Applied-Mathematics PYQ — Page 2

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?

A shopkeeper has 10 litres of pure honey. He sells honey at the cost price of Rs. 300 per litre. After mixing some quantity of water in pure honey he sells the syrup of pure honey and water at Rs. 250 per litre. The quantity of water mixed in pure honey is

If $f(x) = a \log x + \frac{b}{x} + x$ has its extreme values at $x = -1$ and $x = 3$, then $(a, b)$ is equal to:

Match List I with List II | LIST I | LIST II | |---|---| | A. A solution that does not satisfy all the constraints is called | I. Linear | | B. The objective function in an LPP is | II. Convex polygon | | C. Linear inequalities or equations on the variables of LPP are called | III. Infeasible solution | | D. The feasible region in an LPP, formed by the convex combinations of the corner points, is called | IV. Constraints | Choose the correct answer from the options given below:

If the cost function $C(x)$ of producing $x$ units of a commodity is given as $C(x) = x^3 - 60x^2 + 13x + 50$, then the level of output for which the marginal cost is minimum is

From the data given below the Laspeyre's price index for the year 2016 with year 2010 as base year is | Commodity | Price year 2010 | Price year 2016 | Quantity Year 2010 | Quantity Year 2016 | |---|---|---|---|---| | A | 1 | 2 | 10 | 13 | | B | 5 | 10 | 12 | 16 | | C | 6 | 10 | 15 | 18 |

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is:

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

From a population having a mean of 20 and standard deviation 2, a random sample of size 64 is taken and its mean is found to be 19.5. The test statistic to test that the sample is taken from the population is

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are:

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:

An asset costing Rs 2,00,000 has a useful life of 10 years and scrap value of Rs 40,000. Its book value at the end of year 6 by Straight Line Method, is :

In a 1000 m race P beats Q by 100 m and in the same race Q beats R by 200 m. By what distance does P beat R?

If $y = \log_e \left(\frac{x^3}{e^3}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to

If the probability distribution of a random variable X is given as | $x_i$ | 0 | 1 | 2 | 3 | |---|---|---|---|---| | $p_i$ | $2k^2$ | $k^2$ | $3k^2$ | $k$ | Then the mean of X is

A consumer in 2015, paid Rs 20 per kg for a particular variety of rice. The wholesale price index number for this variety of rice for the year 2018, with the year 2015 as the base year is 125. Then the cost per kg of rice in the year 2018 will be:

If the objective function $Z = px + qy$ ($p, q > 0$) of an LPP has minimum value 7p, at the corner points (2, 3) and (7, 0), then

If $y = \log\left(\frac{x^5}{e^5}\right)$, then $\frac{d^2y}{dx^2}$ is,

The point on the curve $y^2 = 16x$ for which the y-coordinate is changing 2 times as fast as the x-coordinate is :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The minimum value of $f(x) = 8x^2 - 4x + 7$ is | (I) 48 | | (B) The maximum value of $f(x) = x + \frac{1}{x}$, $x < 0$ is | (II) 13 | | (C) The maximum slope of the curve $y = -2x^3 + 6x^2 + 7x + 26$ is | (III) $-2$ | | (D) The minimum value of $f(x) = x^2 + \frac{128}{x}$ is | (IV) $\frac{13}{2}$ | Choose the correct answer from the options given below :

A product costs the manufacturer ₹ 20 per unit. The demand function is given by $p(x) = 1000 - 20x$, then the quantity for maximum profit is :

A discrete random variable X has the following probability distribution : | X: | 0 | 1 | 2 | 3 | 4 | 5 | |----|----|----|----|----|----|----| | P(X): | b | 3b | 5b | 3b | 4b | 6b | The value of b is :

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :