CBSE exam SA 2 class 9th solutions of important maths questions of last year’s question papers.
Here CBSE exam SA 2 class 9th solutions of important maths questions of last year’s question papers are given here which has been asked in the last years . These questions are taken from the last 6 years’ question papers. The important maths questions of last year’s question paper classs 9 help the students to get the idea of the type of question asked in the maths paper of the CBSE board. All questions are solved here by a step by step method, so every student can understand the solutions of each question.
You can also study NCERT Solutions
Q1. Find the total surface area of a cube of edge 10 cm.
Answer. The total surface area of the cube is =
side(a) = 10 cm
The total surface area of the cube is = 6 × 10² =6 ×100 = 600
Hence the total surface area of the cube is = 600 sq.cm
Q2. Find the mean of the first 5 natural numbers.
Answer. The first 5 natural numbers are 1,2,3,4 and 5
Q3.Write a linear equation representing a line which is parallel to the y-axis and is at a distance of 2 units on the left side of y-axis.
Answer.In left side of y-axis, the x coordinate is negative
The line is at a distance of 2 units left of y axis will pass through (–2,0)
Since the line is parallel to the y-axis then the equation of this line is x =–2
Q4.If the point (3,4) lies on the graph of linear equation 3y =ax + 7, find the value of a.
Answer.Since the point (3,4) lies on the graph of linear equation 3y =ax + 7 then the coordinates (3,4) must satisfy the equation
3(4) = a(3) + 7
3a = 12 – 7 = 5
Q5.O is the center of a circle that passes through P,Q,R and S as shown in the figure .SR is produced to x . If ∠QRX =133°,find x.
PQRS is a cyclic quadrilateral
∴ ∠QPS +∠QRS = 180°…….(i)(opposite angles of cyclic quadratic angles)
∠QRS + ∠QRX = 180°(linear pair)
∠QRS + 133° = 180°
∠QRS = 180° – 133° =47°
putting the value of ∠QRS in (i)
∠QPS + 47° = 180°
∠QPS = 180° – 47° = 133°
4x + 13 = 133°
4x = 120
x = 30
Q6.Write the edge of cube in term of its volume.
Answer. The volume of the cube(V) =
side of the cube (a) =
Q7. The equation of x-axis is
(a) x = 0 (b) y = 0 (c) x = y (d) x ≠5
Answer. Since the coordinates of y on x axis is 0,so the equation of x axis is y= 0
Q8. Two parallelograms on equal base and between the same parallel lines. The ratio of their areas is
(a)1:2 (b) 2 : 1 (c) 3 : 1 (d) 1 : 1
Answer. The area of parallelograms on the same base and between the same parallel lines are equal, so the ratio of their areas will be (d) 1: 1
Q9.The volume of cuboid formed by joining two cubes of side 2 cm is:
(a) 64 (b) 32 (c) 16 (d) 8
The length of so formed cuboid = 2 +2 = 4 cm
breadth = 2 cm, height = 2 cm
So,volume of the cuboid = l × b× h =4 × 2×2 =16
Hence the answer is (c) 16 .
Q10.If the chord of a circle is equal to the radius of the circle then the angle subtended by it at the center is
(a)30° (b) 120° (c) 50° (d)60°
Answer. Joining both ends of the chord a triangle formed which will be an equilateral because the radius is equal to the length of the chord, therefore each angle will be of 60°. Hence the angle subtended at the center by it is equal to 60°.
Q11. The surface area of a sphere is 154 cm². Find its radius.
Answer. The surface area of a sphere = 4πr²
4πr² = 154
Therefore the radius of the circle is
Q12. In the figure, ABCD is parallelogram AE ⊥DC and CF⊥ AD. If AB =16 cm,AE =8 cm and CF = 10 cm . Find AD.
Answer. Area of ABCD = AD × CF = AD × 10
As base AB area of ABCD = AB× AE = 16 × 8 =128
10 AD = 128
AD = 12.8
Hence the length of AD = 12.8 cm
Q13.A cuboidal water tank is 8 m long ,4m wide and 7 m deep .How many litres of water can it hold .
Answer. The volume of cuboidal water tank is = l × b× h = 8×4 ×7=224
The volume of water tank =
Therefore the cuboidal tank can hold 0.224 l water.
Q14.The percentage of marks obtained by a student in unit tests are given as follows.
|Percentage of marks||68||75||85||58|
On the basis of this data, find the probability that in a unit test student scored more than 74 % marks.
Answer. The student got marks in 4 test, therefore total possible outcomes are =4
The student got more than 74% marks in II and III tests since there are 2 tests in which he got more than 74% marks, so favorable outcome of this event = 2
Let the event of getting more than 74% marks→ E
Therefore the probability that a student get marks more than 74% marks is
Q15. Given , find the value of a and b.
Answer.We are given that
Multiplying the denominator and numerator of the above expression by the conjugate of the denominator
Hence the value of a and b are respectively.
Q16.Out of 35 students participating in a dance competition, 10 are boys. What is the probability that the winner is a girl?
Answer. Total number of students are =35, so total possible outcomes are =35
Number of boys are = 10
Number of girls = 35 – 10 = 25, so favourable outcomes are 25
Let E is the event of winner is girl
Therefore the probability that winner is girl =
Q17.Find the mean of the first 5 composite numbers.
Answer. First 5 composite numbers are 4,6,8,9 and 10
Let the mean of First 5 composite numbers is
Therefore the mean of first 5 composite numbers is =7.4
Q18.In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD and BA is produced to F . If ∠ABC is 70° and ∠FAE =30°, Find ∠BCD.
Answer.ABCD is a cyclic quadrilateral ∠ABC and ∠ADC are its opposite angles
∠ABC + ∠ADC = 180°
70° + ∠ADC = 180°
∠ADC = 110°
∵AE∥CD and AD is transversal
∴ ∠DAE = ∠ADC ( corresponding angle)
∠DAE = 110°
∠FAE + ∠DAE + ∠DAB = 180°
30° + 110° +∠DAB = 180°
∠DAB = 180° –140°= 40°
∠DAB + ∠BCD = 180°
40° + ∠BCD = 180°
∠BCD = 40°
Q19. A right triangle with sides 5 cm, 12 cm, and 13 cm is revolved about the side 12 cm. Find the volume of the solid so formed.
We are given a right triangle which is to be revolved about the side 12 cm ,the solid so formed will be a cone whose height(h) = 12 cm, radius(r) =5 cm and slant height(l) = 13cm
Volume of cone =
Therefore the volume of solid so formed is 100π
Q20.Find the mean salary of 70 workers of a factory from the following table.
|Salary||No of workers|
|Salary(x)||No of workers(f)||fx|
Hence mean salary of worker is Rs49000.