MATHEMATICS, Class – IX QUESTION PAPER
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Q.1 Write the coordinates of points where the line 3x + 4y =12 meets x-axis and y-axis. Q.2 Two coins are tossed simultaneously find the probability of getting at least one tail.
Q.3 The diameter of moon is approximately one fourth of the diameter of the earth; Find the ratio of their surface area. Q.4 Show that area of parallelogram is twice the area of triangle if they lie between same parallels and having same base.
SECTION – B
Q.5. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. Also write any two solutions for the linear equation.
Q.6. Check whether the points (1, 2), (-1,-16), (3,-7) lie on the line y = 9x-7.
Q.7. ABCD is a ‘llgm.’ L and M are points on AB and CD such that AL=CM. Prove that LM and BD bisect each other.
Q.8. In ABC ,D, E,F are midpoints of BC , AC ,AB show that ar( DEF)= ¼ ar ( ABC).
Q.9. AB & AC are diameters of the circles which intersect each other at A and P. Show that points B,P,C are collinear.
Q.10 The circumference of the base of 12 m high wooden solid cone is 66m, find its volume.
SECTION – C
Q.11 If the cost of 5 tables exceeds the cost of 8 chair by Rs 150, Represent a linear equation in two variables, Also find the cost of one table if the cost of one chair is Rs 240.
Q.12 Show that isosceles trapezium is a cyclic quadrilateral.
Q.13 P,Q,R,S are the midpoints of AB,BC,CD,DA of quadrilateral ABCD show that PQRS parallelogram.
Q.14 Prove that the diagonals of a parallelogram divide it into two congruent triangles.
Q.15 Diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD then show that ar ( DOC) = ar ( AOB)
Q.16 Construct a triangle ABC, in which BC = 6.8 cm, ∠B = 300 and AB + AC = 9.8 cm.
Q.17 An edge of a cube is increase by 10%.Find the percentage by which the surface area of the cube increase.
Q18 The following table shows the performance of two sections of 80 students in a mathematics test of 90 marks. Draw histogram and frequency polygon of the given data:
Marks 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Number of students 2 3 12 21 14 17 11
Q.19 The mean marks scored by 100 students were 40. Later on, it was discovered that score of 53 was misread as 83. Find correct mean marks.
Q.20 Find mean, median and mode of the following data : 15,14,19,20,14,15,16,14,15,18,14,19,15,17,15
SECTION – D
Q.21 The taxi fare in a city for first kilometer is Rs.18 and for subsequent distance it is Rs.10 per km taking the distance covered as x km. fare as Rs. y , write a linear equation for this information. If a person covers distance of 25km.find the taxi fare.
Q.22. Draw the graph of the equation 2x + 3y – 6 = 0,
(i) determine whether (3, 0) is the solution, (ii) find value of y, if x = -3,( iii)find x ,if y = -2 and verify these values from graph.
Q.23 In given figure ABCD is the rhombus AE=BF=AB prove that <EFG= 900