Get ready for Mathematics with these CBSE Class 12 MCQs, organized chapter by chapter for 2026-27. They help you master the current exam pattern, and build sharper problem-solving skills.
Why Class 12 Mathematics MCQs Are Worth Your Time
- A wide range of Class 12 Assertion and Reasoning, Case-based, and Fill-in-the-blanks questions for Mathematics.
- Neatly organized by chapter, so you can test your grip on each Mathematics topic one at a time.
- Answers are explained clearly for every Mathematics question, so the reasoning actually makes sense.
- Matched closely to the 2026 CBSE Mathematics textbook and current guidelines.
Browse Class 12 Mathematics MCQs by Chapter
The 2026-27 Mathematics sets below are ready to use. Try them for self-assessment, and to see which topics need extra revision 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.A relation R on a set A is called reflexive if: Answer: (b) (a,a) belongs to R for every a in A. This means every element must be related to itself for the relation to qualify as reflexive.
Q2.A function f: A to B is called one-one, or injective, if: Answer: (b) Distinct elements of A always have distinct images in B. In other words, no two different inputs are ever allowed to give the same output.
Q3.A function f: A to B is called onto, or surjective, if: Answer: (a) Every element of B has at least one pre-image in A. This means the range of the function covers the entire codomain.
Q4.A relation that is reflexive, symmetric, and transitive is called: Answer: (b) An equivalence relation. This particular combination of properties is what allows the relation to partition a set into distinct equivalence classes.
Q5.If f: R to R is defined as f(x) = x squared, then f is: Answer: (b) Neither one-one nor onto. It's not one-one since f(2) equals f(-2), and it's not onto since negative real numbers are never attained as outputs.
Q1.The principal value branch of sin inverse x is: Answer: (b) [-pi/2, pi/2]. Restricting the range this way is what makes the inverse sine function well defined, since the ordinary sine function isn't one-one over its entire domain.
Q2.The principal value branch of cos inverse x is: Answer: (a) [0, pi]. Choosing this particular range ensures cos inverse is a proper, well defined function.
Q3.The domain of the function sin inverse x is: Answer: (b) [-1, 1]. Since the sine function itself only ever produces values within this range, its inverse can only be defined for inputs within the same interval.
Q4.The value of tan inverse(1) is: Answer: (b) pi/4. This corresponds to the well known fact that tan of pi/4 equals 1.
Q5.Which of these identities generally holds for inverse trigonometric functions, within their principal value branches? Answer: (a) sin inverse x + cos inverse x = pi/2. This identity holds for every x within the domain [-1, 1].
Q1.A matrix in which the number of rows equals the number of columns is called: Answer: (b) A square matrix. Only square matrices, for example, can have a determinant or be inverted.
Q2.A matrix in which all elements are zero is called: Answer: (b) A null or zero matrix. It acts somewhat like the number zero does in ordinary arithmetic, particularly for matrix addition.
Q3.Two matrices can be multiplied only if: Answer: (b) The number of columns in the first equals the number of rows in the second. This compatibility condition is essential, otherwise matrix multiplication simply isn't defined.
Q4.The transpose of a matrix is obtained by: Answer: (b) Interchanging its rows and columns. If A is an m by n matrix, its transpose becomes an n by m matrix.
Q5.A square matrix A is called symmetric if: Answer: (a) A equals its transpose. This means the entries are mirrored exactly across the main diagonal.
Q1.The determinant of a 2 by 2 matrix with rows (a,b) and (c,d) is calculated as: Answer: (b) ad-bc. This is the standard formula used for finding the determinant of any 2 by 2 matrix.
Q2.If the determinant of a square matrix is zero, the matrix is said to be: Answer: (b) Singular. A matrix with a zero determinant does not have an inverse.
Q3.The determinant of an identity matrix of any order is always: Answer: (b) 1. This is one of the defining properties of the identity matrix, regardless of its size.
Q4.Cramer's Rule is primarily used to: Answer: (b) Solve a system of linear equations using determinants. It expresses each unknown variable as a ratio of two determinants.
Q5.The area of a triangle with given vertices can be calculated using: Answer: (b) A determinant formed from the coordinates of the vertices. This is a neat, elegant application of determinants that avoids needing to compute the base and height separately.
Q1.A function f is said to be continuous at a point x equal to a if: Answer: (b) The limit of f(x) as x approaches a exists and equals f(a). All three conditions together, the function value, the limit existing, and the two being equal, are needed for continuity at that point.
