Class 10 practice
Class 10 maths questions.
Maths questions for Class 10, at the level of students aged 15–17, each with its answer and a short explanation. Try each one before opening the answer.
An arithmetic progression has a first term of 7 and a common difference of 4. What is the 15th term of this progression?
Level 1 of 5Show the answer
Answer: 63
The nth term is given by a + (n - 1)d. Substituting a = 7, n = 15, and d = 4 yields 7 + (14 × 4) = 63.
In a right-angled triangle, an acute angle θ satisfies cos θ = 3/5. What is the exact value of sin θ?
Level 1 of 5Show the answer
Answer: 4/5
Using the trigonometric identity sin²θ + cos²θ = 1, sin θ equals square root of (1 - 9/25), which simplifies to 4/5.
Aarav bought 3 notebooks and 2 pens for ₹110. Rohan bought 1 notebook and 2 pens of the same kind for ₹70. What is the cost of a single notebook?
Level 1 of 5Show the answer
Answer: ₹20
Subtracting the second purchase from the first leaves 2 notebooks costing ₹40. Hence, one notebook costs ₹40 / 2 = ₹20.
A surveyor maps two points on a grid representing a park in Mysuru. Point P is located at (2, 3) and point Q is at (8, 11). What is the straight-line distance between point P and point Q?
Level 1 of 5Show the answer
Answer: 10 units
Using the distance formula, distance equals square root of ((8 - 2)² + (11 - 3)²), which simplifies to square root of (36 + 64) = 10 units.
Ananya has a cloth pouch containing 6 red, 4 blue, and 5 green marbles. If she draws a single marble at random, what is the probability that the drawn marble is blue?
Level 1 of 5Show the answer
Answer: 4/15
The total number of outcomes is 6 + 4 + 5 = 15. Since 4 marbles are blue, the required probability is 4/15.
A solid metal cylinder has a base radius of 7 cm and a height of 10 cm. Taking π as 22/7, what is the curved surface area of this cylinder?
Level 1 of 5Show the answer
Answer: 440 cm²
The curved surface area of a cylinder is 2πrh. Substituting the values gives 2 × (22/7) × 7 × 10 = 440 cm².
Consider the quadratic equation x² - 7x + 12 = 0. What is the sum of the roots of this equation?
Level 1 of 5Show the answer
Answer: 7
For a standard quadratic equation ax² + bx + c = 0, the sum of roots is -b/a. Here, -(-7)/1 = 7.
A straight line touches a circle of radius 5 cm at point T. Point O is the centre of the circle, and P is a point on the tangent line such that PT = 12 cm. What is the length of OP?
Level 1 of 5Show the answer
Answer: 13 cm
The tangent is perpendicular to the radius at the point of contact. By Pythagoras' theorem, OP equals square root of (5² + 12²) = 13 cm.
A student records the scores of a cricket team over five matches: 180, 210, 190, 240, and 230. What is the median score of this dataset?
Level 1 of 5Show the answer
Answer: 210
Arranging the five numbers in ascending order yields 180, 190, 210, 230, 240. The middle value is the third score, 210.
Two positive integers have a highest common factor of 12 and a lowest common multiple of 360. If one of the integers is 72, what is the other integer?
Level 1 of 5Show the answer
Answer: 60
For any two positive integers, HCF × LCM equals the product of the numbers. Therefore, the other integer is (12 × 360) / 72 = 60.
During an inter-school athletic event, five runners record the following sprint times in seconds: 12, 14, 15, 18, and 21. What is the median time recorded among these runners?
Level 1 of 5Show the answer
Answer: 15 seconds
When five data points are arranged in ascending order, the median is the middle value, which is the third value. Here, that value is 15 seconds.
Ananya saves ₹50 in the first week, ₹80 in the second, and increases her weekly savings by ₹30 each week. What is her total savings at the end of 10 weeks?
Level 2 of 5Show the answer
Answer: ₹1,850
This forms an AP with a = 50, d = 30, and n = 10. Using S_n = (n/2)[2a + (n - 1)d], S_10 = 5[100 + 9(30)] = 5(370) = ₹1,850.
- True or false?
The angle subtended by a circular arc at the centre is equal to half the angle subtended at the circumference.
Level 2 of 5Show the answer
Answer: False
By standard circle geometry theorems, the angle subtended at the centre is double, rather than half, the angle subtended at the circumference.
- True or false?
The angle subtended by an arc at the centre of a circle is half the angle subtended by the same arc at any point on the remaining part of the circle.
Level 2 of 5Show the answer
Answer: False
According to the degree measure theorem, the angle subtended by an arc at the centre is double, not half, the angle subtended by it on the remaining circumference.
- True or false?
In trigonometry, the fundamental identity sin²θ + cos²θ = 1 holds true for every real value of the angle θ.
Level 2 of 5Show the answer
Answer: True
On a unit circle, coordinates are defined as (cos θ, sin θ). Applying the Pythagorean theorem establishes that sin²θ + cos²θ = 1 for all real angles θ.
- Fill in the blank.
A sports academy awards points in an arithmetic progression during a tournament. If the first round awards 5 points and each subsequent round adds 3 points, the points awarded in the tenth round are ___.
Level 2 of 5Show the answer
Answer: 32
The nth term of an arithmetic progression is a + (n - 1)d. Here, a = 5, d = 3, and n = 10, giving 5 + 9 × 3 = 32.
- Fill in the blank.
For the quadratic equation x² - 7x + 12 = 0, the positive difference between the two roots is ___.
Level 2 of 5Show the answer
Answer: 1
Factoring x² - 7x + 12 = 0 gives (x - 3)(x - 4) = 0, so the roots are 3 and 4. The positive difference is 4 - 3 = 1.
- Fill in the blank.
According to Thales's theorem, the angle subtended by a diameter at any point on a circle's circumference is ___ degrees.
Level 2 of 5Show the answer
Answer: 90
An inscribed angle that subtends a semicircle is always a right angle, which measures exactly 90 degrees.
Which of these trigonometric expressions is the odd one out?
Level 2 of 5Show the answer
Answer: cos 30°
The value of cos 30° is √3/2. In contrast, sin 30°, cos 60°, and sin 150° all equal 1/2.
Which of the following quadratic equations is the odd one out?
Level 2 of 5Show the answer
Answer: 2x² - 5x + 2 = 0
The equation 2x² - 5x + 2 = 0 has a discriminant of 9, giving two distinct real roots. The other three equations have a discriminant of zero, yielding equal real roots.
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