Mathematics Mock Test - 10

$A$ and $B$ are two independent witnesses in a case. The probability that $A$ will speak the truth is $1/3$ and the probability that $B$ will speak the truth is $3/4$. If $A$ and $B$ agree on a certain statement, then the probability that the statement is true is:

Complete solution set of $|\frac{x^2}{x-1}|\le 1$ is given by:

A function $f:\mathbb{R}\to \mathbb{R}$ satisfies the equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb{R}$; $f(x)\ne 0$. Suppose that the function $f(x)$ is differentiable at $x=0$ and $f^{\prime }(0)=2$. If $f^{\prime }(x)=\lambda f(x)$, then the value of $\lambda$ is:

If $y=|\cos x-\sin x|$, then $\frac{dy}{dx}$ at $x=\pi /4$ is:

Durgesh is working in a restaurant in which he prepares two types of dishes $A$ and $B$. Dish $A$ takes 20 minutes to be prepared and Dish $B$ takes 30 minutes for the same. He earns Rs 50 to make one packet of dish $A$, while Rs 70 for one packet of dish $B$. He works for 12 hours a day, including 1 hour for personal activities. What will be the objective function if this example is formulated as a linear programming problem? Assume $x$ and $y$ are the packets of dishes $A$ and $B$ respectively.