Math is an essential part of the curriculum in Class 9, and understanding its concepts lays the foundation for higher-level mathematics. In this blog post, we’ll explore 50 multiple-choice questions (MCQs) for Class 9 math, ranging from algebra and geometry to trigonometry. Each question is followed by the answer and an explanation to help solidify your understanding of the topics.
1. What is the value of xxx in the equation 3x−5=163x – 5 = 163x−5=16?
- A) x = 7
- B) x = 5
- C) x = 3
- D) x = 8
Answer: A) x = 7
To solve for xxx:
3x−5=163x – 5 = 163x−5=16
Add 5 to both sides:
3x=213x = 213x=21
Now divide by 3:
x=7x = 7x=7
2. What is the value of the discriminant for the quadratic equation 2×2−3x+1=02x^2 – 3x + 1 = 02×2−3x+1=0?
- A) 5
- B) 7
- C) 3
- D) 9
Answer: B) 7
The discriminant Δ\DeltaΔ of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0 is given by:Δ=b2−4ac\Delta = b^2 – 4acΔ=b2−4ac
For 2×2−3x+1=02x^2 – 3x + 1 = 02×2−3x+1=0, a=2a = 2a=2, b=−3b = -3b=−3, and c=1c = 1c=1.
Substitute these values:Δ=(−3)2−4(2)(1)=9−8=7\Delta = (-3)^2 – 4(2)(1) = 9 – 8 = 7Δ=(−3)2−4(2)(1)=9−8=7
3. The perimeter of a rectangle is 48 cm. If the length is 14 cm, what is the width?
- A) 12 cm
- B) 10 cm
- C) 6 cm
- D) 8 cm
Answer: A) 12 cm
The perimeter PPP of a rectangle is given by:P=2(l+w)P = 2(l + w)P=2(l+w)
Where lll is the length and www is the width.
Substitute the given values:48=2(14+w)48 = 2(14 + w)48=2(14+w)
Divide by 2:24=14+w24 = 14 + w24=14+w
Subtract 14 from both sides:w=12 cmw = 12 \, \text{cm}w=12cm
4. What is the value of 169\sqrt{169}169?
- A) 12
- B) 13
- C) 14
- D) 15
Answer: B) 13
The square root of 169 is 13, as 13×13=16913 \times 13 = 16913×13=169.
5. If the ratio of the sides of two similar triangles is 4:9, what is the ratio of their areas?
- A) 4:9
- B) 16:81
- C) 2:3
- D) 9:4
Answer: B) 16:81
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.(49)2=1681\left(\frac{4}{9}\right)^2 = \frac{16}{81}(94)2=8116
6. What is the area of a triangle with a base of 10 cm and a height of 5 cm?
- A) 25 cm²
- B) 50 cm²
- C) 75 cm²
- D) 100 cm²
Answer: B) 50 cm²
The area of a triangle is given by:Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21×base×height
Substitute the given values:Area=12×10×5=50 cm2\text{Area} = \frac{1}{2} \times 10 \times 5 = 50 \, \text{cm}^2Area=21×10×5=50cm2
7. What is the value of 23+49\frac{2}{3} + \frac{4}{9}32+94?
- A) 109\frac{10}{9}910
- B) 129\frac{12}{9}912
- C) 89\frac{8}{9}98
- D) 69\frac{6}{9}96
Answer: A) 109\frac{10}{9}910
To add fractions, find the least common denominator (LCD). The LCD of 3 and 9 is 9.
Rewrite 23\frac{2}{3}32 as 69\frac{6}{9}96, then add:69+49=109\frac{6}{9} + \frac{4}{9} = \frac{10}{9}96+94=910
8. Which of the following is the solution to the equation 5x+4=295x + 4 = 295x+4=29?
- A) x = 5
- B) x = 4
- C) x = 3
- D) x = 7
Answer: A) x = 5
To solve for xxx:5x+4=295x + 4 = 295x+4=29
Subtract 4 from both sides:5x=255x = 255x=25
Now divide by 5:x=5x = 5x=5
9. What is the value of 3x−5=103x – 5 = 103x−5=10 when solved for xxx?
- A) 5
- B) 7
- C) 3
- D) 15
Answer: B) x = 7
To solve for xxx:3x−5=103x – 5 = 103x−5=10
Add 5 to both sides:3x=153x = 153x=15
Now divide by 3:x=5x = 5x=5
10. What is the area of a circle with radius 7 cm?
- A) 49 cm²
- B) 154 cm²
- C) 22 cm²
- D) 44 cm²
Answer: A) 49 cm²
The area of a circle is given by:Area=πr2\text{Area} = \pi r^2Area=πr2
Substitute r=7r = 7r=7:Area=π×72=π×49≈154 cm2\text{Area} = \pi \times 7^2 = \pi \times 49 \approx 154 \, \text{cm}^2Area=π×72=π×49≈154cm2
11. What is the sum of the angles in a triangle?
- A) 180°
- B) 90°
- C) 360°
- D) 270°
Answer: A) 180°
The sum of the interior angles of a triangle is always 180°.
12. What is the value of the expression (3x+2)=14(3x + 2) = 14(3x+2)=14?
- A) x = 4
- B) x = 6
- C) x = 3
- D) x = 2
Answer: B) x = 4
To solve for xxx:3x+2=143x + 2 = 143x+2=14
Subtract 2 from both sides:3x=123x = 123x=12
Now divide by 3:x=4x = 4x=4
13. The product of two numbers is 56. If one number is 8, what is the other number?
- A) 6
- B) 7
- C) 4
- D) 5
Answer: B) 7
The product of two numbers is given by:8×other number=568 \times \text{other number} = 568×other number=56
Divide both sides by 8:other number=7\text{other number} = 7other number=7
14. If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?
- A) Scalene
- B) Isosceles
- C) Equilateral
- D) Right-angled
Answer: D) Right-angled
A triangle with sides 3 cm, 4 cm, and 5 cm follows the Pythagorean theorem 32+42=523^2 + 4^2 = 5^232+42=52, which makes it a right-angled triangle.
15. What is the volume of a cube with side length 4 cm?
- A) 16 cm³
- B) 64 cm³
- C) 32 cm³
- D) 48 cm³
Answer: B) 64 cm³
The volume of a cube is given by:Volume=side3\text{Volume} = \text{side}^3Volume=side3
Substitute 43=644^3 = 6443=64 cm³.
16. What is the value of 58+34\frac{5}{8} + \frac{3}{4}85+43?
- A) 198\frac{19}{8}819
- B) 178\frac{17}{8}817
- C) 218\frac{21}{8}821
- D) 138\frac{13}{8}813
Answer: B) 178\frac{17}{8}817
To add the fractions, we find the least common denominator (LCD) which is 8. Convert 34\frac{3}{4}43 to 68\frac{6}{8}86 and then add:58+68=178\frac{5}{8} + \frac{6}{8} = \frac{17}{8}85+86=817
17. What is the value of 232^323?
- A) 4
- B) 8
- C) 6
- D) 16
Answer: B) 8
232^323 means multiplying 2 by itself three times:2×2×2=82 \times 2 \times 2 = 82×2×2=8
18. The sum of the first 10 natural numbers is:
- A) 45
- B) 50
- C) 55
- D) 60
Answer: C) 55
The sum of the first nnn natural numbers is given by the formula:S=n(n+1)2S = \frac{n(n + 1)}{2}S=2n(n+1)
For n=10n = 10n=10:S=10(10+1)2=10×112=55S = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = 55S=210(10+1)=210×11=55
19. What is the volume of a cylinder with a radius of 3 cm and height of 5 cm?
- A) 45 cm³
- B) 70 cm³
- C) 90 cm³
- D) 100 cm³
Answer: A) 45 cm³
The volume of a cylinder is given by:V=πr2hV = \pi r^2 hV=πr2h
Substitute r=3r = 3r=3 and h=5h = 5h=5:V=π×32×5=π×9×5=45π≈45 cm3V = \pi \times 3^2 \times 5 = \pi \times 9 \times 5 = 45\pi \approx 45 \, \text{cm}^3V=π×32×5=π×9×5=45π≈45cm3
20. What is the solution to the equation 7x−4=247x – 4 = 247x−4=24?
- A) x = 4
- B) x = 5
- C) x = 6
- D) x = 7
Answer: B) x = 5
To solve for xxx:7x−4=247x – 4 = 247x−4=24
Add 4 to both sides:7x=287x = 287x=28
Now divide by 7:x=5x = 5x=5
21. The length of a diagonal of a square is 10 cm. What is the area of the square?
- A) 100 cm²
- B) 50 cm²
- C) 25 cm²
- D) 20 cm²
Answer: B) 50 cm²
The area AAA of a square is given by:A=side2A = \text{side}^2A=side2
For a square, the length of the diagonal ddd is related to the side sss by:d=s2d = s\sqrt{2}d=s2
Given d=10d = 10d=10, solve for sss:10=s2⇒s=102=52≈7.07 cm10 = s\sqrt{2} \Rightarrow s = \frac{10}{\sqrt{2}} = 5\sqrt{2} \approx 7.07 \, \text{cm}10=s2⇒s=210=52≈7.07cm
Now calculate the area:A=(7.07)2≈50 cm2A = (7.07)^2 \approx 50 \, \text{cm}^2A=(7.07)2≈50cm2
22. What is the value of (4x+5)=21(4x + 5) = 21(4x+5)=21 when solved for xxx?
- A) x = 4
- B) x = 5
- C) x = 3
- D) x = 2
Answer: C) x = 3
To solve for xxx:4x+5=214x + 5 = 214x+5=21
Subtract 5 from both sides:4x=164x = 164x=16
Now divide by 4:x=4x = 4x=4
23. What is the value of the perimeter of a square with side length 6 cm?
- A) 18 cm
- B) 24 cm
- C) 36 cm
- D) 12 cm
Answer: B) 24 cm
The perimeter PPP of a square is given by:P=4×side lengthP = 4 \times \text{side length}P=4×side length
Substitute the side length of 6 cm:P=4×6=24 cmP = 4 \times 6 = 24 \, \text{cm}P=4×6=24cm
24. What is the value of 59−23\frac{5}{9} – \frac{2}{3}95−32?
- A) 19\frac{1}{9}91
- B) 39\frac{3}{9}93
- C) 79\frac{7}{9}97
- D) 89\frac{8}{9}98
Answer: A) 19\frac{1}{9}91
To subtract the fractions, find the least common denominator (LCD), which is 9:59−23=59−69=19\frac{5}{9} – \frac{2}{3} = \frac{5}{9} – \frac{6}{9} = \frac{1}{9}95−32=95−96=91
25. If x=3x = 3x=3, what is the value of 2×2−3x+42x^2 – 3x + 42×2−3x+4?
- A) 10
- B) 12
- C) 15
- D) 18
Answer: B) 12
Substitute x=3x = 3x=3 into the expression:2×2−3x+4=2(3)2−3(3)+4=2(9)−9+4=18−9+4=122x^2 – 3x + 4 = 2(3)^2 – 3(3) + 4 = 2(9) – 9 + 4 = 18 – 9 + 4 = 122×2−3x+4=2(3)2−3(3)+4=2(9)−9+4=18−9+4=12
26. What is the length of the hypotenuse of a right-angled triangle with legs of 6 cm and 8 cm?
- A) 10 cm
- B) 12 cm
- C) 14 cm
- D) 16 cm
Answer: A) 10 cm
Using the Pythagorean theorem:a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
Substitute a=6a = 6a=6 and b=8b = 8b=8:62+82=c2⇒36+64=c2⇒100=c2⇒c=106^2 + 8^2 = c^2 \Rightarrow 36 + 64 = c^2 \Rightarrow 100 = c^2 \Rightarrow c = 1062+82=c2⇒36+64=c2⇒100=c2⇒c=10
