Question : In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108, respectively. What is the 3rd term?

Option 1: 84

Option 2: 83

Option 3: 82

Option 4: 81

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

Option 1: 84

Option 2: 83

Option 3: 82

Option 4: 81

Question : The HCF and LCM of the two numbers are 21 and 84, respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:

Option 1: 12

Option 2: 108

Option 3: 48

Option 4: 84

Question : If $\cot B=9 $, then what will be the value of $\sec ^2 B$?

Option 1: $\frac{98}{81}$

Option 2: $\frac{92}{81}$

Option 3: $\frac{42}{81}$

Option 4: $\frac{82}{81}$

Question : The 3^rd and 8^th terms of an Arithmetic progression are –14 and 1, respectively. What is the 11^th term?

Option 1: 14

Option 2: 16

Option 3: 20

Option 4: 10

Question : What smallest positive number should be subtracted from 2 and 3 so that 4 is the third proportion to them?

Option 1: 1

Option 2: 2

Option 3: 4

Option 4: 3