NET Math

These are a few more questions from the math portion of Nust Entrance Test which were provided by the students last year. Some of these are not complete and some are a bit ambiguous . If anyone of you know the answers do comment below . 

1. A hyperbola eq. was given. 4x^2 - 9y^2 =36 and the question was a tangent is drawn at any point of hyperbola. What will be the product of distances of it from the two foci?

2. A question was: - Which of the two pair intersect each other. Two equations either of circle, hyperbola, ellipse or lines were given in the options
a. sq. root 6 + sq. root 2
b. sq. root 6+ sq. root 3 
c. sq. root 6 - sq. root 2
d. None of these

3. There were two questions related to determinants. In one we had to find value of *a* in the matrix and in other we had to evaluate the value of determinant.

4. In a quadrilateral ABCD,   sinA - sinB=?

5. If sq. root 8 and sq. root 12 are two sides of a triangle and 45 is the angle of biggest side. Find the smallest side?

6. The notation dy/dx was introduced by which person ? (his name is mentioned in book, can bee seen form there)