1. The relation R = {(a, b) : a - b is even} on Z is:

2. A function f: A → B is said to be onto if:

3. The function f(x) = x² is:

4. If f: A → B and g: B → C, then (g∘f)(x) equals:

5. Domain of the function f(x) = √(x-2):

6. Number of relations on a set with 3 elements is:

7. A function is one-one if:

8. If A has m elements and B has n elements, number of functions from A to B is:

9. Identity function f: R → R is defined as:

10. The inverse of f(x) = 2x + 3 is:

11. If a relation is symmetric and transitive, it may not be:

12. A relation on A = {1, 2, 3} given by R = {(1,1), (2,2), (3,3)} is:

13. Range of the constant function f(x) = 7 is:

14. Which of the following is not a function?

15. The number of one-one functions from set A with 3 elements to set B with 5 elements is:

1. The principal value branch of sin⁻¹x is:

2. The domain of cos⁻¹x is:

3. Value of tan⁻¹(1) is:

4. sin⁻¹(sin(π/3)) =

5. The value of cos⁻¹(−1/2) is:

6. tan⁻¹(−√3) equals:

7. sin⁻¹(−1/2) =

8. cos⁻¹(cos(5π/6)) =

9. Domain of tan⁻¹x is:

10. If sin⁻¹x + cos⁻¹x = α, then α equals:

11. The range of tan⁻¹x is:

12. sin⁻¹(1) + cos⁻¹(0) =

13. The function y = sin⁻¹x is:

14. sin⁻¹(sin(5π/6)) =

15. cos⁻¹(−1) =

1. A matrix which has only one row is called:

2. The order of a matrix having 3 rows and 2 columns is:

3. The matrix A = [0] is called:

4. If A is a square matrix, then |A| is called:

5. A matrix A is symmetric if:

6. If A is a 2×2 matrix, then A + Aᵀ is:

7. The product of a matrix of order m×n with another of order n×p is of order:

8. If A = I (identity matrix), then A⁻¹ =

9. (Aᵀ)ᵀ =

10. Matrix multiplication is:

11. The inverse of a matrix exists only if:

12. The identity matrix of order 2 is:

13. If A is a 2×2 matrix and k is a scalar, then (kA)ᵀ =

14. The matrix A = [[0, −1], [1, 0]] is:

15. The transpose of a symmetric matrix is:

1. The determinant of a 2×2 matrix [[a, b], [c, d]] is:

2. If any two rows (or columns) of a determinant are identical, then the determinant is:

3. The value of determinant |1 0 0; 0 1 0; 0 0 1| is:

4. Determinant is defined only for:

5. If determinant |A| = 0, then A is:

6. The value of |2 3; 4 6| is:

7. If A is a matrix and k is a scalar, then |kA| =

8. Interchanging two rows of a determinant:

9. The value of determinant |a b; 0 d| is:

10. Which property is used in Laplace expansion?

11. If A is a 3×3 matrix and |A| ≠ 0, then A⁻¹ exists and is given by:

12. Which of the following is true for |AB|?

13. The adjoint of a matrix is the:

14. If |A| = 5, then |A⁻¹| =

15. Value of determinant |3 2; 1 4| is:

1. A function f(x) is continuous at x = a if:

2. The function f(x) = |x| is:

3. If f(x) = x², then f'(x) is:

4. The derivative of sin(x) is:

5. A function can be continuous but not:

6. If a function is differentiable at a point, then it is:

7. The derivative of tan(x) is:

8. The function f(x) = x³ is:

9. The function f(x) = |x| is not differentiable at:

10. Chain rule is used for:

11. The derivative of log(x) is:

12. Which of the following is NOT differentiable everywhere?

13. If f(x) = eˣ, then f'(x) =

14. Differentiability implies:

15. Derivative of a constant is:

1. The derivative of a function gives:

2. If f'(x) > 0 for all x in (a, b), then f(x) is:

3. A function has a local maximum where:

4. The minimum value of a function occurs at:

5. The point where the derivative is zero is called:

6. A function f(x) is concave upward if:

7. The second derivative test helps in identifying:

8. The slope of the tangent to the curve y = x² at x = 2 is:

9. For the function y = x³, the point of inflection is:

10. The maximum or minimum value of a function in a given interval is called:

11. The rate of change of displacement with respect to time is:

12. If a function changes concavity, the point is called:

13. To find maxima/minima, we usually:

14. If f'(x) changes sign around x = a, then:

15. Derivative of x³ is:

1. The integral of a function is also called its:

2. ∫x dx = ?

3. The symbol ∫ represents:

4. ∫e^x dx = ?

5. ∫1/x dx = ?

6. The process of finding an integral is called:

7. What is ∫cos x dx?

8. Which of the following is the integral of sin x?

9. The definite integral from a to b gives:

10. ∫0^π sin x dx = ?

11. Integration by parts is used when:

12. What is ∫sec²x dx?

13. If F'(x) = f(x), then F(x) is:

14. ∫tan x dx = ?

