CBSE – Class 12 Maths Questions
Subject: Maths
Topic: Relations and Functions
Q. Determine whether the relation R defined by R = {(x, y): y = x²} is a function.
A. Yes, because for every x there is a unique y = x².
Subject: Maths
Topic: Relations and Functions
Q. Find the domain of the function f(x) = √(5 − x).
A. For real values, 5 − x ≥ 0 ⇒ x ≤ 5.
Subject: Maths
Topic: Inverse Trigonometric Functions
Q. Evaluate sin⁻¹(sin 2π/3).
A. $$\sin^{-1}(\sin 2\pi/3) = \pi/3$$
Subject: Maths
Topic: Matrices
Q. Find the order of the matrix A = [[1,2,3],[4,5,6]].
A. Matrix has 2 rows and 3 columns, so order is 2×3.
Subject: Math
Topic: Relations and Functions
Q. What is a one-one function?
A. A function in which different inputs have different outputs.
Subject: Math
Topic: Relations and Functions
Q. What is an onto function?
A. A function whose range is equal to its codomain.
Subject: Math
Topic: Inverse Trigonometric Functions
Q. sin⁻¹x ka domain kya hota hai?
A. [-1, 1]
Subject: Math
Topic: Inverse Trigonometric Functions
Q. cos⁻¹x ka range kya hota hai?
A. [0, π]
Subject: Math
Topic: Matrices
Q. Identity matrix kya hoti hai?
A. Diagonal matrix jisme main diagonal ke sab elements 1 hote hain
Subject: Math
Topic: Matrices
Q. A⁻¹ ka formula kya hai?
A. A⁻¹ = adj(A) / |A|, jab |A| ≠ 0
Subject: Math
Topic: Determinants
Q. Agar |A| = 0 ho to inverse exist karta hai?
A. Nahi
Subject: Math
Topic: Determinants
Q. 2×2 matrix ka determinant formula kya hai?
A. |A| = ad − bc
Subject: Math
Topic: Continuity
Q. Function continuous hone ki condition kya hai?
A. LHL = RHL = f(a)
Subject: Math
Topic: Differentiability
Q. Har differentiable function continuous hota hai?
A. Haan
Subject: Math
Topic: Differentiation
Q. d/dx (sin x) kya hota hai?
A. cos x
Subject: Math
Topic: Differentiation
Q. d/dx (eˣ) kya hota hai?
A. eˣ
Subject: Math
Topic: Applications of Derivatives
Q. Maxima aur minima kis chapter me aata hai?
A. Applications of Derivatives
Subject: Math
Topic: Integrals
Q. ∫1 dx ka value kya hota hai?
A. x + C
Subject: Math
Topic: Integrals
Q. ∫eˣ dx kya hota hai?
A. eˣ + C
Subject: Math
Topic: Definite Integrals
Q. ∫₀ᵃ f(x) dx ka geometric meaning kya hai?
A. Curve ke niche ka area
Subject: Math
Topic: Area Under Curve
Q. Area negative kab hota hai?
A. Jab curve x-axis ke niche ho
Subject: Math
Topic: Differential Equations
Q. Order of differential equation kya hota hai?
A. Highest derivative ka order
Subject: Math
Topic: Vector Algebra
Q. i, j, k kya represent karte hain?
A. Unit vectors
Subject: Math
Topic: Vector Algebra
Q. Dot product ka formula kya hai?
A. a·b = |a||b|cosθ
Subject: Math
Topic: 3D Geometry
Q. Distance formula in 3D kya hai?
A. √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]
Subject: Math
Topic: Probability
Q. P(A ∪ B) ka formula kya hai?
A. P(A) + P(B) − P(A ∩ B)
Subject: Math
Topic: Inverse Trigonometric Functions
Q. What is the principal value of sin⁻¹x?
A. The value of angle whose sine is x and lies in [-π/2, π/2].
Subject: Math
Topic: Inverse Trigonometric Functions
Q. What is sin⁻¹(1)?
A. π/2
Subject: Math
Topic: Matrices
Q. What is a square matrix?
A. A matrix having same number of rows and columns.
Subject: Math
Topic: Matrices
Q. What is the order of a matrix with 3 rows and 2 columns?
A. 3 × 2
Subject: Math
Topic: Matrices
Q. What is the identity matrix?
A. A square matrix with 1s on the main diagonal and 0s elsewhere.
Subject: Math
Topic: Determinants
Q. What is the determinant of an identity matrix?
A. 1
Subject: Math
Topic: Determinants
Q. If two rows of a determinant are equal, what is its value?
A. 0
Subject: Math
Topic: Continuity and Differentiability
Q. What is continuity of a function at a point?
A. If LHL = RHL = value of function at that point.
Subject: Math
Topic: Continuity and Differentiability
Q. Derivative of x² is?
A. 2x
Subject: Math
Topic: Continuity and Differentiability
Q. What is dy/dx of sin x?
A. cos x
Subject: Math
Topic: Applications of Derivatives
Q. What does dy/dx represent geometrically?
A. Slope of the tangent to the curve.
Subject: Math
Topic: Applications of Derivatives
Q. At what point is a function increasing?
A. Where dy/dx > 0
Subject: Math
Topic: Integrals
Q. What is ∫x dx?
A. x²/2 + C
Subject: Math
Topic: Integrals
Q. What is ∫cos x dx?
A. sin x + C
Subject: Math
Topic: Applications of Integrals
Q. What does definite integral represent geometrically?
A. Area under the curve.
Subject: Math
Topic: Differential Equations
Q. What is the order of a differential equation?
A. Highest order of derivative present.
Subject: Math
Topic: Vector Algebra
Q. What is a unit vector?
A. A vector having magnitude 1.
Subject: Math
Topic: Vector Algebra
Q. What is the dot product of two perpendicular vectors?
A. 0
Subject: Math
Topic: Three Dimensional Geometry
Q. What is the distance formula in 3D?
A. √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]
Subject: Math
Topic: Probability
Q. What is classical probability?
A. Favourable outcomes / Total outcomes.
Subject: Maths
Topic: Matrices
Q. If A is a square matrix, write the condition for A to be invertible.
A. Matrix A is invertible if det(A) ≠ 0.
Subject: Maths
Topic: Determinants
Q. Evaluate det | 1 2 ; 3 4 |.
A. $$|A| = (1×4) − (2×3) = −2$$
Subject: Maths
Topic: Determinants
Q. Find the area of triangle with vertices (1,2), (3,4), (5,6).
A. Area = 0, since points are collinear.
Subject: Maths
Topic: Continuity and Differentiability
Q. Find the derivative of f(x) = x³.
A. $$f'(x) = 3x^2$$
Subject: Maths
Topic: Continuity and Differentiability
Q. Check continuity of f(x)=|x| at x=0.
A. Left limit = Right limit = f(0), so function is continuous at x=0.
Subject: Maths
Topic: Applications of Derivatives
Q. Find the slope of tangent to y = x² at x = 1.
A. $$\frac{dy}{dx} = 2x ⇒ slope = 2$$
Subject: Maths
Topic: Integrals
Q. Evaluate ∫ x² dx.
A. $$\int x^2 dx = \frac{x^3}{3} + C$$
Subject: Maths
Topic: Integrals
Q. Evaluate ∫ sin x dx.
A. $$\int \sin x dx = −\cos x + C$$
Subject: Maths
Topic: Applications of Integrals
Q. Write the formula for area under curve y = f(x).
A. $$Area = \int_a^b f(x) dx$$
Subject: Maths
Topic: Differential Equations
Q. What is the order of differential equation (d²y/dx²)+dy/dx+y=0?
A. Order is 2.
Subject: Maths
Topic: Vector Algebra
Q. Find the magnitude of vector 3i + 4j.
A. $$|\vec{a}| = \sqrt{3^2 + 4^2} = 5$$
Subject: Maths
Topic: Vector Algebra
Q. Define dot product of two vectors.
A. $$\vec{a}·\vec{b} = |a||b|\cos\theta$$
Subject: Maths
Topic: Three Dimensional Geometry
Q. Find distance between points (1,2,3) and (4,5,6).
A. $$\sqrt{(3)^2+(3)^2+(3)^2}=3\sqrt{3}$$
Subject: Maths
Topic: Linear Programming
Q. What is feasible region?
A. The common region satisfying all constraints.
Subject: Maths
Topic: Probability
Q. Find P(E) if probability of an event is 0.25.
A. P(E) = 0.25
Subject: Maths
Topic: Continuity and Differentiability
Q. d/dx (sin x) kya hota hai?
A. cos x
Subject: Maths
Topic: Integrals
Q. ∫ x dx ka result kya hota hai?
A. x²/2 + C