ravi maths tuition center ph - 8056206308 - WordPress.com
11
REIVISION TEST 2 [ CHAPTER 2 & 3 ] 12th Standard 2019 EM Maths RAVI MATHS TUITION CENTER PH - 8056206308 Date : 01-Jul-19 Reg.No. : Time : 02:30:00 Hrs Total Marks : 90 20 x 1 = 20 The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is (a) (b) |z| (c) (d) 2|z| 2 2 If z is a non zero complex number, such that 2iz then |z|is then |z| is (a) (b) 1 (c) 2 (d) 3 2 = If then the least value |z| is (a) 1 (b) 2 (c) 3 (d) 5 The solution of the equation |z|-z=1+2i is (a) (b) (c) (d) z ,z and z are complex number such that z1+z2+z3=0 and |z |=|z |=|z |=1 then z +z +z is (a) 3 (b) 2 (c) 1 (d) 0 1 3 3 1 2 3 1 2 2 2 2 3 If z=cos +i sin , then (a) |z| =1, arg(z) = (b) |z| =1, arg(z) = (c) |z|= , arg(z)= (d) |z| = , arg (z) =tan -1 The least positive integer n such that is a positive integer is (a) 16 (b) 8 (c) 4 (d) 2 If z=1-cosθ + i sinθ, then |z| = (a) 2 sin (b) 2 cos (c) 2|sin | (d) 2|cos | If x+iy = , they y = (a) (b) - (c) (d) none of these If ω is the cube root of unity, then the value of (1-ω) (1-ω ) (1-ω ) (1-ω ) is (a) 9 (b) -9 (c) 16 (d) 32 2 4 8 The modular of is ______ (a) (b) 2 (c) 1 (d) A polynomial equation in x of degree n always has (a) n distinct roots (b) n real roots (c) n imaginary roots (d) at most one root If α,β and γ are the roots of x +px +qx+r, then is (a) - (b) (c) (d) - 3 2 According to the rational root theorem, which number is not possible rational root of 4x +2x -10x -5? (a) -1 (b) (c) (d) 5 7 4 3 The number of real numbers in [0,2π] satisfying sin x-2sin x+1 is (a) 2 (b) 4 (c) 1 (d) ∞ 4 2 The polynomial x +2x+3 has (a) one negative and two real roots (b) one positive and two imaginary roots (c) three real roots (d) no solution 3 The number of positive roots of the polynomial (-1) x is rr 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) Padasalai Padasalai www.Padasalai.Or www.Padasalai.Or www.Padasalai.Or www.Padasalai.Or www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasa ww.Padasalai.Org ww.Padasalai.Org ww.Padasalai.Org ww.Padasalai.Org ww.Padasa www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasala ww.Padasalai.Org ww.Padasalai.Org ww.Padasalai.Org ww.Padasalai.Org ww.Padasala Padasalai TrbTnpsc
-
Upload
khangminh22 -
Category
Documents
-
view
3 -
download
0
Transcript of ravi maths tuition center ph - 8056206308 - WordPress.com
REIVISION TEST 2 [ CHAPTER 2 & 3 ]
12th Standard 2019 EM
Maths
RAVI MATHS TUITION CENTER PH - 8056206308
Date : 01-Jul-19
Reg.No. :
Time : 02:30:00 Hrs Total Marks : 9020 x 1 = 20
The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is
(a) (b) |z| (c) (d) 2|z|1
2|z|2 2 3
2|z|2 2
If z is a non zero complex number, such that 2iz then |z|is then |z| is
(a) (b) 1 (c) 2 (d) 3
2=z̄
1
2
If then the least value |z| is
(a) 1 (b) 2 (c) 3 (d) 5
z − = 2∣
∣∣
3
z
∣
∣∣
The solution of the equation |z|-z=1+2i is
(a) (b) (c) (d) − 2i3
2− + 2i
3
22 − i
3
22 + i
3
2
z ,z and z are complex number such that z1+z2+z3=0 and |z |=|z |=|z |=1 then z +z +z is
(a) 3 (b) 2 (c) 1 (d) 01 3 3 1 2 3 1
22
22
3
If z=cos +i sin , then
(a) |z| =1, arg(z) = (b) |z| =1, arg(z) = (c) |z|= , arg(z)= (d) |z| = , arg (z) =tan
π
4π6
π
4π
6
3√
25π
24
3√
2-1( )1
2√
The least positive integer n such that is a positive integer is
(a) 16 (b) 8 (c) 4 (d) 2
( )2i
1+i
n
If z=1-cosθ + i sinθ, then |z| =
(a) 2 sin (b) 2 cos (c) 2|sin | (d) 2|cos |13
θ
2θ
2θ
2
If x+iy = , they y =
(a) (b) - (c) (d) none of these
3+5i
7−6i9
859
855385
If ω is the cube root of unity, then the value of (1-ω) (1-ω ) (1-ω ) (1-ω ) is
(a) 9 (b) -9 (c) 16 (d) 32
2 4 8
The modular of is ______
(a) (b) 2 (c) 1 (d)
(−1+i)(1−i)
1+i 3√
2√ 12
A polynomial equation in x of degree n always has
(a) n distinct roots (b) n real roots (c) n imaginary roots (d) at most one root
If α,β and γ are the roots of x +px +qx+r, then is
(a) - (b) (c) (d) -
3 2 Σ 1α
q
r
p
r
q
r
q
p
According to the rational root theorem, which number is not possible rational root of 4x +2x -10x -5?
(a) -1 (b) (c) (d) 5
7 4 3
54
45
The number of real numbers in [0,2π] satisfying sin x-2sin x+1 is
(a) 2 (b) 4 (c) 1 (d) ∞
4 2
The polynomial x +2x+3 has
(a) one negative and two real roots (b) one positive and two imaginary roots (c) three real roots (d) no solution
3
The number of positive roots of the polynomial (-1) x isΣj=0
n
nCr
r r
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
(a) 0 (b) n (c) < n (d) r
Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots
(a) n (b) n -1 (c) n+1 (d) (n-r)
If (2+√3)x -2x+1+(2-√3)x -2x-1= then x=
(a) 0,2 (b) 0,1 (c) 0,3 (d) 0, √3
2 2 22− 3√
If p(x) = ax + bx + c and Q(x) = -ax + dx + c where ac ≠ 0 then p(x). Q(x) = 0 has at least _______ real roots.
(a) no (b) 1 (c) 2 (d) infinite
2 2
7 x 2 = 14
Given the complex number z=2+3i, represent the complex numbers in Argand diagramz, iz , and z+iz
If z z =1−3i, = −4 , and z = 5 , show that (z +z )+z =z +(z +z )i i 3 1 2 3 1 2 3
Find the modulus of the following complex number
+2 − i
1 + i
1 − 2i
1 − i
Obtain the Cartesian form of the locus of z=x+iy in each of the following cases Im[(1−i)z+1]= 0
Show that the following equations represent a circle, and, find its centre and radius|3x-6+12i|=8
Find a polynomial equation of minimum degree with rational coe�icients, having − as a root.5√ 3√
Solve: (2x-1)(x+3)(x-2)(2x+3)+20=0
Find all zeros of the polynomial x -3x -5x +22x -39x -39x+135, if it is known that 1+2i and are two of its zeros.6 5 4 3 2 3√
Find all real numbers satisfying 4 -3(2 )+2 =0x x+2 5
Examine for the rational roots of x -3x+1=08
7 x 3 = 21
Show that |z+2−i|< 2 represents interior points of a circle. Find its centre and radius.
Find the fourth roots of unity.
