List of top Applied Mathematics Questions on Vectors

Amrita buys a car for which she makes a down payment of ₹ 2,50,000 and the balance is to be paid in 2 years by monthly installments of ₹ 25,448 each. If the financer charges interest at the rate of 20\% p.a., find the actual price of the car.
[Given \( \left(\frac{61}{60}\right)^{-24} = 0.67253 \)]
Determine the probability that the student studied for at most 2 hours.
Quarterly.
A container has 50 litres of juice in it. 5 litres of juice is taken out and is replaced by 5 litres of water. This process is repeated 4 more times. Determine the quantity of juice in the container after final replacement.
[Use \( (0.9)^5 = 0.59049 \)]
Assume an investment’s starting value is ₹ 20,000 and it grows to ₹ 50,000 in 3 years. Calculate CAGR (Compounded Annual Growth Rate).
[Use: \( (2.5)^{1/3} = 1.355 \)]

Find the solution to the following linear programming problem (if it exists) graphically: 

Maximize \( Z = x + y \) 
Subject to the constraints \[ x - y \leq -1, \quad -x + y \leq 0, \quad x, y \geq 0. \]

If \[ A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix} \] find the value of \( k \) such that \[ A^2 - 8A + kI = 0. \]
What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]
If for a Poisson variate \( X \), \( P(X = k) = P(X = k + 1) \), then the variance of \( X \) is: