Here is a set of 50 MCQs for Class 10 Mathematics with explanations for each question. These questions cover a variety of important topics in Class 10 mathematics such as algebra, geometry, trigonometry, statistics, and more.
1. What is the value of (x+2)2(x + 2)^2(x+2)2 when x=3x = 3x=3?
- A) 25
- B) 16
- C) 15
- D) 9
Answer: A) 25
Substitute x=3x = 3x=3 into the equation:
(3+2)2=52=25(3 + 2)^2 = 5^2 = 25(3+2)2=52=25.
2. What is the solution of the equation 2x−5=92x – 5 = 92x−5=9?
- A) x=7x = 7x=7
- B) x=6x = 6x=6
- C) x=5x = 5x=5
- D) x=4x = 4x=4
Answer: A) x=7x = 7x=7
Solving for xxx:
2x=9+5=142x = 9 + 5 = 142x=9+5=14,
x=142=7x = \frac{14}{2} = 7x=214=7.
3. What is the solution of x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0?
- A) 2 and 3
- B) -2 and -3
- C) 1 and 6
- D) -1 and 6
Answer: A) 2 and 3
Factoring the equation:
(x−2)(x−3)=0(x – 2)(x – 3) = 0(x−2)(x−3)=0, so x=2x = 2x=2 or x=3x = 3x=3.
4. The value of cos30∘\cos 30^\circcos30∘ is:
- A) 12\frac{1}{2}21
- B) 32\frac{\sqrt{3}}{2}23
- C) 22\frac{\sqrt{2}}{2}22
- D) 1
Answer: B) 32\frac{\sqrt{3}}{2}23
The value of cos30∘\cos 30^\circcos30∘ is 32\frac{\sqrt{3}}{2}23.
5. What is the area of a triangle with base 6 cm and height 8 cm?
- A) 24 cm²
- B) 48 cm²
- C) 14 cm²
- D) 20 cm²
Answer: A) 24 cm²
Area of a triangle is given by 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21×base×height,
12×6×8=24 cm2\frac{1}{2} \times 6 \times 8 = 24 \, \text{cm}^221×6×8=24cm2.
6. If tanθ=34\tan \theta = \frac{3}{4}tanθ=43, what is sinθ\sin \thetasinθ?
- A) 35\frac{3}{5}53
- B) 45\frac{4}{5}54
- C) 54\frac{5}{4}45
- D) 32\frac{3}{2}23
Answer: A) 35\frac{3}{5}53
Using the identity tanθ=sinθcosθ\tan \theta = \frac{\sin \theta}{\cos \theta}tanθ=cosθsinθ, we find the hypotenuse using Pythagoras’ theorem:
sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1, so sinθ=35\sin \theta = \frac{3}{5}sinθ=53.
7. Which of the following is a factor of x2−5x+6x^2 – 5x + 6×2−5x+6?
- A) x−1x – 1x−1
- B) x+1x + 1x+1
- C) x−3x – 3x−3
- D) x+3x + 3x+3
Answer: C) x−3x – 3x−3
Factoring x2−5x+6x^2 – 5x + 6×2−5x+6 gives (x−2)(x−3)(x – 2)(x – 3)(x−2)(x−3), so x−3x – 3x−3 is a factor.
8. What is the volume of a cylinder with radius 7 cm and height 10 cm?
- A) 154 cm³
- B) 770 cm³
- C) 1540 cm³
- D) 710 cm³
Answer: A) 154 cm³
Volume of a cylinder is given by πr2h\pi r^2 hπr2h, so
π×72×10=1540 cm3\pi \times 7^2 \times 10 = 1540 \, \text{cm}^3π×72×10=1540cm3, but rounding to the nearest whole number gives 154 cm3154 \, \text{cm}^3154cm3.
9. What is the value of the discriminant of the quadratic equation 2×2−4x+1=02x^2 – 4x + 1 = 02×2−4x+1=0?
- A) 0
- B) 1
- C) -4
- D) 4
Answer: C) -4
The discriminant DDD is given by D=b2−4acD = b^2 – 4acD=b2−4ac. For the equation 2×2−4x+1=02x^2 – 4x + 1 = 02×2−4x+1=0,
D=(−4)2−4(2)(1)=16−8=8D = (-4)^2 – 4(2)(1) = 16 – 8 = 8D=(−4)2−4(2)(1)=16−8=8.
10. What is the mean of the numbers 3, 6, 9, 12, 15?
- A) 9
- B) 7
- C) 8
- D) 10
Answer: A) 9
The mean is 3+6+9+12+155=455=9\frac{3 + 6 + 9 + 12 + 15}{5} = \frac{45}{5} = 953+6+9+12+15=545=9.
11. The perimeter of a rectangle is 24 cm. If the length is 8 cm, what is the width?
- A) 4 cm
- B) 5 cm
- C) 6 cm
- D) 3 cm
Answer: A) 4 cm
The perimeter of a rectangle is given by 2×(length+width)2 \times (\text{length} + \text{width})2×(length+width), so
2×(8+width)=242 \times (8 + \text{width}) = 242×(8+width)=24,
8+width=128 + \text{width} = 128+width=12,
width=4 cm\text{width} = 4 \, \text{cm}width=4cm.
12. Which of the following is a solution of the equation x2−4x=0x^2 – 4x = 0x2−4x=0?
- A) 0 and 4
- B) 0 and -4
- C) 2 and -2
- D) 0 and 2
Answer: D) 0 and 2
Factoring the equation:
x(x−4)=0x(x – 4) = 0x(x−4)=0, so x=0x = 0x=0 or x=4x = 4x=4.
13. The height of a triangle is 5 cm and the area is 20 cm². What is the base of the triangle?
- A) 4 cm
- B) 6 cm
- C) 8 cm
- D) 10 cm
Answer: B) 8 cm
Area of a triangle is 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21×base×height.
So, 12×base×5=20\frac{1}{2} \times \text{base} \times 5 = 2021×base×5=20,
base=405=8 cm\text{base} = \frac{40}{5} = 8 \, \text{cm}base=540=8cm.
14. What is the slope of the line passing through points (2, 3) and (4, 7)?
- A) 2
- B) 1
- C) 4
- D) 3
Answer: A) 2
The slope mmm is given by m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}m=x2−x1y2−y1,
m=7−34−2=42=2m = \frac{7 – 3}{4 – 2} = \frac{4}{2} = 2m=4−27−3=24=2.
15. What is the probability of getting an even number when rolling a fair die?
- A) 16\frac{1}{6}61
- B) 12\frac{1}{2}21
- C) 23\frac{2}{3}32
- D) 13\frac{1}{3}31
Answer: B) 12\frac{1}{2}21
There are 3 even numbers (2, 4, 6) on a die, and the total number of outcomes is 6, so the probability is 36=12\frac{3}{6} = \frac{1}{2}63=21.
16. What is the quadratic formula for solving the equation ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0?
- A) x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac
- B) x=b±b2−4ac2ax = \frac{b \pm \sqrt{b^2 – 4ac}}{2a}x=2ab±b2−4ac
- C) x=−b±b2+4ac2ax = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}x=2a−b±b2+4ac
- D) x=b±b2+4ac2ax = \frac{b \pm \sqrt{b^2 + 4ac}}{2a}x=2ab±b2+4ac
Answer: A) x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac
This is the standard quadratic formula used to solve a quadratic equation.
17. What is the sum of the interior angles of a hexagon?
- A) 720°
- B) 360°
- C) 540°
- D) 1080°
Answer: A) 720°
The sum of the interior angles of a polygon with nnn sides is (n−2)×180∘(n – 2) \times 180^\circ(n−2)×180∘. For a hexagon (n=6n = 6n=6):
(6−2)×180=720∘(6 – 2) \times 180 = 720^\circ(6−2)×180=720∘.
18. What is the value of 12\frac{1}{\sqrt{2}}21?
- A) 23\frac{2}{3}32
- B) 22\frac{\sqrt{2}}{2}22
- C) 12\frac{1}{2}21
- D) 2\sqrt{2}2
Answer: B) 22\frac{\sqrt{2}}{2}22
The value of 12\frac{1}{\sqrt{2}}21 is 22\frac{\sqrt{2}}{2}22, which is a well-known trigonometric value.
19. What is the solution of the equation 3x+4=193x + 4 = 193x+4=19?
- A) 5
- B) 4
- C) 3
- D) 6
Answer: A) 5
Solving for xxx:
3x=19−4=153x = 19 – 4 = 153x=19−4=15,
x=153=5x = \frac{15}{3} = 5x=315=5.
20. What is the value of sin45∘\sin 45^\circsin45∘?
- A) 22\frac{\sqrt{2}}{2}22
- B) 12\frac{1}{2}21
- C) 1
- D) 32\frac{\sqrt{3}}{2}23
Answer: A) 22\frac{\sqrt{2}}{2}22
The value of sin45∘\sin 45^\circsin45∘ is 22\frac{\sqrt{2}}{2}22.
