Applied-Mathematics PYQ — Page 10

A company has issued a bond having a face value of Rs. 10,000 paying annual dividends at 8.5%. The bond will be redeemed at par at the end of 10 years, then the purchase price of this bond if the investor wishes a yield rate of 8% is : [Given $(1.08)^{-10} = 0.46319349$]

A carpenter earns a profit of ₹ 50 and ₹ 80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as : | Required | Chair | Table | Available quantity | |----------|-------|-------|--------------------| | Wood | 3 | 5 | 150 | | Labour | 1 | 2 | 56 | The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively :

A car costing ₹ 8,00,000 has scrap value of ₹ 3,00,000. If the book value of car at the end of fourth year is ₹ 6,00,000, then the useful life of the car is :

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is:

A boat takes 6 hr 25 minutes to row upstream a certain distance with a speed which is 14.4 times that of the river current. The time taken by the boat to row down the same distance with same speed is:

A, B and C entered in a partnership business. They invested their capitals in the ratio of $\frac{4}{3} : \frac{5}{2} : \frac{6}{5}$. After 5 months, B invested 40% more than what he had invested earlier. If the total profit at the end of one year was Rs 50,550, then how much profit did A earn?

Which of the following is a statistic ?

Which of the following is a correct set of constraint for a LPP ?

The variance of the number of heads in two tosses of a coin is :

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$ The value of k is

The second order derivative of which of the following functions is $5^x$ ?

The probability distribution of a discrete random variable X is given by : | X | 30 | 10 | -10 | |---|---|---|---| | P(X) | 1/5 | 3/10 | 1/2 | then E(X) is equals to

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are

The least positive integer X satisfying $28 \equiv x (\mod 6)$ is :

the least non-negative remainder when $3^{17}$ is divided by 7 is :

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :

The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant is :

Solution for the inequality $|3x - 7| \leq 2$ is :

$\int \frac{dx}{x^{n+1} - x}\,dx$