If be a complex number satisfying then cannot be :
Option: 1
Option: 2
Option: 3
Option: 4
Option d
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Let be such that the equation, has a repeated root , which is also a root of the equation, . If is the other root of this equation, then is equal to:
Option: 1
Option: 2
Option: 3
Option: 4
Nature of Roots 
Let the quadratic equation is ax^{2} + bx + c = 0
D is the discriminant of the equation.
iii) if roots D = 0, then roots will be real and equal, then

ax^{2} – 2bx + 5 = 0 having equal roots or and
Put in the second equation
Correct Option 2
View Full Answer(1)The number of real roots of the equation, is :
Option: 1
Option: 2 4
Option: 3 1
Option: 4 2
Transcendental function 
Transcendental functions: the functions which are not algebraic are called transcendental functions. Exponential, logarithmic, trigonometric and inverse trigonometric functions are transcendental functions.
Exponential Function: function f(x) such that is known as an exponential function.
Logarithmic function: function f(x) such that is called logarithmic function
If a > 1 If a < 1
Properties of Logarithmic Function

Quadratic Equation 
The root of the quadratic equation is given by the formula:
Where D is called the discriminant of the quadratic equation, given by ,

Let
Now the equation
Let
Only positive value possible so
x=0 is the only solution.
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The least positive value of 'a' for which the equation, has real roots is
Option: 1 8
Option: 2 6
Option: 3 4
Option: 42
Nature of Roots 
Let the quadratic equation is ax^{2} + bx + c = 0
D is the discriminant of the equation.
ii) If D > 0, then roots will be real and distinct.
iii) if roots D = 0, then roots will be real and equal, then

least positive value is 8.
View Full Answer(1)If the equation, has conjugate complex roots and they satisfy , then:
Option: 1
Option: 2
Option: 3
Option: 4
Nature of Roots 
Let the quadratic equation is ax^{2} + bx + c = 0
D is the discriminant of the equation.
i) if D < 0, then root are in the form of complex number,
If a,b,c ∈ R (real number) then roots will be conjugate of each other, means if p + iq is one of
the roots then other root will be p  iq

Let be roots of the equation
so
So,
Correct Option 3
View Full Answer(1)The most abundant elements by mass in the body of a healthy human adult are : Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight (in kg) which a 75 kg person would gain if all atoms are replaced by atoms is :
Option: 1 7.5
Option: 2 10
Option: 3 15
Option: 4 37.5
Given that
Mass of the person = 75 kg
Mass of _{1}H^{1} present in person = 10% of 75 kg = 7.5 kg
Since Mass of _{1}H^{2} is double the Mass of _{1}H^{1}
So, Mass of _{1}H^{2} will be in person = 2 X 7.5 kg =15 kg
Thus, increase in weight = 15  7.5 = 7.5 kg
Therefore, Option (1) is correct
View Full Answer(1)Let be a solution of the differential equation, If then is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
Formation of Differential Equation and Solutions of a Differential Equation 
This is the general solution of the differential equation (2), which represents the family of the parabola (when a = 1) and one member of the family of parabola is given in Eq (1).
Also, Eq (1) is a particular solution of the differential equation (2).
The solution of the differential equation is a relation between the variables of the equation not containing the derivatives, but satisfying the given differential equation.
A general solution of a differential equation is a relation between the variables (not involving the derivatives) which contains the same number of the arbitrary constants as the order of the differential equation.
Particular solution of the differential equation obtained from the general solution by assigning particular values to the arbitrary constant in the general solution.

Correct Option (3)
View Full Answer(1)The correct order of the atomic radii of C, Cs, Al and S is :
Option: 1
Option: 2
Option: 3
Option: 4
Periodicity of atomic radius and ionic radius in period 
In a period from left to right the effective nuclear charge increases because the next electron fills in the same shell. So the atomic size decrease.
 wherein
Electronegativity and atomic radius 
The attraction between the outer electrons and the nucleus increases as the atomic radius decreases in a period.
 wherein
Size of atom and ion in a group 
In a group moving from top to the bottom the number of shell increases.So the atomic size increases.
 wherein
As we know that
From Left to right in a period size decreases and when going down the group size increases
Therefore, Option(2) is correct
View Full Answer(1)
The IUPAC symbol for the element with atomic number 119 would be:
Option: 1 uue
Option: 2une
Option: 3 unh
Option: 4 uun
Nomenclature of elements with atomic number >100 
The name is derived directly from the atomic number of the element using the following numerical roots:
0 = nil
1 = un
2 = bi
3 = tri
4 = quad
5 = pent
6 = hex
7 = sept
8 = oct
9 = enn
Eg:
Atomic number 
Name 
Symbol 
101 
Mendelevium (Unnilunium) 
Md (Unu) 
102 
Nobelium (Unnilbium) 
No (Unb) 

uue
1 1 9
Un Un ennium
Therefore, Option(1) is correct.
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