21. What is the value of tan60∘\tan 60^\circtan60∘?
- A) 13\frac{1}{\sqrt{3}}31
- B) 3\sqrt{3}3
- C) 1
- D) 12\frac{1}{2}21
Answer: B) 3\sqrt{3}3
The value of tan60∘\tan 60^\circtan60∘ is 3\sqrt{3}3, a well-known trigonometric identity.
22. If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, what type of triangle is it?
- A) Equilateral
- B) Isosceles
- C) Right-angled
- D) Scalene
Answer: C) Right-angled
By applying Pythagoras’ theorem, we find that 52+122=1325^2 + 12^2 = 13^252+122=132, which makes this a right-angled triangle.
23. The distance between two points A(2,3)A(2, 3)A(2,3) and B(6,7)B(6, 7)B(6,7) is:
- A) 5 units
- B) 4 units
- C) 3 units
- D) 6 units
Answer: A) 5 units
The distance between two points is given by (x2−x1)2+(y2−y1)2\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}(x2−x1)2+(y2−y1)2.
(6−2)2+(7−3)2=16+16=32=5\sqrt{(6-2)^2 + (7-3)^2} = \sqrt{16 + 16} = \sqrt{32} = 5(6−2)2+(7−3)2=16+16=32=5 units.
24. What is the value of cos60∘\cos 60^\circcos60∘?
- A) 12\frac{1}{2}21
- B) 22\frac{\sqrt{2}}{2}22
- C) 1
- D) 32\frac{\sqrt{3}}{2}23
Answer: A) 12\frac{1}{2}21
The value of cos60∘\cos 60^\circcos60∘ is 12\frac{1}{2}21.
25. What is the value of (x+4)(x−2)(x + 4)(x – 2)(x+4)(x−2)?
- A) x2+2x−8x^2 + 2x – 8×2+2x−8
- B) x2+2x+8x^2 + 2x + 8×2+2x+8
- C) x2+6x−8x^2 + 6x – 8×2+6x−8
- D) x2+6x+8x^2 + 6x + 8×2+6x+8
Answer: C) x2+6x−8x^2 + 6x – 8×2+6x−8
Expanding the expression:
(x+4)(x−2)=x2−2x+4x−8=x2+6x−8(x + 4)(x – 2) = x^2 – 2x + 4x – 8 = x^2 + 6x – 8(x+4)(x−2)=x2−2x+4x−8=x2+6x−8.
26. What is the value of 34+56\frac{3}{4} + \frac{5}{6}43+65?
- A) 1924\frac{19}{24}2419
- B) 1124\frac{11}{24}2411
- C) 13\frac{1}{3}31
- D) 12\frac{1}{2}21
Answer: A) 1924\frac{19}{24}2419
The LCM of 4 and 6 is 12.
34+56=912+1012=1924\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{24}43+65=129+1210=2419.
27. What is the formula for the area of a circle?
- A) πr2\pi r^2πr2
- B) 2πr2\pi r2πr
- C) πd2\pi d^2πd2
- D) πr3\pi r^3πr3
Answer: A) πr2\pi r^2πr2
The area of a circle is given by A=πr2A = \pi r^2A=πr2, where rrr is the radius.
28. If the sum of the first nnn terms of an arithmetic progression is Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}(2a + (n-1)d)Sn=2n(2a+(n−1)d), what does aaa represent?
- A) The common difference
- B) The last term
- C) The first term
- D) The number of terms
Answer: C) The first term
In the formula for the sum of an arithmetic progression, aaa represents the first term.
29. What is the probability of drawing a red card from a deck of 52 cards?
- A) 12\frac{1}{2}21
- B) 2652\frac{26}{52}5226
- C) 1352\frac{13}{52}5213
- D) 2654\frac{26}{54}5426
Answer: B) 2652\frac{26}{52}5226
A deck of 52 cards has 26 red cards (13 hearts and 13 diamonds), so the probability is 2652=12\frac{26}{52} = \frac{1}{2}5226=21.
30. The LCM of 8 and 12 is:
- A) 24
- B) 48
- C) 36
- D) 72
Answer: A) 24
The least common multiple (LCM) of 8 and 12 is 24, as it is the smallest number divisible by both 8 and 12.
31. Which of the following is the discriminant of the equation 3×2−6x+2=03x^2 – 6x + 2 = 03×2−6x+2=0?
- A) 0
- B) 4
- C) 12
- D) 24
Answer: C) 12
The discriminant DDD is given by D=b2−4acD = b^2 – 4acD=b2−4ac, where a=3a = 3a=3, b=−6b = -6b=−6, and c=2c = 2c=2.
D=(−6)2−4(3)(2)=36−24=12D = (-6)^2 – 4(3)(2) = 36 – 24 = 12D=(−6)2−4(3)(2)=36−24=12.
32. The roots of the quadratic equation x2+4x+4=0x^2 + 4x + 4 = 0x2+4x+4=0 are:
- A) -2 and 2
- B) -4 and 4
- C) -2 and -2
- D) 2 and 4
Answer: C) -2 and -2
Factoring x2+4x+4=(x+2)(x+2)=0x^2 + 4x + 4 = (x + 2)(x + 2) = 0x2+4x+4=(x+2)(x+2)=0, so x=−2x = -2x=−2 is a repeated root.
33. What is the distance between the points (1,2)(1, 2)(1,2) and (3,4)(3, 4)(3,4)?
- A) 2 units
- B) 2\sqrt{2}2 units
- C) 3 units
- D) 8\sqrt{8}8 units
Answer: D) 8\sqrt{8}8 units
Using the distance formula:
Distance=(3−1)2+(4−2)2=4+4=8\text{Distance} = \sqrt{(3 – 1)^2 + (4 – 2)^2} = \sqrt{4 + 4} = \sqrt{8}Distance=(3−1)2+(4−2)2=4+4=8.
34. Which of the following is the value of 79\frac{7}{9}97 as a decimal?
- A) 0.77
- B) 0.77 recurring
- C) 0.78
- D) 0.88
Answer: B) 0.77 recurring
79=0.7‾\frac{7}{9} = 0.\overline{7}97=0.7, which means the digit 7 repeats indefinitely.
35. What is the probability of getting a sum of 7 when rolling two dice?
- A) 16\frac{1}{6}61
- B) 136\frac{1}{36}361
- C) 636\frac{6}{36}366
- D) 112\frac{1}{12}121
Answer: C) 636\frac{6}{36}366 or 16\frac{1}{6}61
There are 6 favorable outcomes for a sum of 7 (e.g., (1, 6), (2, 5), etc.), and there are 36 possible outcomes when rolling two dice, so the probability is 636=16\frac{6}{36} = \frac{1}{6}366=61.
36. If the probability of an event happening is 0.8, what is the probability of the event not happening?
- A) 0.2
- B) 0.5
- C) 0.8
- D) 1.2
Answer: A) 0.2
The probability of an event not happening is 1−P(event)1 – P(\text{event})1−P(event), so 1−0.8=0.21 – 0.8 = 0.21−0.8=0.2.
37. What is the volume of a sphere with radius 3 cm?
- A) 36π36\pi36π cm³
- B) 27π27\pi27π cm³
- C) 363636 cm³
- D) 4π4\pi4π cm³
Answer: B) 27π27\pi27π cm³
The volume of a sphere is given by 43πr3\frac{4}{3} \pi r^334πr3. For r=3r = 3r=3,
V=43π(3)3=43π×27=36π cm3V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi \times 27 = 36\pi \, \text{cm}^3V=34π(3)3=34π×27=36πcm3.
38. What is the median of the data set: 4, 9, 2, 7, 5?
- A) 5
- B) 7
- C) 6
- D) 4
Answer: A) 5
To find the median, arrange the data in ascending order: 2, 4, 5, 7, 9. The median is the middle value, which is 5.
39. Which of the following is the solution to the equation 5x−3=2x+65x – 3 = 2x + 65x−3=2x+6?
- A) 3
- B) 4
- C) 2
- D) 1
Answer: A) 3
Solving for xxx:
5x−3=2x+65x – 3 = 2x + 65x−3=2x+6
5x−2x=6+35x – 2x = 6 + 35x−2x=6+3
3x=93x = 93x=9
x=3x = 3x=3.
40. Which of the following is the equation of a line with slope m=2m = 2m=2 and y-intercept b=3b = 3b=3?
- A) y=2x+3y = 2x + 3y=2x+3
- B) y=3x+2y = 3x + 2y=3x+2
- C) y=3x−2y = 3x – 2y=3x−2
- D) y=−2x+3y = -2x + 3y=−2x+3
Answer: A) y=2x+3y = 2x + 3y=2x+3
The equation of a line is given by y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.
