வெல்லுங்கள் CSAT 2025 - 32: மாதிரித் தேர்வு 1 - கணிதவியல்

Questions & Answers - (Multiple Choice) - Model Test 1 - 40 minutes
கொள்குறி வினா- விடைகள் - தேர்வு 1 - கணிதவியல்

After answering all the questions, you can assess yourself by correct answers given at the end.

1. Three vertices of a regular hexagon are chosen at random. The probability that the triangle with three chosen vertices is an equilateral triangle is
a. 0.5 b. 0.2
c. 0.1 d. 0.4

2. If x and y are two positive integers such that x > y and u and v are the multiplicative inverse of x and y respectively then the value of
uy + vx is
a. (u^2 + v^2)/(u + v)
b. (u^2 + v^2)/(x + y)
c. (x^2 + y^2)/(u + v)
d. (x^2 + y^2)/(xy)

3. If we add a fraction to itself and multiply the result by the additive inverse of the fraction then we get
-(578/49), then the integral part of the original fraction is
a. 2 b. 3
c. 3 d. 4

4. In a college, one-fifth of the students like cricket, one-eighth of the remaining students like volley ball and one-fifth of the rest of the students like basket ball. Other students do not like these games. If the number of students who do not like the above three games is 420, what is the total number of students in the college?
a. 375 b. 750
c. 875 d. 1125

5. A boat goes upstream from one point to another point which is 45km apart in 5 hours. It covers the same distance downstream in 3 hours. Find the speed of the stream in km.?
a. 2 b. 4
c. 3 d. 2.5

6. What is the remainder when 3^(333) is divided by 728?

a. 1 b. 333
c. 9 d. 27

7. The sum of digits of a 2-digit number is 11.The number obtained by interchanging the digits increases the original number by 27. The original number is
a. 74 b. 47
c. 65 d. 38

8. Two litres of water evaporates from 12 litres of sea water containing 8% salt. The salt percentage in the remaining solution is
a. 8.6 b. 9.8
c. 7.6 d. 9.6

9. The salary of a person is ₹36000 per month. After six months 30% of his salary is increased due to his performance. After three months it was decreased by 20% due to low performance. Find his salary after nine months.
a. ₹ 39600 b. ₹41040
c. ₹ 37440 d. ₹ 43200

10. A n-digit number (positive) with exactly n digits. 900 distinct n-digit numbers are to be formed using only the three digits 3, 6 and 9. What is the smallest value of 'n' ?
a. 7 b. 6
c. 8 d. 9

11. A is twice as fast as B and together they can do the work in 27 days. A alone can do the work alone in
a. 54 days b. 40.5 days
c. 42days d. 81 days

12. The sum of two numbers relatively prime to each other is 24. If their LCM is 143. Find the difference of the two numbers.
a. 5 b. 4
c. 3 d. 2

13. The difference of any two sides of a triangle
a. is always greater than third side.
b. it has no relation with third side.
c. is always less than third side
d. is equal to third side.

14. Which of the following is represented by the expression given below?
5k - 4
a. 4 more than five times of a number.
b. 5 more than fiour times of a number.
c. 4 less than five times of a number.
d. 5 less than five times of a number.

15. What is the remainder when
(x^2 + 10x + 21) is divided by (x + 3)
a. 0 b. (x+7)
c. (x + 10) d. 1

16. One side of an equilateral triangle is 8cm. The midpoints of its sides are joined to form another triangle whose midpoints are in turnjoin to form still another triangle. This process continues indefinitely. The sum of perimeters of all the triangled thus formed is
a. 64 cm b. 48 cm
c. 32 cm d. 128 cm

17. The sum of all natural numbers upto 101 which are multiples of 6 or 7 is
a. 3111 b. 1311
c. 1231 d. 1131

18. A contractor undertook a piece of work in certain number of days with 60 workers. But two workers dropped out second day ; two more workers dropped out on third day and so on. It took him four days extra to finish the work. The number of days in which the work was completed
a. 18 b. 20
c. 16 d. 14

19. If the selling price of 12 articles is same as the cost price 15 articles, the profit percentage is
a. 25 b. 20
c. 30 d. 18

20. What is the unit digit of the product
(682)^(286)?
a. 2 b. 4
c. 8 d. 6

21. Which one of the following statements is incorrect?
a. 2 is a prime number
b. 2 & 3 are called fundamental primes.
c. The biggest prime in 3 digits is 997.
d. 1 is the first prime number.

22. If a transversal cuts two parallel lines then :
Statement 1 : Alternate angles are equal.
Statement 2 : Sum of corresponding angles is 180°.
Which of the following option is correct for the above statements?
a. Statement 1 is true and 2 is false.
b. Statement 2 is true and 1 is false.
c. Both statements are true.
d. Both statements are false.

23. Two men A and B start from a place walking at 5km and 7.5km per hour respectively. What is the time will they take to be 50km apart if they walk in opposite directions?
a. 2 hrs b. 4 hrs
c. 6 hrs d. 8 hrs

24. When a number divided by X leaves a remainder 8 and when divided by 3X leaves a remainder 21. What is the remainder left, when twice of the number divided by 3X?
a. 13 b. 45
c. 3 d. None.

25. When you reverse the digits of age of mother you will get the age of daughter. One year ago, the age of mother is twice the age of the daughter. The present ages of mother and daughter are
a. 63 and 36 b. 83 and 38
c. 74 and 47 d. 73 and 37