\[\text{Ramesh plans to save some amount required after }10\text{ years for higher studies of his son.}\]\[\text{He expects the cost of these studies to be Rs. }1,00,000.\]\[\text{How much should be saved at the beginning of each year to accumulate this amount at the end of }10\text{ years,}\]\[\text{if the interest rate is }12\%\text{ compounded annually?}\]\[\text{(Given }(1.12)^{11}=3.477\text{)}\]
\[\text{1. Rs. }4029\]
\[\text{2. Rs. }5702\]
\[\text{3. Rs. }5091\]
\[\text{4. Rs. }5901\]

\[\text{If }xy+\frac{x^2}{y}=x^3y+y,\text{ then }\frac{dy}{dx}\text{ is equal to}\]

\[\text{1. }\frac{y(3x^2y^2+2x+y^2)}{x^2y-x^2y^3+x^2-y^2}\]

\[\text{2. }\frac{y(3x^2y^2-2x-y^2)}{xy^2-x^3y^2-x^2-y^2}\]

\[\text{3. }\frac{y(3x^2y^2-2x+y^2)}{x^2y-x^2y^3+x^2+y^2}\]

\[\text{4. }\frac{y(3y^2x^2-y^2+2x)}{x^2y^3-x^2y-x-y^2}\]

\[ \text{Assume } P, Q, R \text{ and } W \text{ are matrices of order } 3 \times 3, a \times 4, b \times c \text{ and } d \times a \text{ respectively} \]\[ \text{If } PQ + WR \text{ is well defined, find the value of } ab + cd \]

\[ \text{1. } 18 \]
\[ \text{2. } 28 \]
\[ \text{3. } 21 \]
\[ \text{4. } 13 \]

\[ \text{Two pipes A and B can fill a tank in 5 hours and 6 hours respectively} \]\[ \text{Pipe C can empty the tank in 12 hours} \]\[ \text{If all three pipes are opened together, find the time taken to fill the tank} \]
\[ \text{1. } 2\frac{3}{4} \text{ hours} \]
\[ \text{2. } 3 \text{ hours} \]
\[ \text{3. } 2 \text{ hours} \]
\[ \text{4. } 3\frac{9}{17} \text{ hours} \]

\[ \text{If the corner points of the bounded feasible region of an LPP are } (0,2), (3,0), (6,0), (6,8) \text{ and } (0,5) \]\[ \text{then the minimum value of the objective function } F = 4x + 6y \text{ occurs at} \]
\[ \text{1. } (0,2) \text{ only} \]
\[ \text{2. } (3,0) \text{ only} \]
\[ \text{3. the midpoint of the line segment joining } (0,2) \text{ and } (3,0) \]
\[ \text{4. every point on the line segment joining } (0,2) \text{ and } (3,0) \]

\[ \text{If } A = \begin{bmatrix} a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c \end{bmatrix} \text{ and } abc = 12, b = 4a \text{, find the value of } |A(\text{adj}A)| \]
\[ \text{1. } 28^3 \]
\[ \text{2. } 12^3 \]
\[ \text{3. } 28^2 \]
\[ \text{4. } 48^2 \]

\[ \text{If } A = \begin{bmatrix} 2 & -2 & 1 \\ 0 & 4 & 2 \end{bmatrix} \text{ and } B = \begin{bmatrix} 1 & -2 & 7 \\ 2 & 0 & 6 \end{bmatrix} \]
\[ \text{are two matrices such that } 3A - 2B + 4C = O \text{, then matrix } C \text{ is equal to:} \]
\[ \text{1. } \begin{bmatrix} 1 & -10 & 11/2 \\ -1 & -3 & 6 \end{bmatrix} \]
\[ \text{2. } \begin{bmatrix} -1 & 1/2 & 11/4 \\ 1 & -3 & 3/2 \end{bmatrix} \]
\[ \text{3. } \begin{bmatrix} -1 & 2 & 3/2 \\ 1 & 3 & 1/2 \end{bmatrix} \]
\[ \text{4. } \begin{bmatrix} -10 & 11/2 & 1 \\ -3 & 6 & -1 \end{bmatrix} \]