27. What is the area of a circle with a radius of 7 cm?
- A) 49 cm²
- B) 22 cm²
- C) 44 cm²
- D) 154 cm²
Answer: A) 49 cm²
The area of a circle is given by:Area=πr2\text{Area} = \pi r^2Area=πr2
Substitute r=7r = 7r=7:Area=π×72=49π≈154 cm2\text{Area} = \pi \times 7^2 = 49\pi \approx 154 \, \text{cm}^2Area=π×72=49π≈154cm2
28. What is the value of (x+2)(x−3)=0(x + 2)(x – 3) = 0(x+2)(x−3)=0?
- A) x = -2 or x = 3
- B) x = 2 or x = 3
- C) x = -2 or x = -3
- D) x = 2 or x = -3
Answer: A) x = -2 or x = 3
The given equation is a factored quadratic equation. Set each factor equal to zero:x+2=0⇒x=−2x + 2 = 0 \Rightarrow x = -2x+2=0⇒x=−2 x−3=0⇒x=3x – 3 = 0 \Rightarrow x = 3x−3=0⇒x=3
29. What is the sum of the angles of a quadrilateral?
- A) 180°
- B) 360°
- C) 540°
- D) 270°
Answer: B) 360°
The sum of the interior angles of any quadrilateral is always 360°.
30. What is the distance between the points (2, 3) and (5, 7) on a coordinate plane?
- A) 5
- B) 4
- C) 6
- D) 7
Answer: A) 5
Use the distance formula:d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2−x1)2+(y2−y1)2
Substitute the coordinates (x1,y1)=(2,3)(x_1, y_1) = (2, 3)(x1,y1)=(2,3) and (x2,y2)=(5,7)(x_2, y_2) = (5, 7)(x2,y2)=(5,7):d=(5−2)2+(7−3)2=32+42=9+16=25=5d = \sqrt{(5 – 2)^2 + (7 – 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5d=(5−2)2+(7−3)2=32+42=9+16=25=5
31. What is the square of 12?
- A) 144
- B) 132
- C) 122
- D) 100
Answer: A) 144
The square of 12 is:122=14412^2 = 144122=144
32. What is the value of 25×34\frac{2}{5} \times \frac{3}{4}52×43?
- A) 59\frac{5}{9}95
- B) 620\frac{6}{20}206
- C) 620\frac{6}{20}206 simplified to 310\frac{3}{10}103
- D) 12\frac{1}{2}21
Answer: C) 620\frac{6}{20}206 simplified to 310\frac{3}{10}103
To multiply fractions, multiply the numerators and denominators:25×34=620\frac{2}{5} \times \frac{3}{4} = \frac{6}{20}52×43=206
Simplify 620\frac{6}{20}206 by dividing both the numerator and denominator by 2:620=310\frac{6}{20} = \frac{3}{10}206=103
33. What is the perimeter of a triangle with sides 5 cm, 12 cm, and 13 cm?
- A) 30 cm
- B) 40 cm
- C) 45 cm
- D) 50 cm
Answer: A) 30 cm
The perimeter PPP of a triangle is the sum of its sides:P=5+12+13=30 cmP = 5 + 12 + 13 = 30 \, \text{cm}P=5+12+13=30cm
34. What is the solution of the equation 2x+7=192x + 7 = 192x+7=19?
- A) x = 5
- B) x = 6
- C) x = 4
- D) x = 3
Answer: A) x = 6
To solve for xxx:2x+7=192x + 7 = 192x+7=19
Subtract 7 from both sides:2x=122x = 122x=12
Now divide by 2:x=6x = 6x=6
35. What is the area of a right-angled triangle with base 6 cm and height 8 cm?
- A) 24 cm²
- B) 36 cm²
- C) 48 cm²
- D) 18 cm²
Answer: A) 24 cm²
The area of a right-angled triangle is given by:Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21×base×height
Substitute the values:Area=12×6×8=24 cm2\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \, \text{cm}^2Area=21×6×8=24cm2
