ECAT 2012 MATH

Note:-please write the answer in comment box.It will help us a lot in finding answer of these questions. 1) There are 30 students in a class.22 study Math,16 study Physics and 2 study neither MATH nor Physics.The number of student who study both Math and Phy is?? a) 12 b) 5 c) 10 d) 8 2) The integral 2 ∫ 2 (lny+y2+msiny)dy equals?? a) 15 b) 20 c) 0 d) 25 3) Function f(x)=sinx/x has a maximum value of: a) 1 as x → 0 b) 1 as x → ∏ c) infinity at x=0 d) infinity at x= ∏ 4) Area under the curve f(x)=x2+x+1 between x=1 and x=3 a) 44/3 b) 22/3 c) 44/5 d) 22/5 5) Function f(x)=3x-7 is defined as x ∈ R & g(x)=12(x-2)-1 is also defined as x ∈ R except x=2.The value(s)of x for which fg(x)=0 is (are): a) +10 b) -5 c) +10 or -5 d) -10 or +5 6) The set of values of x for which (x-6)2 >x are: a) x<4 or x>9 b) x<4 or x>-9 c) x<9 or x>4 d) x<-9or x>-4 7) The function y=3x-x3 for x ≥ 0 has a min.value at: a) (1,2) b) (2,1) c) (3,4) d) (2,2) 8) Solve 2x-3/9-x =32/4x/2 a) 5/8 b) -5/8 c) 8/5 d) -8/5 9) AOB is a sector of a circle whose centre is O and radius 5cm.If the perimeter of the sector is 14cm,then the value of the angle AOB 9in radian) is: a) 0.6 radian b) 0.8 radian c) 0.5 radian d) 1.0 radian 10) The slope(gradient) of the curve y=x3-3x2-9x+11 is 15 when x coordinates are a) +2,-2 b) 3,4 c) -2,+4 d) +5,-5 11) If √ (a+b √ 3) =13(4+ √ 3)-1 then the value of integers a and b are a) -19 and +8 b) +19 and -8 c) -19 and -8 d) +19 and +8 12) The derivative of function e5-2x? (same in 2013 paper) a) -2e5-2x b) e2x c) e5 d) e5-2x 13)The solution of 125x = 25(5x) and 7x ÷ 49y =1: a) (2/5,4/5) b) (4/5,2/5) c) (2/5,-4/5) d) (-2/5,4/5) 14) The solution of log4y+log2y=9 is a) 6 b) 40 c) 50 d) 64