This document contains 30 multiple choice questions related to mathematics. Some of the concepts covered include: properties of complex numbers, sets, arithmetic progressions, trigonometric functions, derivatives, integrals, lines, conic sections, inequalities and vector projections. The questions have 4 possible answer choices labeled a, b, c or d for each problem.

1. ECAT Math:
2006.
1) if x,y ἐ R , then x + iy is purely imaginary if
a) x≠0 , y=0
b) x=0 , y=0
c) x=0 , y≠0
d) x≠0, y≠0
2) A-B is a subset of ________ if B is subset of A
a)empty set
b)b
c) A intersection B
d) A union B
3) If x is = sq. root ( 2 + sq. root ( 2 + sq. root ( 2 + sq. root ( 2 + … , then x=?
a) 0
b) 1
c) 2
d) none
4) the determinant of 3x3 matrix with first column (1, 1, 1), second column (a, b, c) and 3 rd column (b+c,
c+a, a+b) is
a) a+b+c
b) 0
c) -1
d) ab+bc+ca
5) if (x^2+1)/(x^3+1) = A/x + (Bx + C)/(x^2 – x + 1) , then B is
a) 2/3
b) 3/4
c) 1/3
d) -1/2
6) if a is the first term and d is the common difference of an A.P. then its (2m+1)th term is
a) a + 2md
b) a+m
c) a+m+1
d) none of these
7) in common fraction form the recurring decimal 0.2121..is written as
a) 7/33

2. b) 33/7
c) 11/9
d) 9/11
8) nPr =
a) n!/(n+1)!
b) nPr–1
c) n!/(n-r)!
d) n!(n+1)!
9) in expansion of (x+y)^n in every term the sum of the exponents of x and y is:
a) n
b) n+1
c) n-1
d) 2n
10) if sine of an angle is √3 times its cosine then the angle is
a) 30
b) 45
c) 60
d) 75
11) [(-1+√3i)/2]^4 is equal to
a) (-1+√3i)/2
b) (-1-√3i)/2
c) [(-1+√3i)/2]^2
d) none
12) the period if 3sin5x is
a) 2pi
b) 2pi/5
c) 5pi/2
d) 5pi
13) Cos15 – sin15 =
a) -1/√2
b) 1/√2
c) √2
d) -√2
14) tan(45+A) =
a) tanA+1/tanA-1

3. b) 1+tanA/1-tanA
c) 1+tan^2 A/1-tan^2 A
d) 1-tanA/1+tanA
15) a triangle which has not a right angle is called ______ triangle
a) obtuse
b) equilateral
c) oblique
d) none of these
16) if cosA=-1 then _________ , n belongs to Z
a) A≠(2n+1)pie
b) A=(2n+1)pie
c) A=n pie/2
d) none of these
17) cos11+sin11/cos11-sin11 = ?
a) tan56
b) sin56
c) cos56
d) none
18) due to periodicity the trigonometric equations have ________ number of solutions
a) finite
b) infinite
c) two
d) none of these
19) if x approaches to zero then sin6x + sin2x / sin5x + sin3x = ?
a) -√2
b) 0
c) 1
d) √2
20) the solution of dy/dx= -cosec^2 x is
a) c
b) y= cotx + c
c) y = tanx + c
d) y= cot^2 x + c
21) if f(x) = cotx, then f’(pie/4) = ?
a) 2

4. b) 1
c) 0
d) -2
22) ∫e^secxsecxtanx dx =
a) e^secx + c
b) e^tanx + c
c) e^cosecx + c
d) none of these
23) ∫ sin2x dx= ? with limits 0 to pie/4
a) 2
b) 1/2
c) 0
d) 3/2
24) the slope of the line with inclination 120 degree is
a) 0
b) 1
c) -√3
d) undefined
25) equation of a line passing through (a.b) and perpendicular to ax+by+c=0 is
a) bx + ay = 0
b) ax – by = 0
c) bx – ay = 0
d) ax + by = 0
26) a line segment whose end points lie on a circle is called
a) arc of a circle
b) center of a circle
c) chord a circle
d) radius of a circle
27) foci of x^2/a^2 – y^2/b^2 = 1 are
a) (+- a , 0 )
b) ( 0 , + - a)
c) ( 0 , + - ae)
d) ( + - ae , 0)
28) the length of minor axis of ellipse is
a) 2a

5. b) a
c) c/e
d) 2b
29) 2x + 3 < 0 is
a) inequality
b) equality
c) identity
d) none
30) the projection of -2i + 3j + 7k on 2j + k is
a) 13/5
b) 13/4
c) 13/√5
d) 13
2007