1.

If \( y = e^{{2}\log_e t} \) and \( x = \log_3(e^{t^2}) \), then \( \frac{dy}{dx} \) is equal to:

• \( \frac{1}{4t\sqrt{t}} \)
• \({2t^2} \)
• \( \frac{\log_e 3}{4t\sqrt{t}} \)
• \( \frac{2t^2}{e^{\frac{1}{2}\log_e t}} \)

2.

Which option figure will complete the pattern in the given figure?

3.

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:

• 500 m
• 200 m
• 100 m
• 120 m

4.

The cost of a machinery is ₹8,00,000. Its scrap value will be one-tenth of its original cost in 15 years. Using the linear method of depreciation, the book value of the machine at the end of the 10th year will be:

• ₹4,80,000
• ₹3,20,000
• ₹3,68,000
• ₹4,32,000

5.

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:

• \( \begin{bmatrix} 1 & 10 \\ -1 & 0 \end{bmatrix} \)
• \( \begin{bmatrix} 15 & -11 \\ -2 & 4 \end{bmatrix} \)
• \( \begin{bmatrix} 3 & 49 \\ -2 & -20 \end{bmatrix} \)
• \( \begin{bmatrix} 1 & 9 \\ -2 & -20 \end{bmatrix} \)

6.

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:

• (A), (B), and (D) only
• (A) and (D) only
• (C) and (D) only
• (B), (C), and (D) only