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Worksheets12 maths august monthly one mark quiz
Total questions: 50
Worksheet time: 25mins
zeros of polynomial x³+64=0 is
0
4
4i
-4
A polynomial equation in x of degree n always has
n distinct roots
n real roots
exactly n roots
atmost one roots
If z= 12-5i Then |z | is
7
13
12
5
If z=x+iy is a complex number such that |z+2 |= |z-2 | then the locus of z is
real axis
imaginary axis
ellipse
circle
If z is a complex number such that z∈c\R and z+1/z ∈R Then |z | is
0
1
2
3
Area of the triangle formed by the complex numbers z,iz,and z+iz in the argands diagram
1/2 |z|²
|z|²
3/2. |Z|²
2|z|²
The principal argument of (sin 40º+icos40º)⁵ is
-110º
-70º
70º
110º
The principal argument of 3/ -1+i is
-5π/6
-2π/4
-3π/4
-π/2
If ω≠ 1 is a cubic root of unit and (1+ω)⁷= A+Bω then (A ,B) equals
(1 ,0)
(-1 , 1)
(0, 1)
(1 ,1)
If α and β are the roots of x²+x+1=0 then α²⁰²⁰+β²⁰²⁰ is
-2
-1
1
2
The product of all four values of (cosπ/3+isinπ/3)³/⁴ is
-2
-1
1
2
The principal value of the amplitude of (1+i) is
π/4
π/12
3π/4
π
If x=cosθ+isinθ then xⁿ+1/xⁿ is
2cosnθ
2isinnθ
2ⁿcosnθ
-2isinnθ
Which of the following is incorrect?
Re(z)≤|z|
Im(z)≤|z|
Re(z)= |z| when z is real
Re(z)≥|z|
Which of the following is incorrect?
The number of distinct roots is n
The roots are in GP with common rates is 2π/n
The arguments are in AP with common difference (2π/n)
Product of the roots is 0 and the sum of the roots is ±1
When Z = x+iy then iz means
X- iY
-x+iy
Rotation of Z it by 90 degree in the counterclockwise direction
Rotation of digits by 90 degree in the clockwise direction
If α, β, γ are the roots of the equation x³-3x+11=0 then α + β +γ is
0
-3
3
11
If α, β, γ are the roots of the equation 9x³-7x+6=0 then α β γ is
-7/9
7/9
0
-2/3
If α β γ are the roots of x³+px²+qx+r then ∑ 1/α is
-q/r
-p/r
q/r
-q/p
If f and g are polynomials of degree m and n respectively and if h(x) = (f°g) (x) then the degree of h is
mn
m+n
mⁿ
nᵐ
Sin(tan⁻¹x), |x |<1 is equal to
If sin⁻¹x/5 + cosec⁻¹5/4=π/2 then the value of x is
4
5
2
3
If sin⁻¹x + cot⁻¹(1/2)=π/2 then x is equal to
if |x | ≤1 then 2tan⁻¹x-cot⁻¹x= tan⁻¹1/√3
0
if the function f(x)= sin⁻¹(x²-3) then x belongs to
tan⁻¹(1/4)+ tan⁻¹(2/9) is equal to
if x=1/5 the value of cos(cos⁻¹x+ 2sin⁻¹x) is
the domain of the function defined by f(x)= sin⁻¹√x-1 is )
[1,2]
[-1,1]
[0,1]
[-1,0]
sin⁻¹(cosx)=π/2-x is valid for
if sin⁻¹x=2sin⁻¹α has a solution then
the number of real numbers in [0,2π] satisfying sin⁴x-2sin²x+1=0 is
2
4
1
infinte
-1
5
The polynomial x³-kx²+9x has three real zeros if and only if k satisfies
z
1/z
1
1
-1
1
2
3
4
sin⁻¹(sinx)=x if
x∈[-π/2,π/2]
x∈[-1,1]
x∈(0,π)
x∈R
sec⁻¹(-x)=
-sec⁻¹x
sec⁻¹x
π-sec⁻¹ x
π-cos⁻¹x
sin⁻¹(3/5 )- cos⁻¹(12/13 )+ sec⁻¹( 5/3) - cosec⁻¹ (13/12 )is equal to
2π
π
0
-π
the value of sin⁻¹(cosx) 0≤x≤π is
π-x
x-π/2
π/2-x
x-π
cramers rule applicable only when
∆=0
∆x=0
∆≠0
∆ is singular
If AᵀA⁻¹ is symmetric then A²=
A⁻¹
(Aᵀ)²
Aᵀ
(A⁻¹)²
17
14
19
21
1
2
4
3
2
4
3
1
15
12
14
11
If A, Band C are invertible matrices of some order then which one of the following is not true?
adjA=|A| A⁻¹
adj(AB)= (adjA)(adjB)
detA= (detA)⁻¹
(ABC)= C⁻¹ B ⁻¹A⁻¹
If 0≤θ≤π and the system of equation x+(sinθ)y-(cos θ)z=0 ,(cos θ)x-y+z=0 ,(sinθ)x+y-z=0 has a non trivial solution then θ is
2π/3
π/3
5π/6
π/4
If p(A)=p([A |B]) then the system AX=B of linear equation is
Consistent and has unique solution
Consistent
Consistent hand has infinitely many solution
Inconsistent
If |adj(adjA)|=|A|⁹ the order of the square matrix A is
3
4
2
5
