HBSE Class 9 Math Important Question Answer 2024 PDF

NCERT Solution of Class 9 mathematics Important Question Answer solution with pdf. Here We Provides Class 1 to 12 all Subjects NCERT Solution with Notes, Question Answer, CBSE and HBSE Important Questions, MCQ and old Question Papers for Students.

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HBSE ( Haryana Board ) Solution of Class 9 Math important Question And Answer solution of all chapters.

HBSE Class 9 Math Important Question Answer for 2024

HBSE Class 9 Math Chapter 1 Number System Important Questions 2024

Q1. The $\displaystyle \frac{p}{q}$ form of $\displaystyle 0.\overline{{47}}$ is _______ .

Q2. Rationalise the denominator of $\displaystyle \frac{1}{{7+3\sqrt{2}}}$ .

Q3. Rationalize the denominator of $\displaystyle \frac{5}{{\sqrt{3}-\sqrt{5}}}$

Q4. What will be get after rationalize the denominator of $\displaystyle \frac{1}{{\sqrt{5}+\sqrt{2}}}$ ?

Q5. The value of $\displaystyle (3+\sqrt{3})(2+\sqrt{2})$ is

Q6. Find one rational number between 3 and 4.

Q7. Every rational number is an integer. (True/False)

Q8. Simplify: $\displaystyle (3+\sqrt{3})(3-\sqrt{3})$

Q9. Simplify : $\displaystyle {{2}^{{\frac{2}{3}}}}{{.2}^{{\frac{1}{5}}}}$

Q10. Express 0.3333…….= $\displaystyle 0.\overline{3}$ in the form $\displaystyle \frac{p}{q}$ , where p and q are integers and q ≠ 0.

Q11. Express 0.99999 _______ in the form $\displaystyle \frac{p}{q}$

Q12. Express $\displaystyle 0.\overline{6}$ in the form $\displaystyle \frac{p}{q}$ , where p and q are integers and q≠ 0.

HBSE Class 9 Math Chapter 2 Polynomials Important Questions 2024

Q1. Factorize the quadratic polynomial 6x² + 5x – 6 .

Q2. Factorize : 27x³ + y³ + z³ – 9xyz Most Important

Q3. Factorise : 64m³ – 343m³

Q4. Factorise : $\displaystyle \frac{{{{x}^{2}}}}{{100}}-{{y}^{2}}$

Q5. Factorise: 8a³ + b³ + 12a²b + 6ab²Most Important

Q6. Evaluate 103 x 107 without direct multiplication.

Q7. Factorize: 4x² + 9y² + 16z² + 12xy – 24yz – 16xz

Q8. Factorise : x³ + 13x² + 32x + 20

Q9. Factorise: x³ – 2x² – x + 2

Q10. Evaluate 103 x 107 by using identity.

Q11. Without actually calculating the cubes, find the value of (28)³ + (−15)³ + (−13)³.

Q12. Using suitable identity, find the value of (102)².

Q13. Find the value of k for which x – 1 is a factor of the polynomial x² + x + k .

Q14. Zero of p(x) = 3x + 1 is :

Q15. The coefficient of x² in 2 – x² +x³ is _________ .

Q16. The factors of 64m³ – 343n³ are __________.

Q17. What is product of ( x + 4 ) (x + 10) ?

Ans – x² + 14x + 40

Q18. Write $\displaystyle {{[x-\frac{2}{3}y]}^{{-3}}}$ in expanded form.

HBSE Class 9 Math Chapter 3 Coordinate Geometry Important Questions 2024

Q1. In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2) lie? Verify your answer by locating them on the Cartesian plane.

Q2. Plot the following ordered pairs (x, y) of numbers as points in the Cartesian Plane:

x	-2	-3	3	0
y	-3	7	-1	-1.5

Q3. Plot the following ordered pairs of numbers as points on the Cartesian Plane :

x	3	-2	-1	1
y	-1	6	-4	-3

Q4. What is the name of each part of the plane formed by horizontal and the vertical lines in the Cartesian plane?

Q5. Point (5, -7) lies in which Quadrant ?

Q6. The point (0, 0) where x-axis and y-axis intersect is called _________ .

Q7. The abscissa and coordinate of (6, −4 ) is ________.

Q8. From the fig given below :

Write the answer of each of following from figure:

(i) The coordinates of B

(ii) The point identified by the coordinates (-3, -5)

(iii) The abscissa of the point D

(iv) The coordinate of point H

Q9.

Look at the above figure and answer the following:
(i) Coordinates of A, B, C, D, E

(ii) Abscissa of point D

(iii) Ordinate of point E

(iv) Coordinates of point P, Q

HBSE Class 9 Math Chapter 4 Linear Equations in Two Variables Important Questions 2024

Q1. Find the four solutions for the equation 2x + y = 7 .

Q2. The floor of a rectangular hall has the perimeter 250 m. If the cost of the painting the four walls at the rate ₹ 12 per m² is ₹ 18,000, find the height of the hall.

Q3. What is solution of (2x + 1) = x + 3

Q4. Solve the equation 2x + 1 = x – 3 and represent the solution on (i) The number line, (ii) The Cartesian plane.

Q5. Solve the equation 2x + 8 = 0 and represent the solution on (i) the number line (ii) the Cartesian plane.

Q6. Find four different solutions of the equation x+2y = 6.

Q7. Find the value of P if x = 2 , y = 1 is a solution of the equation 2x + 3y = P

Q8. The solution of a linear equation is not affected when the same number is added or subtracted from both the sides of the equation. (True/False)

Ans – True

HBSE Class 9 Math Chapter 5 Introduction to Euclid’s Geometry Important Questions 2024

Q1. What is second postulate of Euclid ?

Q2. Write the first postulate of Euclid.

Ans – A straight line may be drawn from any one point to any other point.

HBSE Class 9 Math Chapter 6 Lines and Angles Important Questions 2024

Q1. Write the name of the point where these two lines intersect.

Q2. Give a definition for each of the following terms:
(i) Parallel lines.
(ii) Line segment

Q3. Define supplementary angle. Give its two examples also.

Q4. In the given figure, AB || CD || EF and y: z = 3 : 7 are given, then find the value of x.

Q5. In fig., AB || CD and CD || EF. And EA ⊥ AB. If ∠BEF 55° then find the values of x, y and z.

Q6. In fig., if PQ ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65°. Then find the values of x and y.

Q7. If in figure AC = BD, then prove that AB = CD : Most Important

Q8. A terminated line can be produced indefinitely. (True / False )

HBSE Class 9 Math Chapter 7 Triangles Important Questions 2024

Q1. Prove that angles opposite to equal sides of an isosceles triangle are equal.

Q2. Show that the angles of an equilateral triangle are 60° each. Most Important

Q3. Construct a triangle ABC in which BC = 8cm, ∠B = 45° and AB – AC = 3.5 cm. Most Important

Q4. ABC is a triangle right angled at C. A line through the mid point M of hypotenuse AB and parallel to BC intersects AC at D. Show that:

(i) D is the mid point of AC

(ii) MDIAC

(iii) CM = MA = $\displaystyle \frac{1}{2}$ AB

Q5. Construct a triangle ABC in which BC = 7 cm, ∠B – 75° and AB + AC = 13 cm. Most Important

Q6. D is a point on side BC of ΔABC such that AD = AC in given figure show that AB > AD.

Q7. ΔABC is a right angled triangle in which ∠A = 90° and AB = AC. What is the value of ∠B and ∠C?

Q8. If ΔPRQ ≅ ΔCBA , then find:

(i) QR =…,.

(ii) PR =……

(iii) PO = …..

(iv) ∠B =…….

Q9. The triangle formed by joining the mid-points of the sides of an isosceles triangle is ________.

Q10. Construct a triangle ABC in which ∠B = 60°, ∠C = 45° and perimeter is 10 cm.

Q11. To construct a triangle we must know at least its ________ parts .

Q12. The sum of any two sides of a triangle is _______ than the third side.

HBSE Class 9 Math Chapter 8 Quadrilaterals Important Questions 2024

Q1. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Q2. Show that the diagonals of a rhombus are perpendicular to each other.

Q3. ABCD is a quadrilateral in which P, Q, R and S are mid points of the sides AB, BC, CD and DA. AC is a diagonal, show that:

(i) SR || AC and SR= $\displaystyle \frac{1}{2}$ AC

(ii) PQ = SR

(iii) PORS is a parallelogram

Q4. If two sides of a cyclic quadrilateral are parallel, prove that:

(i) remaining two sides are equal and

(ii) both diagonals are equal

Q5. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other.

Q6. In cyclic quadrilateral ABCD, AOC is the diameter of circle. Ir ∠CAD = 50°, then ∠ACD is :

Q7. The diagonals of a rectangle are _______ .

HBSE Class 9 Math Chapter 9 Circles Important Questions 2024

Q1. Prove that a cyclic parallelogram is a rectangle.

Q2. In figure angle ∠ABC = 69° and angle ∠ACB =31° find ∠BDC. Most important

Q3. A Roller 120 cm long has a diameter 84 cm. To level a playground, it takes 500 complete revolutions. Determine the area of playground in m² .

Q4. Angles in the same segment of a circle are ______ .

Q5. In the given figure ∠PQR = 100° , where P, Q and R are points on a circle with centre O. Find ∠OPR .

Q6. In fig., A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the are ABC, then ∠ADC will be:

Q7. A circle has only finite numbers of equal chords. (True/False)

Ans – False

HBSE Class 9 Math Chapter 10 Heron’s Formula Important Questions 2024

Q1. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Q2. Sides of a triangle are in the ratio of 3 : 5 : 7 and its perimeter is 300 cm. Find its area.

HBSE Class 9 Math Chapter 11 Surface Areas and Volumes Important Questions 2024

Q1. Find the volume of right circular cone with radius 6 cm and height 7 cm.

Q2. The height of a cone is 15 cm. If its volume is 1570 cm³. the radius of it base is ?

Q3. The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm. Find :
(i) Height of the cone
(ii) Slant height of the cone
(iii) Curved surface area of the cone

Q4. A conical tent is 10 m high and the radius of its base is 24 m. Find:

(i) Slant height of the tent.

(ii) Cost of the canvas required to make the tent, if the cost of 1 m² canvas is ₹ 70.

Q5. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:

(i) Its inner curved surface area.

(ii) The cost of plastering this curved surface at the rate of Rs. 40 per m².

Q6. Volume of a hemisphere with radius r will be ________ .

Q7. Find the total surface area of a hemisphere if its radius is 21 cm

Q8. Find the radius of a sphere whose surface area is 154 cm².

HBSE Class 9 Math Chapter 12 Statistics Important Questions 2024

Q1. The following table gives the lifetimes of 400 neon lamps :

Lifetimes ( In Hours )

Number of Lamps

300-400

400-500

500-600

600-700

700-800

800-900

900-1000

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

Q2. The Blood Groups of 30 students of class IX are recorded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O

Represent this data in the form of a frequency distribution table.

Q3. A family with a monthly income of 6,400 plans his budget for a month as given below :

Grocery	Clothing	Education	Miscellaneous	Savings
2100	600	1200	1500	1000

(i) Represent the above data by a bar-graph.

(ii) On which item they spent more?

Q4. Class mark of class 140-150 is _________.