Class 10 Mathematics MCQ Quiz

Which of these numbers is irrational?

• Square root of 5
• Square root of 9
• 0.25
• 7/3

Answer: Square root of 5. The square root of 5 cannot be written as p/q, so it is irrational. The square root of 9 is 3, and 0.25 and 7/3 are both rational.

What is the sum of the zeroes of the polynomial x² - 7x + 10?

• 2
• 5
• 10
• 7

Answer: 7. For ax² + bx + c, the sum of zeroes is -b/a = 7. Check: x² - 7x + 10 = (x - 2)(x - 5), and 2 + 5 = 7.

What is the 10th term of the AP 2, 7, 12, ...?

• 52
• 47
• 45
• 50

Answer: 47. Here a = 2 and d = 5, so the 10th term = a + 9d = 2 + 45 = 47.

What is the value of sin 30° + cos 60°?

• 0
• 1/2
• 1
• 2

Answer: 1. sin 30° = 1/2 and cos 60° = 1/2, so the sum is 1.

The HCF of 26 and 91 is 13. What is their LCM?

• 91
• 2366
• 182
• 364

Answer: 182. HCF x LCM = product of the numbers, so LCM = (26 x 91) / 13 = 2366 / 13 = 182.

What is the probability of getting a number greater than 4 when a fair die is thrown once?

• 1/3
• 1/2
• 2/3
• 1/6

Answer: 1/3. Only 5 and 6 are greater than 4, so the probability is 2/6 = 1/3.

What is the distance between the points (1, -1) and (7, 7)?

• 8 units
• 14 units
• 10 units
• 12 units

Answer: 10 units. Distance = square root of (6² + 8²) = square root of (36 + 64) = square root of 100 = 10 units.

How many solutions does the pair of equations 2x + 3y = 5 and 4x + 6y = 10 have?

• Infinitely many
• Exactly one
• No solution
• Exactly two

Answer: Infinitely many. The ratios 2/4, 3/6 and 5/10 are all equal to 1/2, so the two lines coincide and every point on the line is a solution.

The volume of a cone is what fraction of the volume of a cylinder with the same base radius and height?

• One-half
• One-third
• Two-thirds
• Equal

Answer: One-third. Cone volume = (1/3) x pi x r² x h, while cylinder volume = pi x r² x h. So three such cones fill one cylinder.

A vertical pole casts a shadow equal to its own height. What is the angle of elevation of the Sun?

• 90°
• 30°
• 60°
• 45°

Answer: 45°. tan of the angle = height / shadow = 1, and tan 45° = 1. So the Sun is at 45°.

What is the nature of the roots of the equation 2x² - 4x + 3 = 0?

• Two distinct real roots
• No real roots
• Two equal real roots
• One root is zero

Answer: No real roots. The discriminant b² - 4ac = 16 - 24 = -8, which is negative, so the equation has no real roots.

In triangle ABC, DE is parallel to BC with D on AB and E on AC. If AD/DB = 3/4 and AE = 6 cm, what is EC?

• 10 cm
• 4.5 cm
• 8 cm
• 14 cm

Answer: 8 cm. By the Basic Proportionality Theorem, AD/DB = AE/EC, so 3/4 = 6/EC and EC = 8 cm.

A point is 13 cm from the centre of a circle of radius 5 cm. What is the length of the tangent from this point to the circle?

• 12 cm
• 8 cm
• 18 cm
• 14 cm

Answer: 12 cm. The tangent is perpendicular to the radius, so by Pythagoras the length = square root of (13² - 5²) = square root of 144 = 12 cm.

What is the area of a sector of angle 90° in a circle of radius 14 cm? (Take pi = 22/7)

• 616 cm²
• 154 cm²
• 308 cm²
• 77 cm²

Answer: 154 cm². Area = (90/360) x (22/7) x 14 x 14 = (1/4) x 616 = 154 cm². 616 cm² is the area of the whole circle.

Which empirical relationship links the mean, median and mode of a moderately skewed distribution?

• Mode = Mean + Median
• 3 Mean = Mode + 2 Median
• 2 Median = Mode + 3 Mean
• 3 Median = Mode + 2 Mean

Answer: 3 Median = Mode + 2 Mean. For moderately skewed data, 3 Median = Mode + 2 Mean, so you can find any one of the three if you know the other two.