
The system of equations $4x + 14y = 18$ and $6x + 21y = 33$ has
The unit place digit of the number $(37)^2$ is:
The value of $\frac{1}{3 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} + ... + \frac{1}{27 \times 31}$ is:
The value of k, for which the system of equations 3x-ky-20 = 0, and 6x-10y+40 = 0 has no solution, is:
There is a match between two teams. Each team has a total of 15 players. After the match, all the players of one team shake hands with all the players of the other team. What is the number of possible hand shakes?
Three unbiased coins are tossed. What is the probability of getting at least 2 heads?
Two candidates, X and Y appeared in an interview for two vacancies for the same post. The probabilities of their selection are 1/4 and 1/7, respectively. What is the probability that one of them will be selected?
Two dice are thrown simultaneously. What is the probability that 4 will come up on at least one die?
Two friends, P and Q, appeared in an interview for two vacancies for the same post. The probability of P's selection is $\frac{1}{3}$ and that of Q's selection is $\frac{2}{7}$. What is the probability that at least one of them will be selected?
Two numbers are in ratio 2:7 and their L.C.M. is 182. The greater number is
Two persons A and B appear in an interview for two vacancies. If the probabilities of their selections are 1/4 and 1/6 respectively, then the probability that none of them is selected shall be:
Two unbiased coins are tossed. The probability of getting at least one head is:
Two water pipelines are represented by the equations $kx + 3y +1 = 0$ and $2x + y + 3 = 0$. For what value of k, the pipelines cross each other?
What is the remainder when the number $(44)^2$ is divided by 9?
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:
Which of the following list of numbers forms an arithmetic progression? (A) 1, -1,-3 -5, ....... (B) -1.2, -3.2, -5.2, -7.2, ........... (C) -2, 2, -2, 2, -2, ........ (D) 2, $\frac{5}{2}$, 3, $\frac{7}{2}$ ...... Choose the correct answer from the options given below:
Which of the following pair of linear equations is inconsistent? (A) x - y = 5; 3x - 3y = 10 (B) 2x + 3y = 4; 4x + 6y = 8 (C) 9x + 6y = 6; 3x + 2y = 3 (D) 2x + 5y = 2; 6x - 15y = 4 Choose the correct answer from the options given below:
Which of the following pair of numbers is relatively prime to each other?
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:
Which one of the following pairs of linear equations has/ have infinite many solutions? (A) $9x + 3y + 12 = 0$, and $18x + 6y + 24 = 0$ (B) $2x - 3y = 13$, and $7x - 2y = 20$ (C) $x + y = 5$, $2x + 2y = 10$ (D) $3x + y - 3 = 0$ and $2x + \frac{2}{3}y = 2$ 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: