In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:

A furniture trader deals in tables and chairs. He has Rs. 75,000 to invest and a space to store at most 60 items. A table costs him Rs. 1,500 and a chair costs him Rs. 1,000. The trader earns a profit of Rs. 400 and Rs. 250 on a table and chair, respectively. Assuming that he can sell all the items that he can buy, which of the following is/are true for the above problem:

(A) Let the trader buy \( x \) tables and \( y \) chairs. Let \( Z \) denote the total profit. Thus, the mathematical formulation of the given problem is:

\[ Z = 400x + 250y, \]

subject to constraints:

\[ x + y \leq 60, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]

(B) The corner points of the feasible region are (0, 0), (50, 0), (30, 30), and (0, 60).

(C) Maximum profit is Rs. 19,500 when trader purchases 60 chairs only.

(D) Maximum profit is Rs. 20,000 when trader purchases 50 tables only.

Choose the correct answer from the options given below:

For predicting the straight-line trend in the sales of washing machines (in thousands) on the basis of 8 consecutive years' data, the company calculates 4-year moving averages. If the sales of washing machines for respective years are \( a, b, c, d, e, f, g, \) and \( h \), then which of the following averages will be computed?
(A) \( \frac{a + b + c + d}{4} \)  
(B) \( \frac{a + c + d + e}{4} \)  
(C) \( \frac{c + d + f + h}{4} \)  
(D) \( \frac{b + c + d + e}{4} \)  
Choose the correct answer from the options given below:

The correct solution of \(-22 < 8x - 6 \leq 26\) is the interval:

Match List-I with List-II.

Choose the correct answer from the options given below:

If \( A = \begin{bmatrix} 5 & 1 \\ -2 & 0 \end{bmatrix} \) and \( B^T = \begin{bmatrix} 1 & 10 \\ -2 & -1 \end{bmatrix} \), then the matrix \( AB \) is: