Applied-Mathematics PYQ — Page 6

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

If $-\frac{1}{3x - 5} \leq 0$, then :

If $\begin{bmatrix} 2x + 3 & y + 1 \\ 2x - z & 3y \end{bmatrix} = \begin{bmatrix} 7 & -2 \\ -4 & -9 \end{bmatrix}$, then matrix $\begin{bmatrix} 3z + 1 & 4 \\ -2 & 4 \end{bmatrix}$ is equal to:

If $y = \log_3(\log_3 x)$, then $\frac{dy}{dx}$

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

If $x = 3at^2$, $y = 3at^4$ then $\frac{dy}{dx}$ is :

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

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

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

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

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

If $K \equiv 5 \pmod{11}$, then all the possible non-negative values of K are :

If $(x+ 1) e^y = 1$ , then :

If the sum of two positive numbers is 25 and their product is maximum when divided in the ratio of cubes of one and squares of the other, then the numbers are:

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success 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 :

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

If the probability distribution of a discrete random variable $X$ is given as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.5 | 2k | 3k | 3k | 2k | Then the value of $k$ is:

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 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 :

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

If the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^T A = I_3$, then $x^2 + y^2 + z^2$ is :

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is: