IX Maths Past Paper Jaycees Public School, Rudrapur 2024-25 PDF

**Jaycees Public School, Rudrapur** **Time 3 Hours Subject-Mathematics M.M. 80** **GENERAL INSTRUCTIONS-** \# This Question Paper has 5 Sections (A to E). \# Section A has 20 MCQs carrying 1 mark each (2 assertion --reason based questions). \# Section B has 5 questions carrying 02 marks each....

**Jaycees Public School, Rudrapur** **Time 3 Hours Subject-Mathematics M.M. 80** **GENERAL INSTRUCTIONS-** \# This Question Paper has 5 Sections (A to E). \# Section A has 20 MCQs carrying 1 mark each (2 assertion --reason based questions). \# Section B has 5 questions carrying 02 marks each. \# Section C has 6 questions carrying 03 marks each. \# Section D has 3 case based questions carrying 04 marks each. \# Section E has 4 questions of 5 marks each. \# Draw neat figures wherever required. Take π =22/7 wherever required if not stated. **[SECTION -- A]** Q1. Rationalizing factor of √3-1 is a\) √3+1 b) 1-√3 c) [\$\\frac{1}{\\sqrt{3} - 1}\$]{.math.inline} d) None of these Q2. The decimal expansion of √2 is a\) a finite decimal b) 1.41421 c\) non terminating recurring d) non terminating non recurring Q3. Rational number between √2 and √3. a\) [\$\\frac{\\sqrt{2} + \\sqrt{}3}{2}\$]{.math.inline}b) 1.5 c) 1. d) [\$\\frac{\\sqrt{2}x\\sqrt{}3}{2}\$]{.math.inline} Q4. Remainder when x^3^-2x^2^+x+1 is divided by x-1 is a\) 1 b) -1 c) 0 d) none Q5. √3 is polynomial of degree a\) 2 b) 0 c) 1 d) 1/2 Q6. Coefficient of x^3^ in 9-13x^2^-x^3^is a\) -1 b) 1 c) 0 d) none Q7. The measure of angle between coordinate axis is a\) 0^⁰^ b) 90^⁰^ c) 180^⁰^ d) 360^⁰^ Q8. Perpendicular distance of point (-7, 4) from x axis. a\) -7 b) 4 c)7 d) none Q9. The ordinate of point is its distance from a\) X axis b) Y axis c) origin d) none Q10. Ordinate of all points on the y axis is a\) 0 b) 1 c) 2 d) Any number Q11. x=2 , y= -1 is a solution of the linear equation a\) x+2y=0 b) x+2y= -4 c\) 2x+y=0 d) 2x+y=5 Q12. 3x+10 = 0 will have: a\) Unique solution b)Two solutions c\) Infinitely many solutions d) No solutions Q13.If measure of two supplementary angles are (3x+15) and (2x+5) , then x is a\) 32 b) 64 c) 14 d) 24 Q14. Two straight lines AB and CD cut each other at O. If [∠*BOD* = 63]{.math.inline}^◦^, then [∠*BOC*]{.math.inline}= a\) 63^◦^ b) 117^◦^ c) 17^◦^ d) 153^◦^ Q15. If [*Δ*]{.math.inline} ABC[ ≅ *Δ*]{.math.inline} LKM, then side of [*Δ*LKM ]{.math.inline}equal to side AC of [*Δ*ABC ]{.math.inline}is a\) LK b) KM c) LM d) none Q16. In an isosceles triangle, if the vertex angle is twice the sum of the base angles, thenthe measure of the vertex angle of the triangle is a\) 100^◦^ b) 120^◦^ c) 110^◦^ d) 130^◦^ Q17. The angles of a quadrilateral are 75^◦^ ,90^◦^ and 75^◦^ , the fourth angle is a\) 90^◦^ b) 95^◦^ c) 105^◦^ d) 120^◦^ Q18. In a rhombus ABCD, if AB=AC , then [∠*ABC* ]{.math.inline}is a\) 120^◦^ b) 90^◦^ c) 60^◦^ d) none Each of the following questions contain STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is correct answer. Mark the correct choice. \(a) Statement1 is true, Statement 2 is true; Statement 2 is a correct explanation for statement 1 \(b) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1 \(c) Statement 1 is true, Statement 2 is false \(d) Statement 1 is false, Statement 2 is true Q19[. Statement 1 (Assertion):] √2 is an irrational number [Statement 2 (Reason):] The sum of rational number and irrational number is an irrational number. Q20. [Statement 1 (Assertion]):In a triangle ABC, if the bisectors of angles [∠*B* ]{.math.inline} and [∠*C*]{.math.inline} meet at a point O, then [∠*BOC* ]{.math.inline}is always an obtuse angle. [Statement 2 (Reason]): In a triangle ABC, if the bisectors of angles [∠*B* and ∠*C*]{.math.inline} meet a point O, then [∠*BOC* = 90]{.math.inline}^⁰^+[\$\\frac{\\angle A}{2}\$]{.math.inline}. **[SECTION -- B]** Q21. Express in the form of p/q 0.2528 Q22. Factorize: 3x^2^-x-4. **OR** Find p(-1) , p(2) for polynomial p(x)=10x-4x^2^-3 Q23. If the coordinates of the two points are P (-2, 3) and Q (-3, 5), find (abscissa of P) - (abscissa of Q). Q24. For what value of K, the linear equation 2x+ky=8 has x=2 and y=1 as its solution. Q25. If the angles (2x-10) ^⸰^ and (x-5) ^⸰^ are complementary angles , find x. **OR** Two supplementary angles are in the ratio 4:5. Find the angles. Q26. If x=7-4√3, find x+[\$\\frac{1}{x}\$]{.math.inline}. Q27. Evaluate using Identity: 107^3^ **OR** Find the rational and irrational no. between √2 and √3 Q28. Factorize a)512x^3^-343y^3^ b)2x^2^+y^2^+8z^2^-2√2xy+4√2yz-8xz Q29. Express x in terms of y and give two solutions of -2x+4y=8. Q30. It is given that [∠*XYZ* = 64]{.math.inline}^⁰^ and XY is produced to point P.Draw a figure from the given information. If ray YQ bisects [∠*ZYP*, ]{.math.inline}find [∠*XYQ* ]{.math.inline}and reflex [∠*QYP*.]{.math.inline} Q31. In an isosceles triangle ABC, with AB=AC, the bisectors of [∠*B* and ∠ *C*]{.math.inline} intersect each other at O. Join A to O. Show that: 1\) OB=OC 2) AO bisects [∠*A*]{.math.inline} Q32. i) If X=4-√15, then find the value of (x+[\$\\frac{1}{x}\$]{.math.inline} )^2^ ii)Evaluate without calculating the cube (25)^3^+(-12)^3^+(-13)^3^ **OR** i\) Expand (5a-3b-4c)^2^ ii\) if a+[\$\\frac{1}{a}\$]{.math.inline} = 7 , find if a^3^+[\$\\frac{1}{a3}\$]{.math.inline} Q33. In the given figure [∠*APC* = 100]{.math.inline}^⁰^ and [∠*BPD*]{.math.inline}=146^⁰^, Find [∠*CPD* ?]{.math.inline} C:\\Users\\Lenovo\\Downloads\\WhatsApp Image 2023-08-23 at 12.12.57 AM.jpeg Q34. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of triangle PQR. Show that: \(i) [△ ]{.math.inline}ABM [ ≅ △]{.math.inline} PQN (ii) [△]{.math.inline} ABC [ ≅  △ PQR]{.math.inline}  Q35. Show that bisectors of angles of parallelogram form a rectangle. Q36. Five friends playing a game in which they are standings at different positions P, S, T, R and Q. C:\\Users\\Lenovo\\Downloads\\WhatsApp Image 2023-08-22 at 11.56.40 PM.jpeg Rohan is watching them playing. Few questions came to Rohan mind while watching the game. Give answer to this question by looking at the figure Q1. What are the co-ordinates of P? \(a) (-1, 1) (b) (1,-1) (c) (1, 1) (d) (-1,-1) Q2. Name the point whose y- co-ordinate is zero? \(a) P (b) Q (c) R (d) S Q3. Name the polygon formed on joining all these five points in an order. \(a) Quadrilateral (b) Hexagon (c) Pentagon (d) Triangle Q4. Name the point lying in the third quadrant. \(a) R (b) P (c) Q (d) T Q37. Read the following passage and answer the following questions: Harry was going on road trip with his father. They were travelling on a straight road. After riding for a some distance, they reach a cross road where one straight road cuts other at 30 degree. Now use the given information, answer the following questions.  Q1. Find the measure of [∠ ]{.math.inline}BOD. (1) Q2. Find the measure of [∠*BOC*]{.math.inline}. (2) Q3. Which property is used.. (1) Q38. Case study of triangles to be added. \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*