1) If ax³+bx²+ is divisible by
x²+my -1, then
a) a²=c(b+c) b) b²=a(c+a)
c) c²= b(a+b) d) a²+c(b+c)=0
2) There are 10 straight line in a plane, no two are parallel no three are concurrent. their points of intersection are joined. the number of new lines formed is N, with digit sum is -----.
a) 7 b) 8 c) 9 d) 11
3) ∫cos 6x . cos⁸x dx at(π,0)
a) π/8 b) π/16 c) π/32 d) π/64
4) the shortest distance between the lines r= s(2i+3j+4k) - (i+j+k) and r= t(3i+4j+5k) - i is
a) 1/√2 b)1/√3 c)√(2/3) d) 1/√6
5) The product of the digits of a four digit number is 72. the number of such numbers is N, with the digit sum
a) 4 b) 5 c) 6 d) 10
6) If 13⁹⁹ is divided by 81, the remainder is divisible by
a) 3 b) 5 c) 7 d) 11
** with the reference solve Q7 and Q8 AOB is a circular sector with bounding radii OA= OB = LM is the midpoint of the circular arc AB. the point D and E lie on OA and OB, Angle AOB= 2π/3
7) if Triangle MDE is equilateral, its area is
a) √3/4 b) 3/16 c)3√3/16 d)√3/8
8) if the triangle MDE is isosceles, its maximum area is.
a) √3/4 b) 3/16 c)3√3/16 d)√3/8
9) A game uses a deck of n different cards, n≥ 6. if the number of possible sets of 6 cards that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. the sum of the digit of n is
