Class 9th is an important phase in the life of students. CBSE conducts examination for the schools affiliated to the central board. Students usually find Maths as one of the most difficult subjects. Main reason due to their fear is due to lack of confidence & practice for the subject. If one wishes to excel in an examination, it is quite essential to practice questions on daily basis.

We at BYJU’S provide students of class 9th with important 4 marks question to practice in order to be aware of the type of questions asked in the final exam.

**Question 1- **Water flows in a tank 150m \(\times\) 100m at the base through a pipe whose cross-section is 2 dm \(\times\) 1.5 dm at the speed of 15 km/h. In what time, will the water be 3m deep?

**Question 2- **A solid cylinder has total surface area of 462 sq cm. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder. (Assume \(\pi = \frac{22}{7}\)).

**Question 3- **A recent survey found that the age of workers in a factory as follows:

Age (in years) |
20-29 |
30-39 |
40-49 |
50-59 |
60 and above |

Number of Workers |
38 |
27 |
86 |
46 |
3 |

If a person is selected at random, then find the probability that the person is

(i) Having age from 30-39 years.

(ii) Under 40 years.

(iii) 40 years or more.

**Question 4- **If each diagonals of a quadrilateral separates it into two triangle of equal area, then show that the quadrilateral is a parallelogram.

**Question 5- **Hindustan metro company manufactures car batteries of a particular type. The life of 32 batteries (in years) were recorded as follows:

2.8 |
3.0 |
3.7 |
3.2 |
2.9 |
4.1 |
3.5 |
4.5 |

3.5 |
2.8 |
3.2 |
3.4 |
3.8 |
3.2 |
4.6 |
3.7 |

2.7 |
4.4 |
3.4 |
3.3 |
2.9 |
3.0 |
4.3 |
3.5 |

3.5 |
3.2 |
3.9 |
3.2 |
3.2 |
3.1 |
3.7 |
3.4 |

(i) Find the probability that the life of a battery randomly select is less than or equal to 3 years.

(ii) If the company gives the warranty of a battery which is less than 4 years, then what is the probability of getting no complaints under the warranty period?

(iii) As per the given data, if the company gives warranty of less than or equal to 2 years, then summit decides to purchase the battery. What his decision shows of getting no complaints under the warranty period.

(iv) Find the probability that the life of a battery randomly selected us less than or equal to 3.5 years.

**Question 6- **A well with 10 m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of m to form an embankment. Find the height of embankment.

**Question 7- ** ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at P. If AB = DC, then prove that

(i) \(\Delta PAB \cong \Delta PDC\)

(ii) PA = PD and PC = PB

(iii) AD \(\parallel\) BC

**Question 8- **The difference between the outside and inside surfaces of a cylindrical metallic pipe 14 cm long is 44 \(cm^{2}\). If the pipe is made of 99 cu. cm of metal, find the outer and inner radii of the pipe.

**Question 9- **In a \(\Delta PQR\), find the measure of angles of the triangle formed by joining the mid-points of the sides of the triangle.

**Question 10- **Construct a triangle in which BC = 8cm , \(\angle B = 30^{\circ}\) and AB – AC = 3.5 cm.

**Question 11- **Construct the histogram and frequency polygon for the following frequency distribution:

Weight(in kg) |
40-45 |
45-50 |
50-55 |
55-60 |
60-65 |
65-70 |

Number of Persons: |
15 |
25 |
28 |
15 |
12 |
5 |

**Question 12- **In Fig. given below, PQ is the diameter of the circle with centre O. If \(\angle PQR = 65^{\circ}, \angle RPS = 40^{\circ}\) and \(\angle PQM = 50^{\circ}\), find \(\angle QPR, \angle PRS\) and \(\angle QPM\).

**Question 13- **Draw the graph of linear equation x + 2y = 8. From the graph drawn, check whether (-1,-2) is a solution of this equation.

**Question 14- **Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

**Question 15- **If \(x = \frac{1}{\sqrt{a} – \sqrt{b}}\) show that \((a-b)^{2}x^{2}+ (a-b)x – (a+b) = \sqrt{a} + \sqrt{b} + 2\sqrt{a}\sqrt{b}\).

Or If a+b+c = 0, then show that \(a^{4}+b^{4} + c^{4} = 2(b^{2}c^{2} + c^{2}a^{2}+ a^{2}b^{2})\)

**Question 16- **A solid cube has been cut into two cuboids of equal volumes. Find the ratio of total surface area of one of the cuboids to that of the given cube.

**Question 17- **A storage tank is in the form of a cube. When it is full of water, the volume of the water is 15.625\(m^{3}\). If the present depth of the water is 1.3m, find the volume of water already used from the tank.

**Question 18- **A spherical cannonball, 28 cm in diameter is melted into a right circular mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.

**Question 19- **In a \(\Delta ABC\), median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.

**Question 20- **The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Also find the force required when the acceleration produced is equal to

(i) 5 \(m/sec^{2}\)

(ii) 6 \(m/sec^{2}\)

(iii) 15 \(m/sec^{2}\)