These CBSE Class 10 Mathematics MCQs are updated for 2026-27, organized by chapter. They help Class 10 students learn the current Mathematics exam style, and build real problem-solving skill along the way.
Why Class 10 Mathematics MCQs Are Worth Your Time
- Strictly based on the 2026 CBSE Mathematics textbook, and guidelines issued by CBSE.
- Covers several formats beyond regular MCQs - Assertion-Reasoning, Case-based, and Fill-in-the-blanks for Mathematics.
- Each Mathematics chapter has its own set, so you can check your understanding topic by topic.
- Accurate answers for every Mathematics MCQ, so you learn the logic behind each correct choice.
Mathematics MCQs for Class 10, by Chapter
Check out the newest 2026-27 Mathematics question sets below. They're great for self-checking, and for finding out which topics need more work before exams.
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Quick Practice - Try a Few Questions First Pick a chapter below, answer a few questions instantly, then jump to the full set list for more. Q1.According to the Fundamental Theorem of Arithmetic, every composite number can be expressed as: Answer: (a) A product of primes, and this factorisation is unique apart from the order of the factors. This theorem guarantees that prime factorisation of any composite number is unique, regardless of the order in which the primes are written.
Q2.The HCF and LCM of two numbers are related to the numbers themselves by which of the following? Answer: (a) Product of the two numbers equals the product of their HCF and LCM. For any two positive integers, the product of the numbers equals the product of their HCF and LCM.
Q3.A number that cannot be written in the form p/q, where p and q are integers and q is not zero, is called: Answer: (b) An irrational number. Irrational numbers, such as the square root of 2, cannot be expressed exactly as a simple fraction.
Q4.Is the number 2 + √3 rational or irrational? Answer: (b) Irrational. Adding a rational number to an irrational number always results in an irrational number.
Q5.The decimal expansion of a rational number is always: Answer: (a) Either terminating or non-terminating repeating. Rational numbers, when converted to decimals, either end after a few digits or repeat a pattern forever.
Q1.The highest power of the variable in a polynomial is called its: Answer: (a) Degree. The degree of a polynomial tells us the highest exponent of the variable present in the expression.
Q2.A polynomial of degree 2 is generally referred to as a: Answer: (b) Quadratic polynomial. A degree 2 polynomial, such as ax² + bx + c, is classified as a quadratic polynomial.
Q3.For a quadratic polynomial, the maximum number of zeroes it can have is: Answer: (b) Two. A quadratic polynomial can have at most two real zeroes, matching its degree.
Q4.The zeroes of a polynomial are the values of the variable for which the polynomial's value becomes: Answer: (a) Zero. By definition, a zero of a polynomial is a value that makes the polynomial equal to zero.
Q5.For a quadratic polynomial ax² + bx + c, the sum of its zeroes is given by: Answer: (a) -b/a. This relationship comes directly from comparing the polynomial with the product of its factors.
Q1.A pair of linear equations in two variables is said to be consistent if it has: Answer: (a) At least one solution. A consistent system has at least one solution, whether it is a unique solution or infinitely many.
Q2.Graphically, a pair of linear equations that has no solution is represented by two lines that are: Answer: (a) Parallel to each other. Parallel lines never meet, which means the equations they represent have no common solution.
Q3.Which of the following methods can be used to solve a pair of linear equations algebraically? Answer: (a) Substitution method. The substitution method is a standard algebraic technique used to solve such systems without drawing graphs.
Q4.If a pair of linear equations has infinitely many solutions, the two lines representing them are: Answer: (a) Coincident, lying exactly on top of one another. When both equations represent the exact same line, every point on that line satisfies both equations.
Q5.A pair of linear equations that intersect at exactly one point is said to have: Answer: (a) A unique solution. Since the lines cross at only one point, there is exactly one pair of values that satisfies both equations.
Q1.A quadratic equation is generally written in the standard form: Answer: (a) ax² + bx + c = 0, where a is not zero. This is the standard form of a quadratic equation, where the coefficient of x² must be non-zero.
Q2.The expression b² - 4ac in a quadratic equation is known as the: Answer: (a) Discriminant. The discriminant helps determine the nature of the roots of the quadratic equation.
Q3.If the discriminant of a quadratic equation is negative, the equation has: Answer: (a) No real roots. A negative discriminant means the roots are not real numbers, so the equation has no real solution.
Q4.If the discriminant of a quadratic equation equals zero, the equation has: Answer: (a) Two equal real roots. A zero discriminant means both roots of the equation are real and identical in value.
Q5.Which of the following is a conceptual method used to find the roots of a quadratic equation? Answer: (a) Factorisation. Factorisation expresses the quadratic as a product of two linear factors, from which the roots can be found.
Q1.An Arithmetic Progression (AP) is a sequence in which: Answer: (a) The difference between consecutive terms remains constant. This constant difference is called the common difference of the AP.
Q2.In an AP, the constant value added to each term to get the next term is called the: Answer: (a) Common difference. The common difference defines how much each term increases or decreases compared to the previous one.
Q3.The nth term of an AP is given by the formula: Answer: (a) a + (n-1)d. Here, 'a' is the first term and 'd' is the common difference, used together to find any term of the AP.
Q4.Which of the following sequences is an example of an Arithmetic Progression? Answer: (a) 2, 4, 6, 8, .... This sequence increases by a constant difference of 2 between consecutive terms, which is the defining property of an AP.
Q5.The sum of the first n terms of an AP can be calculated using a formula that requires knowing: Answer: (a) The first term, the common difference (or last term), and the number of terms. The standard sum formula for an AP combines the first term, common difference, and number of terms.
Q1.Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are: Answer: (a) In the same proportion. Similar triangles have the same shape but not necessarily the same size, with sides in proportion.
Q2.The Basic Proportionality Theorem (Thales' theorem) applies to a line drawn: Answer: (a) Parallel to one side of a triangle, intersecting the other two sides. This theorem states that such a line divides the other two sides of the triangle in the same ratio.
Q3.According to the Pythagoras theorem, in a right triangle, the square of the hypotenuse equals: Answer: (a) The sum of the squares of the other two sides. This fundamental relationship holds true for every right-angled triangle.
Q4.Which of the following criteria can be used to prove two triangles are similar? Answer: (a) AA (Angle-Angle) similarity criterion. If two angles of one triangle are equal to two angles of another, the triangles are similar by the AA criterion.
Q5.In similar triangles, the ratio of their areas is equal to: Answer: (a) The square of the ratio of their corresponding sides. This important property connects the ratio of areas to the square of the ratio of corresponding sides in similar triangles.
Q1.The distance formula used to find the distance between two points in a coordinate plane is derived from which theorem? Answer: (a) Pythagoras theorem. The distance formula essentially applies the Pythagoras theorem to the horizontal and vertical differences between two points.
Q2.The section formula in coordinate geometry is used to find: Answer: (a) The coordinates of a point dividing a line segment in a given ratio. This formula is especially useful for finding a point that divides a segment internally in a specified ratio.
Q3.The coordinates of the midpoint of a line segment joining two points are found by: Answer: (a) Taking the average of the corresponding x-coordinates and y-coordinates. The midpoint formula averages the x-coordinates and the y-coordinates separately.
Q4.In the Cartesian coordinate system, the point where the x-axis and y-axis intersect is called the: Answer: (a) Origin. The origin has coordinates (0, 0) and serves as the reference point for the whole coordinate plane.
Q5.The formula for finding the area of a triangle given the coordinates of its three vertices uses: Answer: (a) A specific formula involving the coordinates of all three vertices. This formula combines the coordinates of all three vertices to compute the enclosed area.
Q1.In a right-angled triangle, the trigonometric ratio sine of an angle is defined as the ratio of: Answer: (a) The side opposite the angle to the hypotenuse. Sine relates the length of the opposite side to the hypotenuse in a right-angled triangle.
Q2.The value of sin 90° is: Answer: (a) 1. At 90°, the ratio defining sine reaches its maximum value of 1 in the standard trigonometric ratios.
Q3.Which trigonometric ratio is defined as the reciprocal of sine? Answer: (a) Cosecant. Cosecant is defined as 1 divided by sine of the same angle.
Q4.The identity sin²θ + cos²θ equals: Answer: (a) 1. This is one of the most fundamental trigonometric identities, true for any angle θ.
Q5.The value of tan 45° is: Answer: (a) 1. At 45°, the opposite and adjacent sides of a right triangle are equal, making the tangent ratio equal to 1.
Q1.The angle of elevation is measured between the horizontal line and the line of sight when the observer looks: Answer: (a) Upward towards an object above the horizontal level. The angle of elevation is formed when looking up at something higher than eye level, such as the top of a tower.
Q2.The angle of depression is measured when an observer looks: Answer: (a) Downward towards an object below the horizontal level. This angle is formed between the horizontal line and the line of sight when looking down at something lower.
Q3.To find the height of a tower using trigonometry, which piece of information is typically required along with an angle? Answer: (a) The distance from the observer to the base of the tower. Knowing the horizontal distance and the angle of elevation allows the height to be calculated using trigonometric ratios.
Q4.In problems involving angles of elevation and depression, the ground is usually assumed to be: Answer: (a) Horizontal and level. Most such problems assume flat, horizontal ground to simplify the use of right-triangle trigonometry.
Q5.Which trigonometric ratio is most directly used when the height and the horizontal distance from the base are both involved in a problem? Answer: (a) Tangent. Tangent relates the opposite side (height) to the adjacent side (distance), making it useful in such problems.
Q1.A tangent to a circle is a line that: Answer: (a) Touches the circle at exactly one point. A tangent line touches the circle at exactly one point, called the point of tangency.
Q2.The tangent to a circle at any point is always: Answer: (a) Perpendicular to the radius drawn at that point. This perpendicularity is a key property used to solve many problems involving tangents.
Q3.From an external point, how many tangents can be drawn to a given circle? Answer: (a) Two. Exactly two tangents can be drawn from any point lying outside a circle.
Q4.The lengths of the two tangents drawn from an external point to a circle are: Answer: (a) Equal to each other. This is a well-known property: tangents drawn from the same external point to a circle are always equal in length.
Q5.A line that intersects a circle at exactly two points is called a: Answer: (a) Secant. Unlike a tangent, a secant line crosses the circle at two distinct points.
Q1.The area of a circle with radius r is given by the formula: Answer: (a) πr². This standard formula gives the area enclosed within a circle of radius r.
Q2.The circumference of a circle with radius r is given by: Answer: (a) 2πr. Circumference measures the total distance around the circle and is calculated using this formula.
Q3.A sector of a circle is the region enclosed between: Answer: (a) Two radii and the arc between them. A sector looks like a 'pie slice' of the circle, bounded by two radii and an arc.
Q4.A segment of a circle is the region enclosed between: Answer: (a) A chord and the corresponding arc. Unlike a sector, a segment is bounded by a straight chord and the arc it separates from the rest of the circle.
Q5.The area of a sector of a circle depends on which two quantities? Answer: (a) The radius of the circle and the angle subtended at the centre. A larger angle at the centre, or a larger radius, both increase the area of the sector.
Q1.When a cone and a hemisphere are combined to form a single solid, its total surface area is found by: Answer: (a) Adding the curved surface areas of both individual solids at their shared surface. For combined solids, only the exposed curved surfaces are added, since the joined flat faces are hidden inside.
Q2.The volume of a cylinder with base radius r and height h is given by: Answer: (a) πr²h. This standard formula calculates the space enclosed within a cylindrical solid.
Q3.The formula for the volume of a sphere with radius r is: Answer: (a) (4/3)πr³. This well-known formula gives the total space enclosed within a sphere of radius r.
Q4.When a solid is converted from one shape to another, such as melting a sphere to form a cylinder, which quantity remains constant? Answer: (a) Volume. Since the same amount of material is used, the total volume stays the same even though the shape changes.
Q5.The curved surface area of a cone with radius r and slant height l is given by: Answer: (a) πrl. This formula uses the slant height rather than the vertical height to compute the curved surface area of a cone.
Q1.The measure of central tendency that represents the middlemost value of an ordered data set is called the: Answer: (a) Median. The median divides the ordered data into two equal halves, with equal numbers of values above and below it.
Q2.The mode of a data set refers to: Answer: (a) The value that occurs most frequently. The mode identifies the most commonly occurring value or class in the given data.
Q3.The mean of grouped data is generally calculated using the: Answer: (a) Midpoints (class marks) of each class interval and their frequencies. For grouped data, each class is represented by its midpoint when calculating the mean.
Q4.A graphical representation showing cumulative frequency against class boundaries is called a: Answer: (a) Ogive. An ogive is used to visually estimate the median and other statistical measures from cumulative frequency data.
Q5.Which of the following best describes 'range' in statistics? Answer: (a) The difference between the highest and lowest values in a data set. Range gives a simple measure of how spread out the values in a data set are.
Q1.The probability of an event is defined as the ratio of: Answer: (a) The number of favourable outcomes to the total number of possible outcomes. This classical definition of probability assumes all outcomes are equally likely.
Q2.The probability of an event can never be: Answer: (a) Less than 0 or greater than 1. Probability values always lie between 0 and 1, inclusive, representing impossibility to certainty.
Q3.If an event is certain to happen, its probability is: Answer: (a) 1. A certain event, one that will definitely occur, is assigned a probability of exactly 1.
Q4.If an event is impossible, its probability is: Answer: (a) 0. An impossible event, one that can never occur, has a probability of exactly 0.
Q5.The sum of the probabilities of an event happening and it not happening always equals: Answer: (a) 1. Since these two outcomes cover every possibility, their probabilities must always add up to 1.
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FAQs
For the 2026-27 session, MCQs and objective-type questions carry around 20% weightage. CBSE has introduced 30% competency based questions as MCQs and they are important part of the Class 10 Mathematics paper.
You can access the latest chapter-wise MCQs for Class 10 Mathematics for free from StudiesToday.com. All questions are based on the latest syllabus and current academic year.
Yes, our Mathematics practice bank includes the new pattern of Assertion Reasoning and Case Study based MCQs. They have been designed to test the analytical skills of Class 10 students.
Solving Class 10 Mathematics MCQs regularly improves speed and accuracy as these are objective questions can get you 100% marks if your understanding of the topic is clear.
Yes, all Class 10 Mathematics MCQs and answers are accessible on any device at your convenience.
No, all Mathematics Multiple Choice Questions (MCQs), practice papers, and solutions for Class 10 are available for free for students to get more marks school exams.