Mathematics Mock Test - 10

A fair die is thrown six times. The probability of getting a factor of 6 exactly four times is:

The solution of the differential equation $\frac{dy}{dx}=\frac{y}{x}+\frac{f(y/x)}{f^{\prime }(y/x)}$ is:

For all real $x$, the vectors $\vec{a}=cx\hat{i}-6\hat{j}+3\hat{k}$ and $\vec{b}=x\hat{i}+2\hat{j}+2cx\hat{k}$ make an obtuse angle with each other. Then the value of $c$ must satisfy:

Match the functions in List I with their corresponding ranges in List II:List IA. $f(x)=\frac{x}{1+x^2}$ B. $f(x)=\frac{3}{2-x^2}$ C. $f(x)=\frac{1}{\sqrt{x-[x]}}$ D. $f(x)=\frac{1}{2-\sin 3x}$ List III. $R_f=(1,\infty )$ II. $R_f=(-\infty ,0)\cup [3/2,\infty )$ III. $R_f=[-1/2,1/2]$ IV. $R_f=[1/3,1]$ Choose the correct option:

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. He earns Rs 50 to make one packet of dish $A$ and Rs 70 for dish $B$. He works for 12 hours a day, using 1 hour for personal activities. What will be the objective function to maximize his earnings? (Let $x,y$ be packets of $A,B$)