CBSE exam SA 2 class IX th solutions of important maths questions of last years question papers. - Future Study Point

# CBSE exam SA 2 class IX th solutions of important maths questions of last years question papers.

## 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 CBSE exam . 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.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

NCERT Solutions of Class 9 Science : Chapter 1 to Chapter 15

## CBSE exam SA 2 class 9th solutions of important maths questions of last year’s question papers.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

## Section A

Q1. Find the total surface area of a cube of edge 10 cm.

Answer. The total surface area of the cube is = 6a²

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

= ∑X/N = (1+2 +3 +4 +5)/5 = 15/5 =3

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

a = 5/3

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.

∴ ∠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) =a³

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

NCERT Solutions Class 10 Science from chapter 1 to 16

Q9.The volume of  cuboid formed by joining two cubes of side 2 cm is:

(a) 64 cm³ (b) 32cm³ (c) 16cm³  (d) 8cm³

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 cm³

Hence the answer is (c) 16 cm³.

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°.

## Section B

Q11. The surface area of a sphere is 154 cm². Find its radius.

Answer. The surface area of a sphere = 4πr²

4πr² = 154

4 ×(22/7) ×r² = 154

r² = (154×7)/(22×4) =49/4

r = 7/2

Therefore the radius of the circle is 7/2 cm

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.

As base  AB  area of ABCD = AB× AE = 16 × 8 =128

Hence the length of AD = 12.8 cm

CBSE 10 maths most important questions of science with solutions

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 = 224 m³

Since 1m³ = 1000 l

224 m³ = 224/1000 = 0.224 l

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.

 Unit test I II III IV 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

P(E) = Favourable outcome/Total possible outcome

P(E) = 2/4 = 1/2

Therefore the probability that a student get marks more than 74% marks is 1/2

Q15. Given (7+√3)/(7-√3), find the value of a and b.

(7+√3)/(7-√3) = a + b√3

Taking L.H.S

(7+√3)/(7-√3)

Multiplying the denominator and numerator of the above expression by the conjugate of the denominator (7+√3)

(7+√3) (7+√3)/(7-√3)(7+√3)

=(7²+ √3²+ 14√3)/(7²- √3²)

=(49 +3 +14√3)/(49-3)

=(52 +14√3)/46

(52 +14√3)/46 = a + b√3

a = 52/46 = 26/23, b = 14√3/46 = 7√3/23

Hence the value of a and b are 26/23 and 7√3/23  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

P(E) = Favourable outcome/Total possible outcome

P(E) = 25/35 = 5/7

Therefore the probability that winner is girl =5/7

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

=  (4 +6 +8 +9 +10)/5 = 37/5 = 7.4

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.

∴ ∠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°

Section C

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 =(1/3) πr²h

= (1/3) ×π×5×5×12

= 100π

Therefore the volume of solid so formed is 100π cm³

How to calculate recoil velocity of the gun

Q20.Find the mean salary of 70 workers of a factory from the following table.

 Salary No of workers 30000 20 40000 15 50000 12 60000 9 70000 6 80000 5 90000 3

 Salary(x) No of workers(f) fx 30000 20 600000 40000 15 600000 50000 12 600000 60000 9 540000 70000 6 420000 80000 5 400000 90000 3 270000 ΣF =70 ΣFX=3430000

Mean = ∑FX/∑F

Mean = 3430000/70

Mean = 49000

Hence mean salary of worker is Rs49000.

### NCERT Solutions for class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions for class 9 science

 Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion Chapter 2-Is matter around us pure? Chapter 10- Gravitation Chapter3- Atoms and Molecules Chapter 11- Work and Energy Chapter 4-Structure of the Atom Chapter 12- Sound Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ? Chapter 6- Tissues Chapter 14- Natural Resources Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources Chapter 8- Motion Last years question papers & sample papers

### Class 9 Physics Important Notes

What is the difference between Distance and Displacement

Difference between velocity and speed

Average Speed and Average velocity

Three equation of Motions

Three laws of motion

The second  law of motion

Recoil velocity of the gun

What is inertia?

Momentum: Definitions,units,formula and Uses in real life:Class 9 CBSE

The universal  law of gravitational force

What is the difference between mass and weight

Thrust and Pressure : Difference

Archimedes Principle: Complete detail

What is the difference between Work,Energy and Power: Class 9 CBSE

CBSE IX Class Science Sample Papers

### Class 9 Chemistry Important Notes

Evaporation, Vapourization, and Latent heat

How does the water kept in an earthen pot become cold during summer?

What are the factors affecting evaporation?,

What is the difference between solution, colloid, and suspension?

What is the difference between the element and the compound?

Atom, Molecule, and Atomicity

Determining Valency, Net Charge and Molecular Formula

Mole concept

Molar mass,molecular mass and mole concept

If energy is conserved then why do we need to save it for future generations?

### Class 9 Biology Important Notes

Difference between Animal cell and Plant Cell

Difference between Smooth Endoplasmic Reticulum and Rough Endoplasmic Reticulum

Function and structure of Mitochondria

Class 9 Science Chapterwise NCERT Solutions and Important notes of Science

Structure and Function of Cell : Cell Biology

What are Chromosomes, DNA and Genes?

Types of plant tissues : Class 9 CBSE Notes

Animal Tissues : Class 9 Science CBSE

What is the green house effect?

E-books of physics,chemistry,biology ,maths and solutions of class 10 previous year’s question papers(click the link)

Scroll to Top