SARVODAYA PUBLIC SCHOOL
ANNUAL EXAMINATION 2024-25
CLASS – IX
MATHS
STUDENT’S NAME: _____ FATHER’S NAME:
CLASS & SECTION: _____ ROLLNO:
Time Allowed: 03 Hrs Maximum Marks: 80
Q1. Tick the correct answer. [1x20=20]
3 2 𝒙 𝒙
1. If (2 ) = 𝟒 , then 𝟑 is equal to
(a) 6 (b) 9 (c) 27 (d) 3
2. The Value of (369) – (368) is equal to
2 2
(a) 1 (b) 37 (c) 81 (d) 737
3. The Points (-5,2) and (2,-5) Lie in the always lies.
(a) In I quadrant (b) In II quadrant (c) Same quadrant (d) II and IV quadrant
4. If (4,19) is a solution of the equation y = ax + 3, then a is equal to
(a) 4 (b) 3 (c) 6 (d) 5
5. Pythagoras was a student of
(a) Thales (b) Euclid (c) Archimedes (d) None of these
6. The measure of an angle is five times its complement. the angle measures.
(a) 250 (b) 650 (c) 350 (d) 750
7. If ∆PQR ≅ ∆EFD, then ∠E =
(a) ∠P (b) ∠R (c) ∠Q (d) None of these
0
8. In rhombus ABCD. if ∠ACB = 40 then ∠ADB =
(a) 450 (b) 700 (c) 500 (d) 600
9. If ∠A, ∠B, ∠C and ∠D of quadrilateral ABCD taken in order are in the ratio 3:7:6:4, then
ABCD is a
(a) Kite (b) rhombus (c) Trapezium (d) Parallelogram
10. A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of
the chord is
(a) 25 cm (b) 30 cm (c) 12.5 cm (d) 9 cm
11. In the fig. O is the centre of a circle and ∠ AOB = 1400 then ∠ACB = ?
(a) 700 (b) 800 (c) 1100 (d) 400 C
A B
140
12. The chord of a circle is equal to its radius. The angle subtended by this chord at the
minor arc of the circle is
(a) 1500 (b) 1200 (c) 750 (d) 450
13. The height of an equilateral triangle is 6 cm Its area is
(a) 𝟔√𝟑 cm2 (b) 12√3 cm2 (c) 12√2 cm2 (d) 18 cm2
14. The area of an equilateral triangle is 81√3 cm2. Its height is
(a) 6√3 cm (b) 9√3 cm (c) 18√3 cm (d) 9 cm
15. The volume of a sphere of radius 10.5 cm is
(a) 9702 cm3 (b) 1940.4 cm3 (c) 4851 cm3 (d) 145.53 cm3
16. A cone and hemisphere have equal bases and equal volumes. The ratio of their height is
(a) 1:2 (b) 4:1 (c) 2:1 (d) √𝟐:1
17. The area of an equilateral triangle is
√𝟑 √𝟑 √𝟑
(a) Side (b) Side2 (c) Side3 (d) None of these
𝟒 𝟒 𝟒
18. In the class intervals 10-20, 20-30, 20 is taken in
(a) The interval 10-20 (b) The interval 20-30
(c) Both intervals 10-20, 20-30 (d) None of the intervals
19. The volume of Hemisphere is
𝟒 𝟒 𝟐
(a) 𝝅r2 s.q (b) 𝝅r3 cubic (c) 𝝅r3 cubic unit (d) None of these
𝟑 𝟑 𝟑
20. The area of isosceles triangle is ……………..
Q2. Solve any six question each of 2 marks. [2x6=12]
1. In ∆ABC, if ∠A = 1000 and AB= AC Find ∠B and ∠C.
2. Find the measure of each exterior angle of an equilateral triangle.
3. If an angle of a parallelogram is two-third of its adjacent angle. Find the angles of a
parallelogram.
4. AB and CD are two equal chords of a circle with centre O such that ∠AOB = 800 then
∠COD = ? A
C 0 B
D
5. Find the area of the triangle, the length of whose sides are 9 cm, 12 cm and 15 cm.
6. The radius of a cone is 5 cm and vertical height is 12 cm. Find the curved surface area of
cone.
7. Find the volume of a right circular cone with radius 4 m and height 9 m.
Q3. Solve each of 3 marks. [3x8=24]
1. Find the surface area of a sphere whose volume is 4851 cm3.
2. The sides of a triangle are in the ratio 3:5:7 and its perimeter is 600 cm. Find the area of
the triangle.
3. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the
chord at a point on the minor are and also at a point on the major arc.
4. Prove that the Perpendicular from the centre on a chord bisect the chord.
5. Prove that the quadrilateral from by the bisect of the angle of a parallelogram is a
rectangle.
𝟏
6. If D is the mid-point of the hypotenuse AC of a right triangle ABC, prove that BD = AC.
𝟐
7. Factorize a6-b6.
𝟒+𝟑√𝟓
8. Find the value of a and b = 𝑎 + 𝑏√5
𝟒−𝟑√𝟓
Q4. Long answer type question each of 4 marks. [4x6=24]
1. Write and prove the mid-point theorem.
2. Find the value of a and b so that the polynomials 𝑥 3 − 𝑎𝑥 2 → 13𝑥 + 𝑏 has 𝑥 + 1 and x +
𝟑 as factor.
3. In the figure three co- planar lines intersect at a point O forming angles as shown in the
figure. Find the value of x, y, z and t.
C y E
x
Z
A t 900 B
40
D
4. The daily wages of 50 workers in a factory are given below.
Daily wages (in ₹) Number of workers
140-180 15
180-220 09
220-260 14
260-300 03
300-340 07
340-380 02
Draw the histogram for the following data.
5. A Hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm.
Find the volume of the steel used in making the bowl.
6. The Perimeter of a triangle field is 540 m and its sides are in the radio 25:17:12. Find the
area of the triangle also find the cost of ploughing the field at Rs 20 Per 10 m2.
