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It allocates marks across Mathematics, General Science, and Aptitude, with specified marking and negative marking rules. 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Any defect found should be brought to the notice of the invigilator immediately.  \n􀂾 Fill in the particulars in the OMR Sheet given to you separately as per the directions given therein.  \n􀂾 This test is of three hours’ duration.  \n􀂾 There are four choices in every question as (a), (b), (c) and (d) . Only one is correct. Each question carries 4 marks.  \n􀂾 The test consists of 75 multiple choice questions comprising of Mathematics (30), General Science (30) and Aptitude (15) carrying maximum of 300 marks.  \n􀂾 -1 will be awarded for each wrong answer/multiple answer.  \n􀂾 No mark will be awarded for any overwriting/scratching answer.  \n􀂾 No candidate shall leave his/her seat during examination.  \n􀂾 Do not tear remove any page of the Booklet.  \n􀂾 Calculation, if any, may be done at the blank pages of this booklet provided at the end for rough work. No calculator is allowed.  \n􀂾 After finishing the test, the booklet with the OMR sheet is to be handed over to the invigilator before leaving the room.  \nMATHEMATICS  \n1. 150 litres of milk contain 20% of water. The amount of water to be added so that amount of water will be 25%, is  \n(a) 20 litres (b) 10 litres (c) 15 litres (d) 30 litres  \n2.  \nIn the above figure-1, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13cm and OT intersects the circle at E, if AB is the tangent  \nto the circle at E, then the length of AB is  \n(a) 103 cm (b) 12cm (c) 17cm (d) 203 cm  \n3. Three horses are tethered with 7 meter long ropes at the three corners ofa triangular field having sides 20 m, 34 m and 42 m. The area of the plot which can be grazed by the horses is  \n(a) 80m2 (b) 100m2 (c) 77m2 (d) 30m2  \n4. If the point (2, 3) is equidistant from the points (a + b, b−a) and (a−b, a +b), then  \n(a) 2a = 3b (b) a + b=1 (c) 3a = 2b (d) b−a=1  \n5. The area of in-circle of an equilateral triangle of side 42cm is  \n(a) 22√3􀜿􀝉 2 (b) 213 􀜿􀝉 2 (c) 924 􀜿􀝉 2 (d) 462 􀜿􀝉 2  \n6. The value ofk, for which the system of equations x + (k + 1)y = 5 and (k + 1) x + 9y = 8k – 1 has infinitely many solutions, is  \n(a) 2 (b)3 (c) 4 (d)5  \n7. If among three numbers the mean of first two numbers is 2, mean of last two numbers is 3 and mean of first and last number is 4, then the mean of these three numbers is  \n(a) 3 (b) 3.5 (c) 9 (d) 4.5  \n8. The largest number which divides 31 and 99, leaving remainders 5 and 8 respectively, is  \n(a)13 (b)65 (c) 875 (d) 1750  \n9. If sinγ + sin2γ = 1 , then cos 2γ + cos4γ = ?  \n(a) 0 (b) −1 (c) 1 (d) 2  \n10.If 3 is the least prime factor of m and 5 is the least prime factor of n, then the least prime factor of (m + n) is  \n(a) 11 (b) 1 (c) 15 (d) 2  \n11. If two dice are rolled together, then the probability that both of them shows either a prime or a composite number is  \n(a) 1318 (b) 2536 (c) 23 (d) 1316  \n12. The number of positive real values of 􀝔 such that 􀝔 􀯫√􀯫 = (􀝔√􀝔)􀯫 , is  \n(a) 1 (b) 4 (c) 2 (d) infinite  \n13.The number of rows in a lecture hall equals the number of seats in a row. If the number of rows is doubled and the number of seats in every row is reduced by 10, the number of seats is increased by 300. If 􀝔 denotes the number of rows in the lecture hall, then the values of 􀝔 is  \n(a)10 (b) 15 (c) 20 (d) 30  \n14.A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top, which is open, is 5cm.It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5cm are dropped into the vessel, one fourth of the water flows out. Then the number of lead shots dropped in the vessel are  \n(a) 500 (b) 300 (c)200 (d)100  \n15.The value of 􀝏􀝅􀝊2 5° + 􀝏􀝅􀝊2 10° + 􀝏􀝅􀝊2 15° + ⋯ + 􀝏􀝅􀝊2 90° is equal to:  \n(a) 8 (b) 8.5 (c) 9.5 (d)9  \n16. In a ∆ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠Band ∠C meet at Q. Then ∠BPC + ∠BQC =?  \n(a) 6","cbCaibH7PPHX263n","https://ap.wps.com/l/cbCaibH7PPHX263n","pdf",874230,11,"English","# Guidelines to the Candidates\n# Mathematics\n## Example Questions (1-26)\n## Assertion-Reason Questions (33-36)","[{\"question\":\"What is the test duration and how many multiple-choice questions are included?\",\"answer\":\"The test duration is three hours and it includes 75 multiple-choice questions.\"},{\"question\":\"What are the marking rules for wrong answers and overwriting/scratching?\",\"answer\":\"A -1 is awarded for each wrong answer/multiple answer, and no marks are awarded for overwriting/scratching answers.\"},{\"question\":\"Which topics are covered in the sample paper and how are marks distributed?\",\"answer\":\"It covers Mathematics (30 questions), General Science (30 questions), and Aptitude (15 questions), with a maximum total of 300 marks.\"}]","DAV S.C.B Aptitude Test - Sample Paper - 2024 | PDF",28]