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## Crack CUET with india's "Best Teachers"

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• Faculty Support #### If  for  then Option: 1 Option: 2 Option: 3 Option: 4 Use

Correct Option (3)

#### If be a complex number satisfying then cannot be :  Option: 1 Option: 2 Option: 3 Option: 4 Complex number -

A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form as a + bi where a is the real part and b is the imaginary part. For example, 5 + 2i is a complex number. So, too, is 3 + 4i√3. We write the complex number by C or z = a + ib, a and b are real number (a, b ∈ R).

• a is real part of the complex number and denoted by Re(z),

• b is the imaginary part of the complex number and denoted by Im(z),

E.g :    z = 2 + 3i is a complex number.

With Re(z) = 2 and Im(z) = 3

-

Area of triangle, circle (formula) -

Equation of Circle:

The equation of the circle whose center is at the point and have radius r is given by If the center is origin then, , hence equation reduces to |z| = r

Interior of the circle is represented by The exterior is represented by Here z can be represented as x + iy and is represented by  -

z = x + iy

|x| + |y| = 4 Minimum value of |z| = Maximum value of |z| = 4 So |z| can't be Correct Option (1)

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• Faculty Support #### The following system of linear equations   has  Option: 1 infinitely many solutions, satisfying Option: 2 infinitely many solutions, satisfying Option: 3 no solution Option: 4 only the trivial solution.

System of Homogeneous linear equations - If ? ≠ 0, then x= 0, y = 0, z = 0 is the only solution of the above system. This solution is also known as a trivial solution.

If ? = 0, at least one of x, y and z are non-zero. This solution is called a non-trivial solution.

Explanation: using equation (ii) and (iii), we have  This is the condition for a system have Non-trivial solution.

-  so infinite non-trivial solution exist

now equation (1) + 3 equation (3)

10x - 20z = 0

x = 2z

Correct Option 2

#### Let If then :    Option: 1 Option: 2 Option: 3 Option: 4 Elementary row operations -

Elementary row operations

Row transformation: Following three types of operation (Transformation) on the rows of a given matrix are known as elementary row operation (transformation).

i) Interchange of ith row with jth row, this operation is denoted by ii) The multiplication of ith row by a constant k (k≠0) is denoted by iii) The addition of ith row to the elements of jth row multiplied by constant k (k≠0) is denoted by In the same way, three-column operations can also be defined too.

- Correct Option (3)

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• Faculty Support #### Let denote the greatest integer and Then the function, is discontinuous, when x is equal to:  Option: 1 Option: 2 Option: 3 Option: 4   Correct Option (1)

#### 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 ax2 + bx + c = 0

D is the discriminant of the equation.

iii) if roots D = 0, then roots will be real and equal, then -

ax2 – 2bx + 5 = 0 having equal roots or and  Put in the second equation  Correct Option 2

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• Faculty Support #### In the expansion of , if is the least value of the term independent of  when  and is the least value of the term independent of  when , then the ratio is equal to :  Option: 1 Option: 2 Option: 3 Option: 4 General Term of Binomial Expansion