36. What is the value of 35+47\frac{3}{5} + \frac{4}{7}53+74?
- A) 4135\frac{41}{35}3541
- B) 4147\frac{41}{47}4741
- C) 2735\frac{27}{35}3527
- D) 3435\frac{34}{35}3534
Answer: A) 4135\frac{41}{35}3541
To add fractions, find the least common denominator (LCD), which is 35.35=2135and47=2035\frac{3}{5} = \frac{21}{35} \quad \text{and} \quad \frac{4}{7} = \frac{20}{35}53=3521and74=3520
Now add the fractions:2135+2035=4135\frac{21}{35} + \frac{20}{35} = \frac{41}{35}3521+3520=3541
37. What is the solution to the quadratic equation x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0?
- A) x = 1 or x = 6
- B) x = 2 or x = 3
- C) x = -2 or x = 3
- D) x = 1 or x = 5
Answer: B) x = 2 or x = 3
Factor the quadratic equation:x2−5x+6=(x−2)(x−3)=0x^2 – 5x + 6 = (x – 2)(x – 3) = 0x2−5x+6=(x−2)(x−3)=0
Set each factor equal to zero:x−2=0orx−3=0x – 2 = 0 \quad \text{or} \quad x – 3 = 0x−2=0orx−3=0
Thus, x=2x = 2x=2 or x=3x = 3x=3.
38. What is the area of a circle with a radius of 7 cm?
- A) 49 cm²
- B) 22 cm²
- C) 44 cm²
- D) 154 cm²
Answer: A) 49 cm²
The area of a circle is given by:Area=πr2\text{Area} = \pi r^2Area=πr2
Substitute r=7r = 7r=7:Area=π×72=49π≈154 cm2\text{Area} = \pi \times 7^2 = 49\pi \approx 154 \, \text{cm}^2Area=π×72=49π≈154cm2
39. What is the slope of the line passing through the points (2, 3) and (4, 7)?
- A) 2
- B) 4
- C) 1
- D) 3
Answer: A) 2
The slope mmm of a line passing through two points (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) is given by:m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}m=x2−x1y2−y1
Substitute the points (2, 3) and (4, 7):m=7−34−2=42=2m = \frac{7 – 3}{4 – 2} = \frac{4}{2} = 2m=4−27−3=24=2
40. What is the value of 52+325^2 + 3^252+32?
- A) 34
- B) 25
- C) 30
- D) 38
Answer: A) 3452=25and32=95^2 = 25 \quad \text{and} \quad 3^2 = 952=25and32=9
Add them together:25+9=3425 + 9 = 3425+9=34
41. What is the volume of a cone with radius 4 cm and height 9 cm?
- A) 36 cm³
- B) 108 cm³
- C) 75 cm³
- D) 50 cm³
Answer: A) 36 cm³
The volume of a cone is given by:V=13πr2hV = \frac{1}{3} \pi r^2 hV=31πr2h
Substitute r=4r = 4r=4 and h=9h = 9h=9:V=13π(4)2(9)=13π×16×9=144π3=36 cm3V = \frac{1}{3} \pi (4)^2 (9) = \frac{1}{3} \pi \times 16 \times 9 = \frac{144\pi}{3} = 36 \, \text{cm}^3V=31π(4)2(9)=31π×16×9=3144π=36cm3
42. What is the value of (x2+2x+1)(x^2 + 2x + 1)(x2+2x+1)?
- A) (x+1)2(x + 1)^2(x+1)2
- B) (x−1)2(x – 1)^2(x−1)2
- C) (x+2)2(x + 2)^2(x+2)2
- D) (x−2)2(x – 2)^2(x−2)2
Answer: A) (x+1)2(x + 1)^2(x+1)2
The expression x2+2x+1x^2 + 2x + 1×2+2x+1 is a perfect square trinomial, and it factors as:x2+2x+1=(x+1)2x^2 + 2x + 1 = (x + 1)^2×2+2x+1=(x+1)2
43. The sum of the angles in a quadrilateral is:
- A) 180°
- B) 360°
- C) 270°
- D) 540°
Answer: B) 360°
The sum of the interior angles of any quadrilateral is always 360°.
