Question : If a³ + b³ = 217 and a + b = 7, then the value of ab is:

Option 1: – 6

Option 2: – 1

Option 3: 7

Option 4: 6

Question : If $\cos A = \sin ^2A$, and $a \sin ^{12}A+b \sin ^{10}A+c \sin ^{8}A+ \sin ^{6}A=1$, then $a + b + c$?

Option 1: 7

Option 2: 8

Option 3: 9

Option 4: 6

Question : Directions: A series of figures are given which can be grouped into classes. Select from the alternatives one set of groups into which the figures can be classified.

Option 1: 1, 3, 6; 2, 4, 6; 5, 7, 9

Option 2: 1, 4, 9; 3, 6, 8; 2, 5, 7

Option 3: 3, 4, 7; 9, 8, 7; 4, 3, 1

Option 4: 2, 3, 6; 9, 3, 4; 6, 3, 2

Question : If A : B = 3 : 4 and B : C = 6 : 5, then A : ( A + C) is equal to:

Option 1: 9 : 10

Option 2: 10 : 9

Option 3: 9 : 19

Option 4: 19 : 9

Question : If $\frac{2}{3}$ of A = 75% of B = 0.6 of C, then $A:B:C$ is:

Option 1: $2:3:3$

Option 2: $3:4:5$

Option 3: $4:5:6$

Option 4: $9:8:10$