ENG 202 CBT PRACTICE

1. If every minor of order ‘r’ of a matrix is zero then ρ (A) =?

2. Which of the following correctly defines ordinary differential equations?

3. Which one of the following is not a criterion for linearity of an ordinary differential equation?

4.

5. In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.

6. Which of the following is not an example of linear differential equation?

7. Elliptic equations have no characteristic curves.

8. The inverse of a symmetric matrix (if it exists) is?

9. Rank of the following matrix is A =

10. Find ∂z∂x where z=ax²+2by²+2bxy.

11. Which of the following statements is true?

12. Copy - The p^th derivative of a q^th degree monic polynomial, where p, q are positive integers and 2p⁴ + 3pq^3⁄₂ = 3q^3⁄₂ + 2qp³ is given by?

13. The first and second derivatives of a quadratic Polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) – f(0) Is given by?

14. Which of the following is the condition for a second order partial differential equation to be hyperbolic?

15. Find the rank of the matrix

16. The condition that a second order partial differential equation should satisfy to be parabolic is b²-ac=0.

17. Which of the following is a type of Iterative method of solving non-linear equations?

18. What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)² + 1 = 0?

19. Singular solution of a differential equation is one that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.

20. The condition which a second order partial differential equation must satisfy to be elliptical is
b²-ac=0.

21. What is the order of the partial differential equation,

22. A partial differential equation is one in which a dependent variable (say ‘y’) depends on one or more independent variables (say ’x’, ’t’ etc.)

23. The following moves are performed on g(x).
(i) Pick (x₀, y₀) on g(x) and travel toward the left/right to reach the y = x line. Now travel above/below to reach g(x). Call this point on g(x) as (x₁, y₁)
(ii) Let the new position of (x₀, y₀)be (x₀, y₁)
This is performed for all points on g(x) and a new function is got. Again these steps may be repeated on new function and another function is obtained. It is observed that, of all the functions got, at a certain point (i.e. after finite number of moves) the n^th derivatives of the intermediate function are constant, and the curve passes through the origin. Then which of the following functions could be g(x)

24. What is the degree of the differential equation, 4x³-6x² y³+2y=0?

25.

26. The first, second and third derivatives of a cubic polynomial f(x) at x = 1, are 1³, 2³ and 3³respectively. Then the value of f(0) + f(1) – 2f(-1) is?

27. The p^th derivative of a q^th degree monic polynomial, where p, q are positive integers and 2p⁴ + 3pq^3⁄₂ = 3q^3⁄₂ + 2qp³ is given by?

28. Copy - Which of the following correctly defines ordinary differential equations?

29. Find

30. The solution of the general form of second order non-linear partial differential equation is obtained by Monge’s method.

31. Copy -

32. What is the order of the differential equation, y”+y’-x3y=sinx?

33.

34.

35. Find ∂z/∂x where z=sinx² x cosy²