Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 The line l is horizontal if m is undefined m=0 m=1 m=0-1
2 The coordinates of a point P(x,y) referred to XY-system are (x+y,y+k) (x-h,y-k) (x,y) (x-h,y-k)
3 The point of concurrency of the medians of the ΔABC is called its Orthocenter Centriod Circumcentre Incentre
4 If the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a unique point then p = -14 p = -1 p =0 p=12
5 If the points (a,2b):(c,a+b):(2c-a,h) lie on the same line then h=2a h=a+b h=ab h=ac
6 Area bounded between the curve xy=2 and the lines x=1 and x=2 ln2 square units ln√2 square units ln4 square units Square units
7 The degree of differential equation is the power of the Lowest order derivative Highest order derivative Integral All are correct
8 An equation containing at least one derivative of a depends variable with respect to independent variable is a (an) Implicit equation Differential equation General equation None of these
9 The process of finding a function whose derivative is given is called a Differentiation Integration Differential None
10 The set of all antiderivaties of f(= ∫f(x)dx) is the Definite integral Indefinite integral Integral Area
11 The function ø(x) is ananti derivativeof function f (x),x∈Df if ø′(x) =∫f(x)dx ø(x) =∫f(x)dx ø′(x) =f(x) ø(x) =∫′(x)dx
12 The number of arbitrary constants in the general solution of a differential equation is equal to the different equation Order Degree Variables All are correct
13 The different of tan x is sec2 x ln |sec x| sec2 xdx -cos ec2 x
14 The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is 1.2% 1.5% 0.16% 100.16%
15 ∛8.6 is approximately equal to 2.488 2.48 2.0488 2.05
16 The approximate increase in the area of a circular disc if its diameter increased form 44cm to 44.4cm is 0.4cm 8.8πcm 17.6 πcm 35.2πcm
17 f(x)g(x)- ∫g(x) f′(x) dx is equal to ∫f(x)g′(x)dx ∫f′(x)g(x)dx ∫f′(x)g(x)′dx ∫f(x)g(x)dx
18 The area bounded by y = x (x2 - 4) and below x - axis is 4 0 -4 8
19 Archimedes approximate the function by horizontal function and the area under f by the sum of small Parallelograms Squares Retangles Polygons
20 If y = 2x , then y1 -ln2y = 0 y2-(ln2)2 y = 0 y2-(ln2)y1 = 0 All are correct
21 Two positive integers whose sum is 30 and their product will be maximum are 12,18 10,20 15,15 14,16
22 The velocity and acceleration at any point t of a particle which moves along straight line x = 5r-3 5,3 5,-3 5,0 10,0
23 The distance of a moving particle at any instant t is x = 3t2 +1 then velocity of particle at t = 10 is 50 cm/sec 60 cm/sec 61 cm/sec None of these
24 If y=sin(ax+b) then y4=________: sin4(ax+b) a4sin(ax+b) a4cos(ax+b) None of these
25 If f(√x)=sin x , then f′(x) =______; 2xcosx2 cosx2 cos√x None of these
26 If f (x) = |x|, then (0,0) is the Critical point Inflection point Stationary point None of these
27 If f (x)=a0 +a1x+a2x2+a3x3-----+0n-1xn-1+anxn then f(n) (x) is equal to n! ann! 0 an
28 If y = eax sin bx and y2 - 2ay1 + (a2+b2) y=0 the for what values of a and b we have y2+10y1+34y =0 a = -10,b=34 a=-5,b=3 a=5,b=3 a=10,b=34
29 A stationary point x is a relative exterma of y= f(x) is f′′ (x) > 0 f′′ (x) < 0 f′′ (x) ≠ 0 f′′(x) = 0
30 The interval in which f(x)=x3-6x2+9x is increasing 1<x<3 x<1 and x>3 X ≥1 and x ≤ 3 -∞ < x < ∞
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