Applied-Mathematics PYQ — Page 5

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

Match List I with List II | LIST I | LIST II | |---|---| | A. The solution of $3x + 7 > 12$ is | I. $[-1, \infty)$ | | B. The solution of $\frac{3x+5}{2} \geq 1$ is | II. $\left[\frac{17}{8}, \infty\right)$ | | C. The solution of $2x + 5 < 7x + 9$ is | III. $\left(\frac{5}{3}, \infty\right)$ | | D. The solution of $6x - 5 \geq -2x + 12$ is | IV. $\left(-\frac{4}{5}, \infty\right)$ | Choose the correct answer from the options given below:

Mr. Jain takes a personal loan of rupees 10,00,000 at 12% rate of interest per annum for three years. His EMI by flat rate method is :

The set of values of $x$ satisfying $26 \equiv 5 \pmod{x}$ is _______.

The increase in the sale of shawls during winters is an example of :

A die is thrown. If A is the event 'the number appearing is a multiple of 3 and B is the event 'the number appearing is even', then A and B are

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 ?

Given the data for the sales of a product in a state is as follows: | Year | 2005 | 2006 | 2007 | 2008 | 2009 | |---|---|---|---|---|---| | Sales (In lakh Rs) | 150 | 130 | 160 | 170 | 200 | The equation of the straight-line trend by method of least squares is:

Which of the following statements are correct ? (A) $\text{var}(aX + b) = a^2 \text{var}(X)$ (B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$ (C) $E(aX + b) = aE(X) + b$ (D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$ Choose the correct answer from the options given below :

Matrix $A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is skew - symmetric, then the values of a, b c are :

The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$. The output $x$ at which the marginal cost is minimum is :

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$. Which of the following are correct ? A. 2.6 is the marginal cost when 5 units are produced. B. $\frac{2x}{25} + 2$ is the marginal cost function. C. $\frac{x}{25} + 2$ is the average cost function. D. 2.4 is the marginal cost when 5 units are produced. E. $\frac{x}{25} + 1$ is the average cost function. Choose the correct answer from the options given below:

A matrix has 24 elements , which of the following cannot be the possible order of the matrix

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 :

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 :

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ 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 :

If $x = 6t^2$, $y = \frac{6}{t^2}$, then $\frac{d^2 y}{dx^2}$ is equal to :

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 sum of Rs 60,000 invested at r percent compounded quarterly will provide payment at rupees 600 each at the end of every three months , then the value of r is :

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

Let A be a square matrix. Then, (A) $A + A^T$ is a symmetric matrix (B) $A - A^T$ is a skew-symmetric matrix (C) $AA^T$ is a skew-symmetric matrix (D) $A^T A$ is a symmetric matrix Choose the correct answer from the options given below :

For a 3 $\times$ 3 matrix A = [a$_{ij}$], whose element a$_{ij}$ is given by $a_{ij} = \sqrt{i^2 + 3j}$ then what is element a$_{31}$?

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 :