Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 ∀x∈(a,b),f(x) is increasing if f′(x) >0 f′(x) <0 f′′(x) >0 f′′(x) =0
2 (fog)′(x) =f′(g(x))g′(x) is derivative by Chain rule Reciprocal rule Power rule Product rule
3 The range of function f(x)=-x2+2x-1 is R (-∞,0] (-∞,1] [0,∞)
4 Inverse of the function y-10x is y=logx y=lnx x=10y x=10y
5 If f(α) = b2 and g (c) =d where c=b2 then (gof)(a) is α c b d
6 x = r2, y = 1 are the parametric equation of Circle Hyperbola Ellipse Parabola
7 The set of points {(x,y)|y = f(x),∀x∈} is called Relation Graph of f Function All are correct
8 If f (x) = 2x+1 then fof (x) = _______; 4x+3 2x +3 4x +1 None of these
9 The function f(x) =|x| is a/an_______function Even Odd Both even as well as odd Neither even nor odd
10 Domain of cosh x is R R -{0} [1,∞) [0,∞)
11 The function discontinuous at x = 0 is (1) tan x (II) cot x (III) sec x (iv)cosec x) I & III I & IV II & IV II & III
12 The curve f(x,y) = 0 has a central symmetry if f(-x,-y)=f(x,y) f(x,-y)=f(x,y) f(-x,y)=f(x,y) f(-x,-y)≠f(x,y)
13 The only function which is both even and odd is f(x) =α f(x) = x f(x) =0 Both A & B
14 The range of the function f : x→ y is defined by {x| y = f (x) ∀x∈ X ∧y∈y} {(x,y) |y = f (x)∀x∈ X} {y|y = f (x) ∀x∈ X ∧y∈y} Y
15 An even function is symmetric about the line y = x x = 0 y = -x y = 0
16 If a tangent line touches the function y = f (x) in more than one point then y = f (x) is Periodic Surjective Bijective Injective
17 Composition of functions is Non-commutative (fg ≠ gf) non-associative [8(fh) ≠(8f)h] Commutative (fg = gf) f of-1≠ 1
18 x = secθ,y = tanθ are the parametric equations of Circle Hyperbola Ellipse parabola
19 The range of y=x2 + 1 is the set of non-negative real numbers except 0≤ y < 1 0 < y < 1 0≤ y≤ 1 0 < y≤1
20 The function f : x→ y defined as f (x) =α∀x∈ X,α∈ y is called Constant function Polynomial function Identity function Linear function
21 f (x) = | x | is a/an Injective function Bijective function Surjective function Implicit function
22 Point (2,0) lies on trigonometric function f(x)=______; sinx cosx tanx secx
23 The domain of y = cos-1 x is -∞ < x < ∞ -1≤ x≤ 1 x≤ -1 or x ≥ 1 None of these
24 For any equilateral r :R :η :r1 :r2 :r3 = 1:2:3:4:5 1:2:3:3:3 1:2:4:4:4 2:1 :2 :2 :2
25 Area of inscribed circle is π R2 π η2 π r22 π r2
26 In any triangle ABC,with usual notationαsinβ =____; b sinα bsinβ αsinα None of these
27 The law of cosines reduces to a2 +c2 =b2 for α = 90° β = 90° γ = 90° α +β +γ =180°
28 e-radii are denoted by η r2 r3 All of these
29 In-radius is denoted by r η r2 R
30 A circle which touches one side of a triangle extermally and the other two sides produced is called In-circle Circumcircle e-circle Point circle
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