44. The value of 10×10−50÷510 \times 10 – 50 \div 510×10−50÷5 is:
- A) 75
- B) 80
- C) 85
- D) 90
Answer: A) 75
Follow the order of operations (PEMDAS):
First, divide:50÷5=1050 \div 5 = 1050÷5=10
Now, multiply and subtract:10×10−10=100−10=7510 \times 10 – 10 = 100 – 10 = 7510×10−10=100−10=75
45. What is the value of (x−4)(x+4)(x – 4)(x + 4)(x−4)(x+4)?
- A) x2−16x^2 – 16×2−16
- B) x2+16x^2 + 16×2+16
- C) x2−8x^2 – 8×2−8
- D) x2+8x^2 + 8×2+8
Answer: A) x2−16x^2 – 16×2−16
The expression (x−4)(x+4)(x – 4)(x + 4)(x−4)(x+4) is a difference of squares, and it simplifies to:x2−16x^2 – 16×2−16
46. What is the value of 8×3+6÷28 \times 3 + 6 \div 28×3+6÷2?
- A) 28
- B) 26
- C) 24
- D) 22
Answer: A) 28
Follow the order of operations (PEMDAS):
First, multiply and divide:8×3=24and6÷2=38 \times 3 = 24 \quad \text{and} \quad 6 \div 2 = 38×3=24and6÷2=3
Now, add:24+3=2824 + 3 = 2824+3=28
47. What is the value of 3(x+5)=213(x + 5) = 213(x+5)=21 when solved for xxx?
- A) 4
- B) 5
- C) 6
- D) 7
Answer: C) 6
To solve for xxx:3(x+5)=213(x + 5) = 213(x+5)=21
Divide both sides by 3:x+5=7x + 5 = 7x+5=7
Now, subtract 5 from both sides:x=2x = 2x=2
48. The length of the diagonal of a square is 10 cm. What is the area of the square?
- A) 50 cm²
- B) 100 cm²
- C) 144 cm²
- D) 25 cm²
Answer: B) 100 cm²
For a square, the diagonal ddd is related to the side length sss by:d=s2d = s\sqrt{2}d=s2
Given d=10d = 10d=10, solve for sss:10=s2⇒s=102⇒s≈7.0710 = s\sqrt{2} \quad \Rightarrow s = \frac{10}{\sqrt{2}} \quad \Rightarrow s \approx 7.0710=s2⇒s=210⇒s≈7.07
The area of the square is:A=s2⇒A=7.072=50 cm2A = s^2 \quad \Rightarrow A = 7.07^2 = 50 \, \text{cm}^2A=s2⇒A=7.072=50cm2
49. What is the volume of a cube with edge length 4 cm?
- A) 64 cm³
- B) 48 cm³
- C) 40 cm³
- D) 36 cm³
Answer: A) 64 cm³
The volume of a cube is given by:V=side3V = \text{side}^3V=side3
Substitute the edge length of 4 cm:V=43=64 cm3V = 4^3 = 64 \, \text{cm}^3V=43=64cm3
50. What is the value of x2+6x+9x^2 + 6x + 9×2+6x+9?
- A) (x+3)2(x + 3)^2(x+3)2
- B) (x−3)2(x – 3)^2(x−3)2
- C) (x+2)2(x + 2)^2(x+2)2
- D) (x−2)2(x – 2)^2(x−2)2
Answer: A) (x+3)2(x + 3)^2(x+3)2
The expression x2+6x+9x^2 + 6x + 9×2+6x+9 is a perfect square trinomial, and it factors as:x2+6x+9=(x+3)2x^2 + 6x + 9 = (x + 3)^2×2+6x+9=(x+3)2
This concludes the set of 50 MCQs for Class 9 Math. Let me know if you need any further assistance!
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