Applied-Mathematics PYQ — Page 8

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$ (A) Maximum value of $f(x)$ is 8 (B) Minimum value of $f(x)$ is 8 (C) Minimum value of $f(x)$ is 16 (D) No maximum value of $f(x)$ Choose the correct answer from the options given below :

Area of the region bounded by the curve $x^2 = 4y$, $x$ - axis and $x = 3$ is

Let $P = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, $R = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, then the matrix S such that QS - RP = 0 will be :

The objective function $z = 4x + 3y$ can be maximised subject to the constraints $3x + 4y \leq 24$, $8x + 6y \leq 48$, $x \leq 5$, $y \leq 6$, $x \geq 0$, $y \geq 0$ :

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$ then $(3A + 2B)'$ is :

Consider the following data : | Year | 2012 | 2013 | 2014 | 2015 | 2016 | |------|------|------|------|------|------| | Sales (in ₹ crores) | 8 | 10 | 7 | 9 | 12 | The equation of the straight line trend by the method of least squares 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 :

The present value of a perpetual income of ₹ $x$ payable at the end of each 6 months is ₹ 1,80,000. If the money is worth 5% compounded semi-annually, then the value of $x$ is ₹ :

T- test : A t- test is a test of difference for parameter data $t = \frac{\overline{x1} - \overline{x2}}{s\sqrt{\frac{1}{n1} + \frac{1}{n2}}}$ Then read the following statements and choose the correct statements (A) the null hypothesis and the alternative hypothesis have the same viewpoint (B) In t- test testing the significance of mean value is done, when sample size is small (C) T - test for two independent groups when variance is equal (D) Testing is a process used by statisticians to accept or reject the hypothesis (E) if the value of test statistics is greater than the table values, we do not reject the null hypothesis Choose the correct answer from the options given below :

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

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 :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) In a binomial distribution, if $n = 10$, $q = 0.25$, then its mean is | (I) 12 | | (B) If the mean of a binomial distribution is 6 and its variance is 3, then p is | (II) 7.5 | | (C) In a binomial distribution, the probability of getting a success is $\frac{1}{4}$ and the standard distribution is 3, then its mean is | (III) 16 | | (D) If the mean and variance of a binomial distribution are 4 and 3 respectively, then the number of trials is | (IV) $\frac{1}{2}$ | Choose the correct answer from the options given below :

A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :

The set of all positive integers less than 50 forming the equivalence class of 8 for modulo 11 is :

If Mr. Ravi borrows a sum of ₹ 1,50,000 at an interest rate of 10% (flat) for a tenure of 3 years, then his EMI based on above data is (approximately) ₹ :

The demand function of a monopolist is given by $p = 1500 - 2x - x^2$, then value of marginal revenue when $x = 20$ is :

$5^{100} (\mod 9) =$

The present value of a perpetuity of Rs. 2,500 payable at the end of each year, if money is worth 10% compounded annually, is :

Match List - I with List - II. Given that $\Sigma p_0 q_0 = 150$, $\Sigma p_0 q_1 = 80$, $\Sigma p_1 q_0 = 240$, $\Sigma p_1 q_1 = 200$. | List - I | List - II | |---|---| | (A) Laspeyre's index | (I) 160 | | (B) Paasche's index | (II) 200 | | (C) Fesher's index | (III) 205 | | (D) Dorbish and Bowley's | (IV) 250 | Choose the correct answer from the options given below :

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

The EMI (in Rs.) under the flat rate on a loan of Rs. 6,00,000 with 20% annual interest for 5 years is :

Two inlet pipes can fill a tank in 20 minutes and 24 minutes respectively . An outlet pipe can empty 30 liters of water per minute. If all three pipes working together can fill the tank in 15 minutes. The capacity of the tank is :

Match List - I with List - II. | List - I (Functions) | List - II (Maximum value) | |---|---| | (A) $f(x) = -x^2, x \in (-\infty, \infty)$ | (I) 8 | | (B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$ | (II) 7 | | (C) $f(x) = x + 1, x \in [0, 6]$ | (III) 1 | | (D) $f(x) = x^3, x \in [0, 2]$ | (IV) 0 | Choose the correct answer from the options given below :

The effective rate that is equivalent to a nominal rate of 12% compounded quarterly is :