15. The constant of integration is written as:

1. The area bounded by a curve y = f(x), the x-axis and vertical lines x = a and x = b is given by:

2. The area enclosed between two curves y = f(x) and y = g(x) from x = a to x = b is:

3. Area under a curve can be negative if:

4. If the curve lies entirely above x-axis from a to b, then area =

5. Area between curves y = sin x and y = cos x from x = 0 to x = π/2 is:

6. Area enclosed between y = x and y = x² from x = 0 to x = 1 is:

7. The graphical method to visualize area under curves is:

8. The integral ∫0 to 2 (4 − x²) dx gives the area of:

9. If ∫a to b f(x) dx = A and ∫a to b g(x) dx = B, then area between f(x) and g(x) is:

10. The definite integral gives:

11. If curve lies below x-axis, then ∫a to b f(x) dx is:

12. Which integral calculates the area between x = 0 and x = 1 for f(x) = x²?

13. The area enclosed between curves y² = x and x = y is calculated by integrating:

14. If the area under y = x from 0 to 2 is calculated, it equals:

15. Which technique is essential to calculate area between curves?

1. A differential equation is an equation involving:

2. The order of a differential equation is the order of:

3. The degree of a differential equation is defined only when:

4. The solution of dy/dx = 3x² is:

5. dy/dx = ky represents which kind of growth?

6. The general solution of a differential equation contains:

7. The process of finding the differential equation from a given solution is called:

8. The method of separation of variables can be applied when:

9. Which of the following is a linear differential equation?

10. What is the order of d²y/dx² + 3 dy/dx + y = 0?

11. The degree of (d²y/dx²)³ + dy/dx = 0 is:

12. A solution without arbitrary constants is called:

13. dy/dx = (x + y) can be solved using:

14. A differential equation which cannot be expressed as polynomial in derivative is:

15. The equation dy/dx = y/t is separable in:

1. A vector quantity has:

2. The magnitude of vector **a = 3i + 4j** is:

3. Two vectors are equal if they have:

4. The unit vector in the direction of **a = 6i - 8j** is:

5. The dot product of **a = i + j** and **b = i - j** is:

6. If two vectors are perpendicular, their dot product is:

7. The angle between two perpendicular vectors is:

8. If |a| = 2 and |b| = 3 and angle between them is 60°, then **a · b** is:

9. Cross product of two vectors is:

10. The vector product of two parallel vectors is:

11. Which is true for i × j?

12. The angle between vector and itself is:

13. The projection of vector a on b is given by:

14. The cross product of i and i is:

15. The value of (a × b) · c is called:

1. Direction cosines of a line are:

2. The sum of the squares of direction cosines is:

3. Direction ratios of a vector are:

4. The angle between two lines with direction cosines (l₁, m₁, n₁) and (l₂, m₂, n₂) is given by:

5. A line passing through (x₁, y₁, z₁) and having direction ratios a, b, c is represented as:

6. The line x = 1 + 2t, y = 3 − t, z = 4t passes through:

7. The equation of x-axis in vector form is:

8. The angle between two lines is 90° when their dot product is:

9. Two lines are parallel if their direction ratios are:

10. Distance between two skew lines is calculated using:

11. The shortest distance between two parallel lines is:

12. A plane can be represented as:

13. A plane perpendicular to z-axis has equation:

14. A line lies in a plane if:

15. The equation of a plane containing point A(x₁, y₁, z₁) and perpendicular to vector n⃗ = ai + bj + ck is:

1. Linear programming is used to:

2. The function to be maximized or minimized in an LPP is called:

3. The inequalities in an LPP are called:

4. The solution set of constraints is known as:

5. The feasible region of a linear programming problem is always:

6. The optimal value of the objective function occurs at:

7. Which method is used for solving LPP graphically?

8. If feasible region is unbounded, then:

9. LPP is applicable when:

10. In graphical method of LPP, maximum number of decision variables allowed is:

11. A solution that satisfies all constraints is called:

12. What is not a possible outcome of a linear programming problem?

13. If all constraints are satisfied but not the objective function, then solution is:

14. LPP problems are used in:

15. Which of the following is not a constraint?

1. If A and B are two independent events, then P(A ∩ B) =

2. The probability of an event lies between:

3. If P(A) = 0.3, P(B) = 0.4 and A, B are mutually exclusive, then P(A ∪ B) =

4. If A and B are independent, then A^c and B are:

5. Bayes’ Theorem is used for:

6. P(A ∪ B) =

7. Events which cannot occur together are called:

8. If A and B are independent, then P(A|B) =

9. If two events are mutually exclusive, then P(A ∩ B) =

10. The total probability of sample space is:

11. Conditional probability is written as:

12. If A and B are independent, then P(A ∩ B^c) =

13. What is the probability of a sure event?

14. A fair die is rolled. What is the probability of getting a number less than 5?

15. The complement of an event A is: