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 class 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.

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

Question : A, B, and C are three angles of a triangle. If $A-B=45^{\circ}$ and $B-C=15^{\circ}$ then $\angle A=$?

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 $b>c$)

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