Increase in the number of patients in the hospitals due to heat stroke is:

1. Secular trend
2. Irregular variation
3. Seasonal variation
4. Cyclic variation

\[ \text{A random variable } X \text{ denotes the number of sixes obtained in three throws of a die} \]\[ \text{Find the mean of the distribution} \]
\[ \text{1. } \frac{1}{3} \]
\[ \text{2. } \frac{1}{2} \]
\[ \text{3. } \frac{1}{8} \]
\[ \text{4. } \frac{2}{3} \]

\[ A = \begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix} \]
\[ A^{-1} = \begin{bmatrix} \frac{1}{2} & -4 & \frac{5}{2} \\ -\frac{1}{2} & 3 & -\frac{3}{2} \\ \frac{1}{2} & y & \frac{1}{2} \end{bmatrix} \]
\[ \text{Find the value of } 8x + 5y \]
\[ \text{1. } 0 \]
\[ \text{2. } 1 \]
\[ \text{3. } 2 \]
\[ \text{4. } 3 \]

\[ \text{A fair coin is tossed 100 times} \]
\[ \text{Find the probability of getting head an odd number of times} \]

\[ \text{Options:} \]
\[ \text{1. } \frac{1}{2} \]
\[ \text{2. } \frac{1}{8} \]
\[ \text{3. } \frac{3}{8} \]
\[ \text{4. } \frac{80}{100} \]

\[ \text{A man takes a personal loan of Rs. } 3,00,000 \text{ at } 6\% \text{ per annum} \]
\[ \text{compounded monthly to be repaid by equal monthly installments in } 3 \text{ years} \]
\[ \text{Find the EMI using flat rate method} \]

\[ \text{Options:} \]
\[ \text{1. Rs. } 9833.33 \]
\[ \text{2. Rs. } 11,333.3 \]
\[ \text{3. Rs. } 17,333.3 \]
\[ \text{4. Rs. } 12,833.3 \]

\[ \text{Let } A \text{ be a non-singular matrix of order } n \times n \]
\[ \text{Then } |\text{adj}(3A)| \text{ is equal to:} \]

\[ \text{Options:} \]
\[ \text{1. } 3|A|^{n-1} \]
\[ \text{2. } 3^{n(n-1)}|A|^{n-1} \]
\[ \text{3. } 3^{n}|A|^{n-1} \]
\[ \text{4. } 3^{n}|A|^{n} \]

\[ \text{In a survey of a sample of } 300 \text{ individuals, } 180 \text{ gave response `Yes', } \]
\[ 100 \text{ gave response `No' and } 20 \text{ gave `No response'} \]
\[ \text{Find the point estimate of proportion in the population who responded `Yes'} \]

\[ \text{Options:} \]
\[ \text{1. } 0.5 \]
\[ \text{2. } 0.2 \]
\[ \text{3. } 0.6 \]
\[ \text{4. } 0.4 \]

\[ \text{A piece of machinery is bought for Rs. } 50,000 \]
\[ \text{In the first year, it depreciates by } 15\% \]
\[ \text{In each subsequent year, the depreciation rate increases by } 5\% \]
\[ \text{Find the value of the machinery after } 3 \text{ years} \]

\[ \text{Options:} \]
\[ \text{1. Rs. } 32,700 \]
\[ \text{2. Rs. } 24,000 \]
\[ \text{3. Rs. } 25,500 \]
\[ \text{4. Rs. } 42,000 \]

\[ \text{Consider } f(x) = \sin(3x) + 4, \; \forall x \in \mathbb{R} \]

\[ \text{(A) Maximum value of } f(x) \text{ is } 5 \]
\[ \text{(B) Minimum value of } f(x) \text{ is } 3 \]
\[ \text{(C) Maximum value of } f(x) \text{ is attained at } x = \frac{\pi}{3} \]
\[ \text{(D) Minimum value of } f(x) \text{ is attained at } x = 0 \]

\[ \text{Choose the correct answer from the options given below:} \]

\[ \text{1. (A), (B) and (C) only} \]
\[ \text{2. (A), (B) and (D) only} \]
\[ \text{3. (C) and (D) only} \]
\[ \text{4. (B) and (D) only} \]