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Yes. It is designed for EAMCET Engineering aspirants for chapter-wise revision, speed practice and AI-generated mock papers from previous-year style questions.

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EAMCET Engineering Maths Practice Test Online

Half of your EAMCET engineering score comes down to this one section — get comfortable with speed, and Maths becomes your biggest scoring opportunity, not your biggest time sink.

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About this EAMCET Engineering Math practice test

Maths alone is worth 80 of the 160 marks in AP and Telangana's engineering entrance, which means how you handle this section decides your rank more than any other. The real challenge isn't difficulty — it's the clock: roughly a minute per question, drawn straight from the Intermediate 1A/1B syllabus across Calculus, Algebra, Trigonometry, Vectors and Coordinate Geometry. This set is built the way the real paper is: one clean concept per question, solvable fast once the pattern clicks. Work through it, then swap in your own previous-year questions to keep the difficulty honest and the pace realistic before exam day.

EAMCET Engineering Maths Practice Test sample questions

These starter questions help you launch a math mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

1. Find the domain of the real function f(x) = √(x² - 5x + 6).
2. Evaluate: lim(x→0) [sin 5x / tan 3x].
3. If y = x³ ln x, find dy/dx.
4. Find the equation of the tangent to the curve y = x² - 3x + 2 at the point where x = 2.
5. If y = e^(2x) sin 3x, find the value of dy/dx at x = 0.
6. Evaluate: ∫ x e^(x²) dx.
7. Evaluate: ∫₀^(π/2) sin²x dx.
8. Evaluate: ∫₁² (3x² - 4x + 1) dx.
9. Find the order and degree of the differential equation (d²y/dx²)³ + (dy/dx)² + y = 0.
10. Solve the differential equation dy/dx = y/x.
11. If A = [[1, 2], [3, 4]], find |A| and state whether A is invertible.
12. Evaluate the determinant |2 0 1; 3 1 0; 1 -1 2| and state whether the matrix is singular.
13. In how many ways can 5 different books be arranged on a shelf so that 2 particular books are always together?
14. Find the middle term in the expansion of (x + 1/x)^6.
15. Given that the sum of the first n odd natural numbers 1 + 3 + 5 + ... + (2n - 1) equals n², find the sum of the first 12 odd natural numbers.
16. Solve for x in [0, 2π): 2 sin²x - 1 = 0.
17. If sin θ = 3/5 and θ is acute, find the value of cos 2θ.
18. Find the value of tan⁻¹(1/2) + tan⁻¹(1/3).
19. Find the value of sin⁻¹(sin(3π/4)).
20. In triangle ABC, a = 7, b = 8, c = 9. Find cos A.
21. In a triangle, a = 5, b = 6 and C = 60°. Find the length of side c.
22. Find the magnitude of the vector a = 3i - 4j + 12k.
23. Find the angle between the vectors a = i + j and b = i - j.
24. Find the distance between the points A(1, 2, 3) and B(4, 6, 3).
25. Find the equation of the line joining the points (2, 3) and (5, 11).
26. Find the center and radius of the circle x² + y² - 6x + 4y - 12 = 0.
27. Find the eccentricity of the ellipse x²/25 + y²/16 = 1.
28. A fair die is rolled once. Find the probability of getting a number greater than 4.
29. Two dice are rolled together. Find the probability that the sum of the numbers obtained is 8.
30. Find the variance of the data set 2, 4, 6, 8, 10.

Syllabus & Core Topics

calculusvectorscoordinate geometrytrigonometrymatrices

EAMCET Maths rewards speed over depth, so time yourself strictly on Intermediate 1A/1B exercises — calculus alone accounts for a large share of the paper. Keep a formula sheet for triangle properties, vector identities and conic standard equations handy, since the exam mostly checks fast recall rather than derivation.

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Why this practice page is useful

EAMCET Maths carries 80 of 160 marks for engineering aspirants — this drill targets that scoring section.
Speed-focused: EAMCET allows ~1 minute per question, so practice with mixed types builds pace.
Replace the starter with previous-year EAMCET questions to generate a fresh chapter-specific mock.

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

1. Find the domain of the real function f(x) = √(x² - 5x + 6).
(-∞, 2] ∪ [3, ∞)
Factorize the expression under the root: x² - 5x + 6 = (x-2)(x-3), which must be ≥ 0 for the square root to be real. This holds when x ≤ 2 or x ≥ 3.
2. Evaluate: lim(x→0) [sin 5x / tan 3x].
5/3
Divide numerator and denominator by x: sin5x/tan3x = (sin5x/x)/(tan3x/x). As x→0, sin5x/x→5 and tan3x/x→3, giving the limit 5/3.
3. If y = x³ ln x, find dy/dx.
x²(3 ln x + 1)
Apply the product rule to x³ and ln x: d/dx(x³)·ln x + x³·d/dx(ln x) = 3x² ln x + x². Factor out x² to simplify.
4. Find the equation of the tangent to the curve y = x² - 3x + 2 at the point where x = 2.
x - y - 2 = 0
At x=2, y = 4-6+2 = 0, so the point of tangency is (2,0). The derivative y' = 2x-3 gives slope 1 at x=2, so the tangent is y = x - 2.
5. If y = e^(2x) sin 3x, find the value of dy/dx at x = 0.
3
Differentiate using the product rule: dy/dx = 2e^(2x) sin3x + 3e^(2x) cos3x. Substituting x=0 gives e^0(0+3) = 3.
6. Evaluate: ∫ x e^(x²) dx.
(1/2)e^(x²) + C
Substitute u = x², so du = 2x dx. The integral becomes (1/2)∫e^u du = (1/2)e^u, giving the result in terms of x.
7. Evaluate: ∫₀^(π/2) sin²x dx.
π/4
Use the identity sin²x = (1-cos2x)/2 to rewrite the integrand. Integrating from 0 to π/2 gives [x/2 - sin2x/4], which evaluates to π/4.
8. Evaluate: ∫₁² (3x² - 4x + 1) dx.
2
The antiderivative of 3x²-4x+1 is x³-2x²+x. Evaluating at x=2 gives 2, and at x=1 gives 0, so the definite integral is 2.
9. Find the order and degree of the differential equation (d²y/dx²)³ + (dy/dx)² + y = 0.
Order 2, Degree 3
The highest derivative present is d²y/dx², so the order is 2. Since this term is raised to the power 3, the degree of the equation is 3.
10. Solve the differential equation dy/dx = y/x.
y = kx
Separate the variables: dy/y = dx/x. Integrating both sides gives ln|y| = ln|x| + C, which simplifies to y = kx for an arbitrary constant k.
11. If A = [[1, 2], [3, 4]], find |A| and state whether A is invertible.
|A| = -2, A is invertible
The determinant of a 2×2 matrix [[a,b],[c,d]] is ad-bc, so |A| = (1)(4)-(2)(3) = -2. Since this is nonzero, A is invertible.
12. Evaluate the determinant |2 0 1; 3 1 0; 1 -1 2| and state whether the matrix is singular.
0, matrix is singular
Expanding along the first row: 2(1·2-0·(-1)) - 0(3·2-0·1) + 1(3·(-1)-1·1) = 4 + 0 - 4 = 0. Since the determinant is zero, the matrix is singular.
13. In how many ways can 5 different books be arranged on a shelf so that 2 particular books are always together?
48
Treat the 2 particular books as a single unit, giving 4 units to arrange in 4! ways. Within that unit, the two books can be arranged in 2! ways, so the total is 4!×2! = 48.
14. Find the middle term in the expansion of (x + 1/x)^6.
20
For (x+1/x)^6, there are 7 terms and the middle one occurs at r=3. T4 = C(6,3) x^(6-3)(1/x)^3 = 20, since the x powers cancel out.
15. Given that the sum of the first n odd natural numbers 1 + 3 + 5 + ... + (2n - 1) equals n², find the sum of the first 12 odd natural numbers.
144
The sum of the first n odd numbers follows the pattern n², a result established by mathematical induction. For n=12, the sum is simply 12² = 144.
16. Solve for x in [0, 2π): 2 sin²x - 1 = 0.
π/4, 3π/4, 5π/4, 7π/4
Rearranging gives sin²x = 1/2, so sinx = ±1/√2. Within [0,2π), this occurs at x = π/4, 3π/4, 5π/4, 7π/4.
17. If sin θ = 3/5 and θ is acute, find the value of cos 2θ.
7/25
Since θ is acute, cosθ = 4/5 follows from sinθ=3/5. Using cos2θ = 1-2sin²θ = 1 - 2(9/25) = 7/25.
18. Find the value of tan⁻¹(1/2) + tan⁻¹(1/3).
π/4
Using the addition formula tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1-xy)] with x=1/2, y=1/3, since xy=1/6<1: (5/6)/(5/6) = 1, so the sum equals tan⁻¹(1).
19. Find the value of sin⁻¹(sin(3π/4)).
π/4
Since 3π/4 lies outside the principal range [-π/2, π/2] of sin⁻¹, use sin(3π/4) = sin(π/4). Hence sin⁻¹(sin(3π/4)) = π/4.
20. In triangle ABC, a = 7, b = 8, c = 9. Find cos A.
2/3
By the cosine rule, cosA = (b²+c²-a²)/(2bc) = (64+81-49)/144 = 96/144, which reduces to 2/3.
21. In a triangle, a = 5, b = 6 and C = 60°. Find the length of side c.
√31
By the cosine rule, c² = a²+b²-2ab cosC = 25+36-2(5)(6)(1/2) = 61-30 = 31. Taking the square root gives c = √31.
22. Find the magnitude of the vector a = 3i - 4j + 12k.
13
The magnitude of a vector (x,y,z) is √(x²+y²+z²). Here that's √(9+16+144) = √169 = 13.
23. Find the angle between the vectors a = i + j and b = i - j.
90°
The dot product a·b = (1)(1)+(1)(-1) = 0, which means the vectors are perpendicular. Hence the angle between them is 90°.
24. Find the distance between the points A(1, 2, 3) and B(4, 6, 3).
5 units
Apply the 3D distance formula: √[(4-1)²+(6-2)²+(3-3)²] = √(9+16+0) = √25 = 5.
25. Find the equation of the line joining the points (2, 3) and (5, 11).
8x - 3y - 7 = 0
The slope through (2,3) and (5,11) is (11-3)/(5-2) = 8/3. Using point-slope form and simplifying gives 8x - 3y - 7 = 0.
26. Find the center and radius of the circle x² + y² - 6x + 4y - 12 = 0.
Center (3, -2), radius 5
Completing the square: (x-3)² + (y+2)² = 9+4+12 = 25. This is a circle centered at (3,-2) with radius 5.
27. Find the eccentricity of the ellipse x²/25 + y²/16 = 1.
3/5
Since 25 > 16, the major axis lies along the x-axis with a²=25, b²=16. Eccentricity e = √(1-b²/a²) = √(9/25) = 3/5.
28. A fair die is rolled once. Find the probability of getting a number greater than 4.
1/3
Outcomes greater than 4 on a die are 5 and 6, giving 2 favorable outcomes out of 6 total. The probability simplifies to 1/3.
29. Two dice are rolled together. Find the probability that the sum of the numbers obtained is 8.
5/36
The pairs summing to 8 are (2,6),(3,5),(4,4),(5,3),(6,2), giving 5 favorable outcomes out of 36 total. The probability is 5/36.
30. Find the variance of the data set 2, 4, 6, 8, 10.
8
The mean of the data is 30/5 = 6. The squared deviations are 16,4,0,4,16, summing to 40, and dividing by 5 gives the variance.

Curriculum Mapping & Learning Guide

Use this breakdown to identify which skills each question tests and guide post-test review.

Calculus Foundations (Questions 1-10)

Tests domains and limits, differentiation rules including the product rule, tangent lines and exponential-trigonometric derivatives, basic substitution and definite integration, and classifying or solving simple differential equations.

Algebra, Counting and Trigonometry (Questions 11-20)

Covers matrices and determinants through invertibility and singularity checks, permutation arrangements and a binomial expansion term, an induction-based summation result, and trigonometric equations with inverse trigonometric simplifications.

Geometry and Applied Mathematics (Questions 21-30)

Applies the cosine rule in triangles, computes vector magnitude and angle between vectors, works with standard forms of lines, circles and ellipses in coordinate geometry, and closes with basic probability and variance calculations.

EAMCET Engineering Math units covered

Chapter 1: Functions, Limits and Continuity
Chapter 2: Differentiation and Applications of Derivatives
Chapter 3: Indefinite and Definite Integrals
Chapter 4: Differential Equations
Chapter 5: Matrices and Determinants
Chapter 6: Permutations, Combinations and Binomial Theorem
Chapter 7: Mathematical Induction
Chapter 8: Trigonometric Ratios and Equations
Chapter 9: Inverse Trigonometric Functions
Chapter 10: Properties of Triangles
Chapter 11: Vector Algebra and 3D Geometry
Chapter 12: Coordinate Geometry (Lines, Circles, Conics)
Chapter 13: Probability and Random Variables
Chapter 14: Statistics

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