Question : Which of the following numbers will completely divide 4¹² + 4¹³ + 4¹⁴ + 4¹⁵?

Option 1: 3

Option 2: 7

Option 3: 11

Option 4: 17

Question : Two items A and B are sold at a profit of 10% and 15%, respectively. If the amount of profit received is the same, then the cost price of A and B may be:

Option 1: Rs. 1,000 and Rs. 1,500

Option 2: Rs. 5,000 and Rs. 2,000

Option 3: Rs. 3,000 and Rs. 2,000

Option 4: Rs. 3,000 and Rs. 5,000

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 : The sum of three numbers is 2, the 1^st number is $\frac{1}{2}$ times the 2^nd number and the 3^rd number is $\frac{1}{4}$ times the 2^nd number. The 2^nd number is:

Option 1: $\frac{7}{6}$

Option 2: $\frac{8}{7}$

Option 3: $\frac{9}{8}$

Option 4: $\frac{10}{9}$

Question : A point D is taken from the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then:

Option 1: AB² + CD² = BC² + AD²

Option 2: CD² + BD² = 2AD²

Option 3: AB² + AC² = 2AD²

Option 4: AB² = AD² + BD²