Question : The mean of marks secured by 50 students in Division A of class X is 61, 25 students in Division B is 57 and that of 50 students in Division C is 55. What will be the mean marks of the students of the three divisions of Class X?

Option 1: 57.1

Option 2: 56.4

Option 3: 59.2

Option 4: 57.8

Question : In a class of 50 students, 22 girls scored an average of 35 marks in the test. What are the average marks of the boys if the class average is 42 marks?

Option 1: 50

Option 2: 52.5

Option 3: 47.5

Option 4: 55

Question : If $x+\frac{1}{x}=c+\frac{1}{c}$, then the value of $x$ is:

Option 1: $c,\frac{1}{c}$

Option 2: $c,c^{2}$

Option 3: $c,2c$

Option 4: $0, 1$

Question : If $x+\frac{1}{x}=2$, then the value of $x^{57}+\frac{1}{x^{57}}$ is:

Option 1: 1

Option 2: –2

Option 3: 0

Option 4: 2

Question : The mean proportional of $a$ and $b$ is $c$. What is the mean proportion of $a^2c$ and $b^2c$?

Option 1: $c$

Option 2: 3$c$

Option 3: $c^3$

Option 4: $c^2$

Question : Alloy A contains metals x and y only in the ratio 5 : 2, while alloy B contains them in the ratio 3 : 4. Alloy C is prepared by mixing alloys A and B in the ratio 4 : 5. The percentage of $x$ in alloy C is:

Option 1: $55 \frac{1}{9}\%$

Option 2: $55 \frac{2}{9}\%$

Option 3: $55 \frac{5}{9}\%$

Option 4: $55 \frac{4}{9}\%$