Applied-Mathematics PYQ — Page 5

Consider the following hypothesis test : $\mu_o : \mu \leq 26$ $\mu_a : \mu > 26$ A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :

If $x^{2/3} + y^{2/3} = a^{2/3}$, then $\frac{dy}{dx}$ is equal to :

If the objective function for an L.P.P. is $z = 3x + 4y$ and the corner points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of $z$ occurs at :

The digit in the unit's place of $13^{37}$ is :

If objective function $Z = 20x + 30y$ of an LPP is subject to the constraints $3x + 4y \geq 12$, $4x + y \geq 4$, $x \geq 0, y \geq 0$, then Z has : (A) Min at (0, 4) (B) Max at (0, 4) (C) Min at (4, 0) (D) Max at (4, 0) (E) Min at $\left(\frac{4}{13}, \frac{36}{13}\right)$ Choose the **correct** answer from the options given below :

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | If $y = x^2 - 8$ and $\frac{dy}{dx} = 0$, then $x = ?$ | (I) | 1 | | (B) | If $p(x) = 3x + 1$, then $R(x)$ at $x = 2$ | (II) | 0 | | (C) | If $y = x^3$, then $\frac{dy}{dx}$ at $x = -1$ | (III) | 14 | | (D) | If $C(x) = 100 + 5x$, $R(x) = 102 + 3x$, then break-even point | (IV) | 3 | Choose the **correct** answer from the options given below :

A retailer has 250 kg of rice a part of which he sells at 10% profit. The remaining quantity of rice is of low quality and he sold it at 5% loss. Overall he made a profit of 7%. The quantity of rice sold at 5% loss is :

Which of the following statements are correct ? (A) Index number are free from units (B) Index number represents specialised averages in percentage (C) $P_{01} = \frac{\Sigma P_0}{\Sigma P_1} \times 100$ (D) Index numbers are helpful in formulating and adopting appropriate economic policies Choose the **correct** answer from the options given below :

Let $f : R \to R$ be a function defined as $f(x) = 2x^3 - 21x^2 + 36x - 20$, then : (A) maximum value of $f(x)$ is $-3$ (B) minimum value of $f(x)$ is $-128$ (C) maximum value exists at $x = 6$ (D) minimum value exists at $x = 1$ Choose the **correct** answer from the options given below :

Ram and Ankur make a partnership. Ram invests Rs. 35,000 for 6 months and Ankur invests some money for 7 months. Ankur claims $\frac{4}{7}$ of total profit. Then the money invested by Ankur is :

Pipes A and B can fill a tank in 20 hours and 30 hours respectively and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will be needed to make the tank full ?

If A is square matrix of order 3 with $|A| = 3$, then $|4 \text{ adj} A|$ is equal to :

The purchase price P of a Rs. 50,000, 6% bond, dividends payable semi-annually, redeemable at par in 10 years, if the yield rate is to be 5% compounded semi-annually. Then P is equal : [Given $(1.025)^{-20} = 0.61027094$]

For the data : | Variable | Price - Base year | Price - Current year | Weights | |---|---|---|---| | X | 50 | 60 | 5 | | Y | 20 | 25 | 7 | | Z | 30 | 40 | 4 | The weighted aggregative index number is :

In an LPP if the objective function $z = ax + by$ has same maximum value on two corner points of the feasible region, then the number of points at which maximum value of $z$ occurs is :

If the probability distribution of X is : | X | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---| | P(X) | 1/15 | 2/15 | 3/15 | 4/15 | 5/15 | Then variance is equal to :

Five litres of water is added to a certain quantity of pure milk costing Rs. 60 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, then the amount of pure milk in the mixture is :

If the matrix $\begin{bmatrix} 0 & 2 & 5x \\ -2 & 0 & 6 \\ 10 & -6 & y \end{bmatrix}$ is skew-symmetric matrix, then the value of $(y - 4x)$ is :

The wholesale price index (or price relative) of rice in 2018 compared to 2014 is 150. If the cost of rice was Rs. 16 per kg in 2014, then per kg cost of rice in 2018 is :

The assumption opposite of what is made in the null hypothesis is known as the _________ hypothesis.

If $y = 3e^{2x} + 2e^{3x}$, then which one of the following is true ?

Match **List - I** with **List - II**. | | List - I (Matrix) | | List - II (Type) | |---|---|---|---| | (A) | $\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$ | (I) | Lower Triangular Matrix | | (B) | $\begin{bmatrix} 1 & 5 & 0 & -1 \end{bmatrix}$ | (II) | Row Matrix | | (C) | $\begin{bmatrix} 3 & 0 & 0 \\ 1 & -1 & 0 \\ 2 & 5 & 4 \end{bmatrix}$ | (III) | Diagonal Matrix | | (D) | $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ | (IV) | Scalar Matrix | Choose the **correct** answer from the options given below :

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | Left tailed test | (I) | $H_0 : \mu = 50$ | | (B) | Two tailed test | (II) | $H_1 : \mu > 50$ | | (C) | Null hypothesis | (III) | $H_1 : \mu < 50$ | | (D) | Right tailed test | (IV) | $H_1 : \mu \neq 50$ | Choose the **correct** answer from the options given below :

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | For break-even point | (I) | $< 0$ | | (B) | For maxima $\frac{d^2y}{dx^2}$ | (II) | $\frac{dy}{dx} = 0$ | | (C) | For points of maxima/minima | (III) | $R(x) - C(x)$ | | (D) | $P(x) = $ Profit function | (IV) | $R(x) = C(x)$ | Choose the **correct** answer from the options given below :