Math practice based on Combined Graduate Level Examination 2024 Tier I

Extended Intelligence Quiz

Extended Intelligence and Reasoning Quiz

Time: 00:00

Q1. Which digits should come in place * and $, respectively, if the number 72864*$ is divisible by both 8 and 5?

Q2. The total number of soaps sold by companies Q and S together in May is what percentage more than the number of soaps sold by company P in July?

Q3. In a triangle PQR, S is a point on the side QR such that PS ⊥ QR. Which of the following options is true?

Q4. Simplify 15.5 - [3 - (7 - (5 - (14.5 - 13.5)))].

Q5. The incomes of P, Q and R are in the ratio 10:12:9 and their expenditures are in the ratio 12:15:8. If Q saves 25% of his income, then what is the ratio of the savings of P, Q and R?

Q6. If at least 40% marks in Mathematics are required for pursuing higher studies in Mathematics, how many students will be eligible to pursue higher studies in Mathematics?

Q7. In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles are congruent by SAS criterion if:

Q8. Two pipes, A and B, can fill a tank in 10 minutes and 20 minutes, respectively. The pipe C can empty the tank in 30 minutes. All the three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. In what time will the tank be full (in minutes)?

Q9. A payment of ₹120 is made with ₹10, ₹5 and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?

Q10. If 28.9: x:: x: 36.1, and x > 0, then find the value of x.

Q11. If the total number of successful start-ups is 2910, then find the number of start-ups in the education and agriculture sectors.

Q12. The height of a cylinder is 20 cm. The lateral surface area is 1760 cm². Its volume is:

Q13. Raj divides ₹1,200 in the ratio 2:1:3 among three of his friends. The amount equal to the sum of three times the largest share and two times the smallest share is:

Q14. A shopkeeper marked an article at ₹7,500. The shopkeeper allows successive discounts of 20%, 15% and 10%. The selling price of the article is:

Q15. The average of 12 numbers is 48. The average of the first 5 numbers is 45 and the average of next 4 numbers is 52. If the 10th number is 10 less than the 11th number and is 5 more than the 12th number, then the average of the 11th and 12th numbers is:

Q16. Find the value of the following expression. √[(1 + sinθ) / (1 - sinθ)]

Q17. The value of [(sinθ - 2sin³θ) / (2cos³θ - cosθ)]³ * (1 / tanθ) - sec²θ is:

Q18. Let t = 2/5, then the value of the expression t³ + (2/5)³ + (9/5)t is:

Q19. M and N walk along a circular track. They start at 5:00 a.m. from the same point in the opposite directions. M and N walk at a speed of 5 rounds per hour and 2 rounds per hour, respectively. How many times will they cross each other before 6:30 a.m. on the same day?

Q20. Two circles C1 and C2 touch each other externally. The radius of C1 = 16 cm and the radius of C2 = 8 cm. Find the length (in cm) of their common tangent.

Q21. If x + (1/x) = 15, then the value of (7x² - 9x + 7) / (x² - x + 1) is:

Q22. In which of the given year(s) was the production of B type refrigerator closest to its average production over the given years?

Q23. The measures of the three angles of a triangle are in the ratio 17:13:15. Find the positive difference between the greatest and the smallest of these three angles.

Q24. If 2cosec²θ + 3cot²θ = 17, then the value of 'θ' when 0° ≤ θ ≤ 90° is:

Q25. A certain sum of money becomes seven times itself when invested at a certain rate of simple interest, in 14 years. How much time (in years, rounded off to 2 decimal places) will it take to become 18 times itself at the same rate?

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