Q2.Every differentiable function is necessarily: Answer: (b) Continuous. However, the reverse isn't always true, since a function can be continuous at a point without being differentiable there, as with a sharp corner in the graph.
Q3.The chain rule in differentiation is used to differentiate: Answer: (b) A composite function. It essentially breaks the differentiation down into the derivative of the outer function multiplied by the derivative of the inner function.
Q4.The derivative of a constant function is always: Answer: (b) 0. Since a constant function never changes value, its rate of change, and hence its derivative, is always zero.
Q5.Rolle's Theorem requires that a function be: Answer: (b) Continuous on a closed interval, differentiable on the open interval, with equal values at the endpoints. Under these conditions, the theorem guarantees at least one point where the derivative equals zero.
Q1.The derivative of a function gives the: Answer: (b) Rate of change or slope of the tangent to the curve. This interpretation is exactly what makes derivatives so useful for studying how quantities change.
Q2.A function is said to be increasing on an interval if its derivative is: Answer: (b) Positive throughout that interval. A positive derivative means the function's value keeps rising as x increases.
Q3.At a point of local maximum, the first derivative of a function is: Answer: (c) Zero, assuming the function is differentiable there. This is why setting the derivative equal to zero is the standard first step in locating maxima and minima.
Q4.The second derivative test is used to determine: Answer: (a) Whether a critical point is a maximum or a minimum. A negative second derivative at a critical point indicates a local maximum, while a positive one indicates a local minimum.
Q5.Derivatives are commonly used to solve real world problems involving: Answer: (a) Rate of change, such as speed or growth rate. Applications range from finding the maximum profit for a business to analysing how quickly a population is growing.
Q1.Integration is essentially the reverse process of: Answer: (b) Differentiation. Given a function's derivative, integration lets you work backward to recover a form of the original function.
Q2.The integral of a constant, k, with respect to x is: Answer: (b) kx + C. Here, C represents the arbitrary constant of integration, since infinitely many functions share the same derivative.
Q3.A definite integral, unlike an indefinite integral, gives: Answer: (b) A specific numerical value, calculated between two given limits. This value often represents a quantity like the area under a curve between those two points.
Q4.Integration by parts is a technique primarily used to integrate: Answer: (b) The product of two functions. It's based on a formula derived from the product rule of differentiation.
Q5.Which method is commonly used to integrate a function by substituting a new variable to simplify it? Answer: (a) Method of substitution. This technique often turns a complicated expression into a much simpler one that's easier to integrate directly.
Q1.Definite integrals are commonly used to calculate: Answer: (b) The area under a curve between two points. This is one of the most important practical applications of definite integrals.
Q2.To find the area between two curves, you generally: Answer: (b) Integrate the difference between the two functions over the given interval. Subtracting the lower curve from the upper one, then integrating, gives the enclosed area between them.
Q3.The area of a circle can be derived using integral calculus by integrating: Answer: (b) The equation of the circle over the appropriate limits. Setting up and evaluating this integral correctly reproduces the familiar formula for the area of a circle.
Q4.When calculating area using integration, if a curve lies below the x-axis over an interval, the definite integral over that interval will be: Answer: (b) Negative, so its absolute value must be taken for actual area. Since area itself is always a positive quantity, this sign has to be accounted for when the region lies below the axis.
Q5.Application of integrals is commonly used in real life to calculate quantities such as: Answer: (a) Area, volume, and displacement. These are all quantities that can be expressed as the integral of some related rate or function.
Q1.A differential equation is an equation that involves: Answer: (b) A function and its derivatives. These equations are used to model how quantities change in relation to one another.
Q2.The order of a differential equation refers to: Answer: (b) The highest order derivative present in the equation. For example, an equation containing only a first derivative is called a first order differential equation.
Q3.A differential equation is said to be linear if: Answer: (a) The dependent variable and its derivatives appear only to the first degree. There should also be no products of the dependent variable with its own derivatives.
Q4.The general solution of a differential equation contains: Answer: (b) Arbitrary constants, whose number matches the order of the equation. A particular solution is then obtained by assigning specific values to these constants, typically using given initial conditions.
Q5.The method of separation of variables is used to solve differential equations where: Answer: (b) The equation can be rearranged so all terms of one variable are on one side and the other variable on the other side. Once separated this way, each side can be integrated independently.
Q1.A vector quantity is one that has: Answer: (b) Both magnitude and direction. This is what distinguishes a vector, like velocity or force, from a scalar quantity, like mass or temperature, which has magnitude alone.
Q2.The dot product, or scalar product, of two vectors results in: Answer: (b) A scalar quantity. It's calculated using the magnitudes of the two vectors along with the cosine of the angle between them.
Q3.The cross product, or vector product, of two vectors results in: Answer: (b) A vector quantity perpendicular to both original vectors. Its direction is determined using the right hand rule.
Q4.Two vectors are said to be perpendicular to each other if their dot product equals: Answer: (b) 0. This is a very useful test, since it lets you check perpendicularity between two vectors without needing to measure any actual angles.
Q5.The magnitude of a vector a = xi + yj + zk is given by: Answer: (b) The square root of x squared plus y squared plus z squared. This formula is a direct extension of the Pythagorean theorem into three dimensions.
Q1.In three dimensional geometry, a point is generally represented using: Answer: (b) Three coordinates, x, y, and z. These represent the point's position along each of the three mutually perpendicular axes.
Q2.The direction cosines of a line are the cosines of the angles the line makes with: Answer: (b) The three coordinate axes. Together, these three values fully describe the direction a line points in three dimensional space.
Q3.Two lines in three dimensional space are said to be perpendicular if: Answer: (b) The sum of the products of their corresponding direction ratios equals zero. This condition is essentially the three dimensional version of the dot product test used for vectors.
Q4.The equation of a plane in three dimensional geometry can be represented in: Answer: (b) Both Cartesian and vector form. Depending on the given information, one form is often more convenient to use than the other.
Q5.The shortest distance between two skew lines in space is measured: Answer: (a) Along a line perpendicular to both. Skew lines never intersect and aren't parallel, so this perpendicular distance is the standard way of measuring how far apart they actually are.
Q1.Linear Programming is a mathematical technique used to: Answer: (b) Find the optimal value, maximum or minimum, of a linear function subject to given constraints. It's widely used in business and economics for problems like maximising profit or minimising cost.
Q2.In a Linear Programming Problem, the function to be maximised or minimised is called the: Answer: (b) Objective function. It represents exactly what the decision maker is trying to optimise, whether that's profit, cost, or some other quantity.
Q3.The feasible region in a Linear Programming Problem represents: Answer: (b) The set of all points satisfying every given constraint simultaneously. The optimal solution to the problem always occurs at one of the corner points of this region.
Q4.According to the Corner Point Theorem, the optimal value of the objective function occurs at: Answer: (b) One of the corner points, or vertices, of the feasible region. This is exactly why solving these problems usually involves evaluating the objective function only at each corner point, rather than every point in the region.
Q5.Constraints in a Linear Programming Problem are generally expressed as: Answer: (b) Linear inequalities. Along with non-negativity restrictions, these inequalities define the boundaries of the feasible region.
Q1.The probability of an event always lies between: Answer: (b) 0 and 1, inclusive. A probability of 0 means the event is impossible, while a probability of 1 means it's certain to happen.
Q2.Conditional probability, written P(A given B), refers to: Answer: (a) The probability of event A occurring, given that event B has already occurred. This concept becomes particularly important when the two events aren't independent of each other.
Q3.Two events A and B are said to be independent if: Answer: (b) P(A and B) equals P(A) times P(B). This formula only holds true when the occurrence of one event has genuinely no effect on the probability of the other.
Q4.Bayes' Theorem is primarily used to: Answer: (b) Revise or update the probability of an event based on new evidence. It's a particularly useful tool in situations involving multiple possible causes for an observed outcome.
Q5.A random variable is best described as: Answer: (b) A variable whose value is a numerical outcome of a random phenomenon. Its actual value can differ across different repetitions of the same random experiment, following some underlying probability distribution.
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| Chapter 04 Determinants MCQs Set 03 |
| Chapter 04 Determinants MCQs Set 01 |
| Chapter 04 Determinants MCQs Set 02 |
| Chapter 07 Integrals MCQs Set 04 |
| Chapter 07 Integrals MCQs Set 01 |
| Chapter 07 Integrals MCQs Set 03 |
| Chapter 07 Integrals MCQs Set 02 |
| Case Study Problems MCQs |
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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 12 Mathematics paper.
You can access the latest chapter-wise MCQs for Class 12 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 12 students.
Solving Class 12 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 12 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 12 are available for free for students to get more marks school exams.