Limited, Saraswati Bhavan, Second Floor, Lotus Link Square, New Link Road, D.N. Nagar Metro Station, Andheri (W), Mumbai - 400 058 Ph.: (Andheri: 8080-220-888); (Chembur: 8080-220-888); (Navi Mumbai: 900-460-3450); (Thane: 41617777); (Kandivali: 808-088-3438) Web: www.fiitjee.com email:
[email protected] IOQM MOCK TEST – 3 OLYMPIADS 2024-25 Time: 180 minutes Maximum Marks: 100 Please read the instructions carefully. INSTRUCTIONS A: General: 1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball point pen. 2. Use Black Ball Point Pen only for writing particulars on Answer Sheet. Use of pencil is strictly prohibited. 3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 4. The answer sheet, a machine-gradable Objective Response Sheet (ORS) is provided separately. 5. Do not Tamper/mutilate the ORS or this booklet. 6. No additional sheets will be provided for rough work. 7. On completion of this test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. B: Questions paper format & Marking Schema: 1. The question paper consists of 30 questions of Mathematics. 2. Each question has one- or two-digit(s) Integer as an answer. 3. Question 1 to 10 carry 2 marks each; question no. 11 to 20 carry 3 marks each; questions 21 to 30 carry 5 marks each. 4. All questions are compulsory. 5. Do all rough work in the space provided below for it. You also have blank pages at the start of questions paper to continue with rough work. 6. The name, email address, and date of birth entered on the Digital Answer Key 7. Incompletely, incorrectly or carelessly filled information may disqualify your candidature. Enrollment No. : Batch : Name : Candidate’s Signature Invigilator’s Signature: 20249993 TEST ID
- THE FUNDAMENTAL APPROACH... IOQM MOCK TEST-3-2024-25-2 Limited, Saraswati Bhavan, Second Floor, Lotus Link Square, New Link Road, D.N. Nagar Metro Station, Andheri (W), Mumbai - 400 058 Ph.: (Andheri: 8080-220-888); (Chembur: 8080-220-888); (Navi Mumbai: 900-460-3450); (Thane: 41617777); (Kandivali: 808-088-3438) Web: www.fiitjee.com email:
[email protected] 1. A bag contains 8 red balls, a number of white balls, and no other balls. If ହ of the balls in the bag are white, then find the number of white balls in the bag. 2. A total of n points are equally spaced around a circle and are labelled with the integers 1 to n, in order. Two points are called diametrically opposite if the line segment joining them is a diameter of the circle. If the points labelled 7 and 35 are diametrically opposite, then find the value of n. 3. If (x + a)(x + 8) = xଶ + bx + 24 for all values of x, then find the value of a + b. 4. In the diagram, PQRS is a square. Square PQRS is divided into five rectangles, as shown. Find the area of the shaded rectangle. SPACE FOR ROUGH WORK PART – I: Mathematics
IOQM MOCK TEST-3-2024-25-3 - THE FUNDAMENTAL APPROACH... Limited, Saraswati Bhavan, Second Floor, Lotus Link Square, New Link Road, D.N. Nagar Metro Station, Andheri (W), Mumbai - 400 058 Ph.: (Andheri: 8080-220-888); (Chembur: 8080-220-888); (Navi Mumbai: 900-460-3450); (Thane: 41617777); (Kandivali: 808-088-3438) Web: www.fiitjee.com email:
[email protected] 5. Fifty numbers have an average of 76. 40 of these numbers have an average of 80. The average of the other ten numbers is N. Find N. 6. If ௫ି௬ ௭ି௬ = −10, find the value of ௫ି௭ ௬ି௭ . 7. How many four-digit integers between 5000 and 6000 are there for which the thousands digit equals the sum of the other three digits? 8. There are six identical red balls and three identical green balls in a pail. Four of these balls are selected at random and then these four balls are arranged in a line in some order. How many different looking arrangements are possible? 9. Let a and b be positive integers for which 45a + b = 2021. Find the minimum possible value of a + b. 10. How many 7 − digit positive integers are made up of the digits 0 and 1 only, and are divisible by 6? SPACE FOR ROUGH WORK
- THE FUNDAMENTAL APPROACH... IOQM MOCK TEST-3-2024-25-4 Limited, Saraswati Bhavan, Second Floor, Lotus Link Square, New Link Road, D.N. Nagar Metro Station, Andheri (W), Mumbai - 400 058 Ph.: (Andheri: 8080-220-888); (Chembur: 8080-220-888); (Navi Mumbai: 900-460-3450); (Thane: 41617777); (Kandivali: 808-088-3438) Web: www.fiitjee.com email:
[email protected] 11. In the diagram, two circles touch at P. Also, QP and SU are perpendicular diameters of the larger circle that intersect at O. Point V is on QP and VP is a diameter of the smaller circle. The smaller circle intersects SU at T, as shown. If QV = 9 and ST = 5, what is the sum of the lengths of the diameters of the two circles? 12. In the diagram, triangle PQR is right-angled at P and PR = 12. If point S is on PQ so that SQ = 11 and SR = 13, then find the perimeter of triangle QRS. 13. Last summer, Pranay worked at a summer camp. For each day that he worked, he earned ₹ 100 and he was not charged for food. For each day that he did not work, he was not paid and he was charged Rs. 20 for food. After 70 days, the money that he earned minus his food costs equalled ₹ 5440. On how many of these 70 days did Pranay work? SPACE FOR ROUGH WORK
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