Question : Three science classes (A, B, and C) take a life science test. The average score for class A is 83. The average score for B is 76. The average score in class C is 85. The average score of classes A and B is 79 and the average score of classes B and C is 81. Then the average score of classes A, B, and C is:

Option 1: 81.5

Option 2: 81

Option 3: 80.5

Option 4: 80

Question : If $(a+b+c)=16$ and $\left(a^2+b^2+c^2\right)=90$, find the value of $(a b+b c+c a)$.

Option 1: 84

Option 2: 83

Option 3: 82

Option 4: 81

Question : In a class, the average height of all students is $a$ cm. Among them, the average height of 10 students is $b$ cm, and the average height of the remaining students is $c$ cm. Find the number of students in the class. (Here $a>c$ and $b>c$)

Option 1: $\frac{\left ( a\left ( b-c \right ) \right )}{\left ( a-c \right )}$

Option 2: $\frac{\left ( b-c \right )}{\left ( a-c \right )}$

Option 3: $\frac{\left ( b-c \right )}{10\left ( a-c \right )}$

Option 4: $\frac{10\left ( b-c \right )}{\left ( a-c \right )}$

Question : If $a^2+1=9a$ and $a\neq0$, then the value of $a^2+\frac{1}{a^2}$ is:

Option 1: 81

Option 2: 18

Option 3: 79

Option 4: 83

Question : In an examination, a candidate had to sit for three papers, A, B, and C. The candidate secured 75% marks in Paper A, 80% marks in Paper B, and 60% marks in Paper C. If the weightage assigned to Papers A, B, and C were 40%, 50%, and 10%, respectively, find the weighted percentage of marks obtained by the candidate, when all the three papers were taken together.

Option 1: 77%

Option 2: 74%

Option 3: 72%

Option 4: 76%