Simplify the following:i i i ...i2 3 40
Obtain the Cartesian form of the locus of z in the cases.|2z-3-i|=3
Find the locus of z if Re =0 where z=x+iy.( )z+1z−i
If p is real, discuss the nature of the roots of the equation 4x +4px+p+2=0 in terms of p.2
Solve the equation 2x +11x −9x−18=0.3 2
If the roots of x +px +qx+r=0 are in H.P. prove that 9pqr = 27r +2p.3 2 3
Solve the equation x -5x -4x+20=03 2
Find solution, if any, of the equation 2cos x-9cosx+4=02
14 x 5 = 70
(OR)
Find the value of the real numbers x and y, if the complex number (2+i)x+(1−i)y+2i −3
and x+(−1+2i)y+1+iare equal
Let z ,z , and z be complex numbers such that and z +z +z 0 prove that
=r
1 2 3 ⌊ ⌋ = | | = | | = r > 0z1 z2 z3 1 2 3 ≠∣
∣∣
+ +z1z2 z2z3 z3z2
+ +z1 z2 z3
∣
∣∣
(OR)
If z=x+iy and arg ,then show that x +y =1.( ) =z − 1
z + 1
π
22 2
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41) a)
b)
42) a)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
*****************************************
If 1, ω, ω are the cube roots of unity then show that (1+5ω +ω ) (1+5ω+ω ) (5+ω+ω ) =642 2 4 2 5
(OR)
Find all the roots and also find the product of its roots.(2 − 2i)1
3
Show that, if p,q,r are rational, the roots of the equation x −2px+p −q +2qr−r =0 are rational.2 2 2 2
(OR)
Discuss the nature of the roots of the following polynomials:x +1947x +15x +26x +20192018 1950 8 6
If a, b, c, d and p are distinct non-zero real numbers such that (a +b +c ) p -2 (ab+bc+cd) p+(b +c +d )≤ 0 the n. Prove
that a,b,c,d are in G.P and ad=bc
2 2 2 2 2 2 2
(OR)
Find the product in rectangular from(cos + isin ) .6(cos + isin )3
2
π
3
π
3
5π
6
5π
6
Represent the complex numbe in polar form.1 + i 3√
(OR)
Show that the equation 2x −6x+7=0 cannot be satisfied by any real values of x.2
Solve the equation (x-2)(x-7)(x-3)(x+2)+19=0
(OR)
Find the principal argument Arg z , when z = −2
1 + i 3√
Show that the polynomial 9x +2x -x -7x +2 has at least six imaginary roots.9 5 4 2
b)
43) a)
b)
44) a)
b)
45) a)
b)
46) a)
b)
47) a)
b)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
For answers WhatsApp 8056206308
REVISION TEST 1 [ CHAPTER 1 & 2 ]
12th Standard 2019 EM
Maths
RAVI MATHS TUITION CENTER , PH - 8056206308
Date : 01-Jul-19
Reg.No. :
Time : 02:30:00 Hrs Total Marks : 9020 x 1 = 20
If A = 3 51 2 , B = adj A and C = 3A, then
|adjB||C| =
(a) 13 (b)
19 (c)
14 (d) 1
[ ]
If A = 2 01 5 and B =
1 42 0 then |adj (AB)| =
(a) -40 (b) -80 (c) -60 (d) -20
[ ] [ ]
If P =
1 x 01 3 02 4 −2
is the adjoint of 3 × 3 matrix A and |A| = 4, then x is
(a) 15 (b) 12 (c) 14 (d) 11
[ ]If A A is symmetric, then A =
(a) A (b) (A ) (c) A (d) (A )
T −1 2
-1 T 2 T -1 2
If A =
35
45
x35
and A = A , then the value of x is
(a) −45 (b)
−35 (c)
35 (d)
45
[ ] T −1
The rank of the matrix
12−1
24−2
36−3
48−4
is
(a) 1 (b) 2 (c) 4 (d) 3
[ ]If ρ(A) = ρ([A | B]), then the system AX = B of linear equations is
(a) consistent and has a unique solution (b) consistent (c) consistent and has infinitely many solution (d) inconsistent
Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=
(a) ±2 (b) ±4 (c) ±8 (d) ±12
The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if
(a) k ≠ 0 (b) -1 < k < 1 (c) -2 < k < 2 (d) k=0
If A =cosx sinx−sinx cosx and A(adj A) =λ
1 00 1 then λ is
(a) sinx cosx (b) 1 (c) 2 (d) none
( ) ( )In the non - homogeneous system of equations with 3 unknowns if ρ(A) = ρ([AIB]) = 2, then the system has _______
(a) unique solution (b) one parameter family of solution (c) two parameter family of solutions (d) in consistent
Cramer's rule is applicable only when ______
(a) Δ ≠ 0 (b) Δ = 0 (c) Δ =0, Δ =0 (d) Δ = Δ = Δ =0x x y z
The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
(a) 1
2|z|2 (b) |z| (c)
3
2|z|2 (d) 2|z|2 2
If z is a non zero complex number, such that 2iz z̄ then |z|is then |z| is
(a) 1
2 (b) 1 (c) 2 (d) 3
2=
If z − 2 + i ≤ 2 then the greatest value of |z| is
(a) √3 − 2 (b) √3 + 2 (c) √5 − 2 (d) √5 + 2If |z =1,|z |=2|z |=3 and |9z z +4z z +z z |=12, then the value of |z +z +z | is
(a) 1 (b) 2 (c) 3 (d) 41| 2 3 1 2 1 3 2 3 1 2 3
If z is a complex number such that zεC /R and z +1
zϵR then|z| is
(a) 0 (b) 1 (c) 2 (d) 3
If ω = cis2π
3, then the number of distinct roots of
z + 1 ω ω2
ω z + ω2 1
ω2 1 z + ω
(a) 1 (b) 2 (c) 3 (d) 4
| |The complex number z which satisfies the condition
1+z1−z =1 lies on
(a) circle x +y =1 (b) x-axis (c) y-axis (d) the lines x+y=1
| |2 2
If x=cosθ + i sinθ, then x +1
xn is ______
(a) 2 cos nθ (b) 2 i sin nθ (c) 2 cosθ (d) 2 i sinθ
n
n n
10 x 2 = 20
If F(α) =
cosα 0 sinα0 1 0
−sinα 0 cosα, show that [F(α)] = F(-α).[ ] -1
If A = 3 27 5 and B =
−1 −35 2 , verify that (AB) = B A[ ] [ ] -1 -1 -1
Find the matrix A for which A5 3−1 −2 =
14 77 7 .[ ] [ ]
Find the rank of the following matrices by row reduction method:
125
1−1−1
137
3411
[ ]Solve the following system of linear equations by matrix inversion method:2x + 5y = −2, x + 2y = −3
Write the following in the rectangular form:¯
(5 + 9i) + (2 − 4i)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
If z=x+iy , find the following in rectangular form.
Re1
z
( )If |z|= 3, show that 7 ≤ |z + 6 − 8i| ≤ 13.
Find the square roots of 4+3i
Show that the following equations represent a circle, and, find its centre and radius
|2z + 2 − 4i| = 210 x 3 = 30
Find a matrix A if adj(A) =
7 7 −7−1 11 711 5 7
.[ ]Verify the property (A ) = (A ) with A =
2 91 7 .T -1 -1 [ ]
Prove that cosθ −sinθsinθ cosθ is orthogonal[ ]
Solve 2x - 3y = 7, 4x - 6y = 14 by Gaussian Jordan method.
If the rank of the matrix
λ −1 00 λ −1−1 0 λ
is 2, then find ⋋.[ ]If z =3-2i and z =6+4i, find
z1
z21 2
Find the cube roots of unity.
Simplify the following:
∑102n=1i
n
Show that the complex numbers 3 + 2i, 5i, -3 + 2i and -i form a square.
Find the locus of Z if |3z - 5| = 3 |z + 1| where z=x+iy.
7 x 5 = 35
(OR)
Find the condition on a, b and c so that the following system of linear equations has one parameter family ofsolutions: x + y + z = a, x + 2y + 3z = b, 3x + 5y + 7z = c.
If z =3+4i,z =5-12i, and z =6+8 , find |z |,|z |,|z |,|z +z |,|z -z |,and|z +z |1 2 3 1 2 3 1 2 2 3 1 3
(OR)
Find the modulus and principal argument of the following complex numbers:
−√3 − i
Find the rank of the following matrices which are in row-echelon form :
6000
0200
−9000
[ ]
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41) a)
b)
42) a)
b)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
*****************************************
(OR)
Find the quotient
2 cos9π
4+ isin
9π
4
4 cos−3π
2+ sin
−3π
2
in rectangular form( )
( ( ) ( ))
Find the following i(2 + i)3
(1 + i)2| |(OR)
Find the radius and centre of the circle zz̄-(2+3i)z-(2-3i)z̄+9 =0 where z is a complex number.
If z=x+iy and argz − 1
z + 1=
π
2 ,then show that x +y =1.( ) 2 2
(OR)
Test for consistency of the following system of linear equations and if possible solve:4x − 2y + 6z = 8, x + y − 3z = −1, 15x − 3y + 9z = 21.
Find the rank of each of the following matrices:
4 3−3 −16 7
1 −2−2 4−1 2[ ]
(OR)
Using Gaussian Jordan method, find the values of λ and μ so that the system of equations 2x - 3y + 5z = 12, 3x + y + λz=μ, x - 7y + 8z = 17 has (i) unique solution (ii) infinite solutions and (iii) no solution.
Let z ,z , and z be complex numbers such that z1 = z2 = z3 = r > 0and z +z +z ≠ 0 prove that
z1z2 + z2z3 + z3z2
z1 + z2 + z3 =r
1 2 3 ⌊ ⌋ | | | | 1 2 3
| |(OR)
Test for consistency of the following system of linear equations and if possible solve:x - y + z = -9, 2x - 2y + 2z = -18, 3x - 3y + 3z + 27 = 0.
In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball le� to go in the last over. The last ball wasbowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equationof the path is y = ax + bx + c with respect to a xy-coordinate system in the vertical plane and the ball traversed throughthe points (10, 8), (20, 16) (30, 18) can you conclude that Chennai Super Kings won the match?Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with thefarthest boundary line is (70, 0).)
2
43) a)
b)
44) a)
b)
45) a)
b)
46) a)
b)
47) a)
b) Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
REVISION TEST 1 [ CHAPTER 1, 2, 3 ]
12th Standard 2019 EM
Maths
RAVI MATHS TUITION CENTER ,GKM COLONY, CH- 82. PH: 8056206308
Date : 26-Jun-19
Reg.No. :
Time : 02:30:00 Hrs Total Marks : 90FOE ANSWERS WHATSAPP - 8056206308 20 x 1 = 20
If |adj(adj A)| = |A| , then the order of the square matrix A is
(a) 3 (b) 4 (c) 2 (d) 5
9
If A = 2 01 5 and B =
1 42 0 then |adj (AB)| =
(a) -40 (b) -80 (c) -60 (d) -20
[ ] [ ]If A, B and C are invertible matrices of some order, then which one of the following is not true?
(a) adj A = |A|A (b) adj(AB) = (adj A)(adj B) (c) det A = (det A) (d) (ABC) = C B A-1 -1 -1 -1 -1 -1 -1
If A A is symmetric, then A =
(a) A (b) (A ) (c) A (d) (A )
T −1 2
-1 T 2 T -1 2
If A = 1 tan
θ2
−tanθ2 1
and AB = I , then B =
(a) cos2θ2 A (b) cos2
θ2 AT (c) cos2θ I (d) (Sin θ
2)A
[ ]( ) ( ) ( ) 2
If x y = e , x y = e , Δ = m bn d , Δ =
a mc n , Δ =
a bc d , then the values of x and y are respectively,
(a) e , e (b) log (Δ /Δ ), log (Δ /Δ ) (c) log (Δ /Δ ), log(Δ /Δ ) (d) e ,e
a b m c d n1 | | 2 | | 3 | |
(Δ /Δ )2 1 (Δ /Δ )3 1 1 3 2 3 2 1 3 1(Δ /Δ )1 3 (Δ /Δ )2 3
Which of the following is/are correct?(i) Adjoint of a symmetric matrix is also a symmetric matrix.(ii) Adjoint of a diagonal matrix is also a diagonal matrix.(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λ adj(A).(iv) A(adjA) = (adjA)A = |A|I
(a) Only (i) (b) (ii) and (iii) (c) (iii) and (iv) (d) (i), (ii) and (iv)
n
If A is a square matrix of order n, then |adj A| =
(a) |A| (b) |A| (c) |A| (d) Nonen-1 n-2 n
If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2. is inconsistent then k is
(a) -3, - 12 (b) - 1
2 (c) 1 (d) 2
The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is
(a) 1
2|z|2 (b) |z| (c)
3
2|z|2 (d) 2|z|2 2
If z is a non zero complex number, such that 2iz z̄ then |z|is then |z| is
(a) 1
2 (b) 1 (c) 2 (d) 3
2=
If z − 2 + i ≤ 2 then the greatest value of |z| is
(a) √3 − 2 (b) √3 + 2 (c) √5 − 2 (d) √5 + 2
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
If |z|=1, then the value of 1 + z
1 + z is
(a) z (b) z̄ (c) 1
2 (d) 1
If |z =1,|z |=2|z |=3 and |9z z +4z z +z z |=12, then the value of |z +z +z | is
(a) 1 (b) 2 (c) 3 (d) 41| 2 3 1 2 1 3 2 3 1 2 3
If z=x+iy is a complex number such that |z+2|=|z−2|, then the locus of z is
(a) real axis (b) imaginary axis (c) ellipse (d) circle
The principal argument of (sin 40°+i cos40°)5 is
(a) −110° (b) −70° (c) 70° (d) 110°
A polynomial equation in x of degree n always has
(a) n distinct roots (b) n real roots (c) n imaginary roots (d) at most one root
If α,β and γ are the roots of x +px +qx+r, then Σ1α is
(a) -qr (b)
pr (c)
qr (d) - q
p
3 2
The number of real numbers in [0,2π] satisfying sin x-2sin x+1 is
(a) 2 (b) 4 (c) 1 (d) ∞
4 2
The polynomial x +2x+3 has
(a) one negative and two real roots (b) one positive and two imaginary roots (c) three real roots (d) no solution
3
ANSWER 7 ONLY [ Q.NO 30 COMPULSORY ] 7 x 2 = 14
If A = 8 −4−5 3 , verify that A(adj A) = |A|I .[ ] 2
Given A = 1 −12 0 , B =
3 −21 1 and C =
1 12 2 , find a matrix X such that AXB = C.[ ] [ ] [ ]
Decrypt the received encoded message 2 −3 20 4 with the encryption matrix −1 −12 1
and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 - 26 to the letters A -Z respectively, and the number 0 to a blank space.