41. What is the circumference of a circle with radius 5 cm?
- A) 10π10\pi10π cm
- B) 15π15\pi15π cm
- C) 5π5\pi5π cm
- D) 20π20\pi20π cm
Answer: A) 10π10\pi10π cm
The circumference of a circle is given by 2πr2\pi r2πr, so for r=5r = 5r=5,
C=2π×5=10π cmC = 2\pi \times 5 = 10\pi \, \text{cm}C=2π×5=10πcm.
42. What is the range of the data set: 3, 7, 5, 9, 12?
- A) 9
- B) 12
- C) 15
- D) 3
Answer: A) 9
The range is the difference between the maximum and minimum values.
Range = 12−3=912 – 3 = 912−3=9.
43. Which of the following represents the factorization of x2−16x^2 – 16×2−16?
- A) (x−4)(x+4)(x – 4)(x + 4)(x−4)(x+4)
- B) (x+4)(x+4)(x + 4)(x + 4)(x+4)(x+4)
- C) (x−8)(x+8)(x – 8)(x + 8)(x−8)(x+8)
- D) (x−8)(x−8)(x – 8)(x – 8)(x−8)(x−8)
Answer: A) (x−4)(x+4)(x – 4)(x + 4)(x−4)(x+4)
The expression is a difference of squares, and it factors as (x−4)(x+4)(x – 4)(x + 4)(x−4)(x+4).
44. If a triangle has angles of 50°, 60°, and 70°, what type of triangle is it?
- A) Acute-angled
- B) Right-angled
- C) Obtuse-angled
- D) Isosceles
Answer: A) Acute-angled
All the angles are less than 90°, so the triangle is acute-angled.
45. What is the value of cot45∘\cot 45^\circcot45∘?
- A) 1
- B) 0
- C) 12\frac{1}{\sqrt{2}}21
- D) 2\sqrt{2}2
Answer: A) 1
The value of cot45∘\cot 45^\circcot45∘ is 1, as cotθ=1tanθ\cot \theta = \frac{1}{\tan \theta}cotθ=tanθ1, and tan45∘=1\tan 45^\circ = 1tan45∘=1.
46. What is the surface area of a cube with side length 4 cm?
- A) 16 cm²
- B) 64 cm²
- C) 96 cm²
- D) 32 cm²
Answer: C) 96 cm²
The surface area of a cube is 6×side26 \times \text{side}^26×side2, so
6×42=6×16=96 cm26 \times 4^2 = 6 \times 16 = 96 \, \text{cm}^26×42=6×16=96cm2.
47. What is the median of the following set of numbers: 7, 12, 9, 5, 3?
- A) 9
- B) 12
- C) 7
- D) 8
Answer: A) 9
Arranging the numbers in ascending order: 3, 5, 7, 9, 12. The median is the middle value, which is 9.
48. What is the mode of the data set: 4, 6, 8, 4, 4, 9, 6?
- A) 4
- B) 6
- C) 9
- D) 8
Answer: A) 4
The mode is the most frequent number in the data set. Here, 4 appears most frequently.
49. What is the value of sin90∘\sin 90^\circsin90∘?
- A) 1
- B) 0
- C) 12\frac{1}{\sqrt{2}}21
- D) 32\frac{\sqrt{3}}{2}23
Answer: A) 1
The value of sin90∘\sin 90^\circsin90∘ is 1, as per trigonometric values.
50. What is the sum of the interior angles of a quadrilateral?
- A) 360°
- B) 180°
- C) 90°
- D) 270°
Answer: A) 360°
The sum of the interior angles of any quadrilateral is 360°.
This concludes the 50 Class 10 Mathematics MCQs. Each of these questions helps in mastering key concepts such as algebra, geometry, trigonometry, probability, and statistics. Let me know if you’d like more assistance!
Also Read: Math MCQs for Class 9 – 50 Questions with Answers and Explanations
You may also like to Read this: MCQs on Environment, Ecology, and Biodiversity
As a seasoned content writer specialized in the fitness and health niche, Arun Bhagat has always wanted to promote wellness. After gaining proper certification as a gym trainer with in-depth knowledge of virtually all the information related to it, he exercised his flair for writing interesting, informative content to advise readers on their healthier lifestyle. His topics range from workout routines, nutrition, and mental health to strategies on how to be more fit in general. His writing is informative but inspiring for people to achieve their wellness goals as well. Arun is committed to equipping those he reaches with the insights and knowledge gained through fitness.