[ ][ ] [ ]
The complex numbers u,v, and w are related by 1
u=
1
v+
1
w If v=3−4i and w=4+3i, find u in rectangular form.
Show that 2 + i√3 10 − 2 − i√3 10
( ) ( )
Which one of the points10 − 8i , 11+ 6i is closest to1+ i .
If z and z are 1-i, -2+4i then find Imz1z2¯z1
.1 2 ( )If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid, then the volume is increased by 52cubic units. Find the volume of the cuboid.
Find the sum of squares of roots of the equation 2x -8x+6x -3=0.4 2
Find a polynomial equation of minimum degree with rational coe�icients, having 2+√3i as a root.
ANSWER 7 ONLY [ Q.NO 40 COMPULSORY ] 7 x 3 = 21
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
If adj A =
−1 2 21 1 22 2 1
, find A .[ ] −1
Solve the following system of equations, using matrix inversion method:
2x + 3x + 3x = 5, x - 2x + x = -4, 3x - x - 2x = 3.1 2 3 1 2 3 1 2 3
Determine the values of λ for which the following system of equations (3λ − 8)x + 3y + 3z = 0, 3x + (3λ − 8)y + 3z = 0, 3x + 3y +
(3λ − 8)z = 0. has a non-trivial solution.
Simplify 1 + i
1 − i
3−
1 − i
1 + i
3( ) ( )If
z + 3
z − 5i=
1 + 4i
2, find the complex number z
Find z if z=(2+3i)(1− i).−1,
Show that 19 + 9i
5 − 3i
15−
8 + i
I + 2i
15 is purely imaginary.( ) ( )
If α and β are the roots of the quadratic equation 17x +43x−73 = 0 , construct a quadratic equation whose roots are α + 2
and β + 2.
2
Find the condition that the roots of x +ax +bx+c = 0 are in the ratio p:q:r.3 2
Obtain the condition that the roots of x +px +qx+r=0 are in A.P.3 2
ANSWER 7 ONLY 7 x 5=35
(OR)
Test for consistency of the following system of linear equations and if possible solve:x - y + z = -9, 2x - 2y + 2z = -18, 3x - 3y + 3z + 27 = 0.
Find the rank of the matrix
2−36
−242
4−2−1
3−17
by reducing it to an echelon form.[ ]
(OR)
Investigate for what values of λ and μ the system of linear equationsx + 2y + z = 7, x + y + λz = μ, x + 3y − 5z = 5 has(i) no solution(ii) a unique solution(iii) an infinite number of solutions
Solve: 2x+
3y+
10z= 4,
4x−
6y+
5z= 1,
6x+
9y−
20z
=2
(OR)
For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ is consistent.2
Solve the equation (x-2)(x-7)(x-3)(x+2)+19=0
(OR)
Solve: (2x - 3x + 1) (2x + 5x + 1) = 9x .2 2 2
Discuss the nature of the roots of the following polynomials:x -19x +2x +5x +115 4 3 2
(OR)
If the sum of the roots of the quadratic equation ax + bx + c = 0 (abe≠ 0) is equal to the sum of the squares of their
reciprocals, then ac,ba,cb
are H.P.
2
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41) a)
b)
42) a)
b)
43) a)
b)
44) a)
b)
45) a)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
*****************************************
If z ,z and z ,are complex numbers such that |z |=|z |=|z |=|z +z +z |=1 find the value of 1
z1+
1
z2+
1
z31 2 3 1 2 3 1 2 3 | |
(OR)
Find the following i(2 + i)3
(1 + i)2| |Find the modulus and principal argument of the following complex numbers.
−√3 + i
(OR)
Find the radius and centre of the circle zz̄-(2+3i)z-(2-3i)z̄+9 =0 where z is a complex number.
Solve, by Cramer’s rule, the system of equationsx - x = 3, 2x + 3x + 4x = 17, x + 2x = 7.1 2 1 2 3 2 3
b)
46) a)
b)
47) a)
b)
Pada
sala
i
Pada
sala
i
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
www.Padasalai.Org
Padasalai TrbTnpsc
