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CBSE Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 5 - MCQExams.com

Find the modulus and amplitude of 3i
  • |z|=2;amp(z)=5π6
  • |z|=4;amp(z)=5π6
  • |z|=4;amp(z)=π6
  • none of these
Find the value of x3+7x2x+16, where x=1+2i
  • 17+24i
  • 24+17i
  • 1724i
  • 2417i

The amplitude of

sinπ5+i(1cosπ5)

  • π5
  • 2π5
  • π10
  • π15
If z_1, z_2, \varepsilon C are such that |z_1 + z_2|^2 = |z_1|^2 + |z_2|^2 then \displaystyle \frac{z_1}{z_2} is
  • zero
  • purely real
  • purely imaginary
  • complex
(1 + i)^8 + (1 -i)^8 =
  • 16
  • -16
  • 32
  • -32
Modulus of \displaystyle \frac{cos \theta- isin\theta }{sin\theta - icos\theta} is
  • 0
  • 2\theta
  • \pi - 2\theta
  • none of these
The number of real solutions of the equation \displaystyle{\left(\frac{5}{7}\right)^2}=-x^2+2x-3 is equal to 
  • 2
  • zero
  • 1
  • none of these
Number of integer values of k for which the quadratic equation \displaystyle 2x^{2}+kx-4=0 will have two rational solutions is
  • 1
  • 2
  • 4
  • 5
Find the value of: i^2 + i^4 + i^6 +..... upto (2n +1) terms.
  • i
  • -i
  • 1
  • -1
i^n + i^{n + 1} + i^{n + 2}+ i^{n + 3} (n   \in   N) is equal to
  • 4
  • 1
  • 0
  • 2
The argument of the complex number z = sin  \alpha + i (1 - cos  \alpha) is
  • 2 sin \displaystyle \frac{\alpha}{2}
  • \displaystyle \frac{\alpha}{2}
  • \alpha
  • none of these
Solve:
 \displaystyle \left|(1 + i)\frac{(2+i)}{(3 + i)}\right|
  • \dfrac{1}{2}
  • \dfrac{-1}{2}
  • 1
  • -1
In the argand diagram, if O,P and Q represents respectively the origin and the complex numbers z and z+iz then the \angle OPQ is
  • \displaystyle\frac {\pi}{4}
  • \displaystyle\frac {\pi}{3}
  • \displaystyle\frac {\pi}{2}
  • \displaystyle\frac {2\pi}{3}
The modulus of (1 + i) (1 + 2i) (1 + 3i) is equal to
  • \sqrt10
  • \sqrt 5
  • 5
  • 10
The number of real roots of the equation \displaystyle \frac{A^{2}}{x} +\frac{B^{2}}{x-1}=1 where A and B are real numbers not equal to zero simultaneously, is :
  • 1 \;or\; 2
  • 1
  • 2
  • None
Find the value of k for which the quadratic equation \displaystyle \left ( k-2 \right )x^{2}+2\left ( 2k-3 \right )x+5k-6=0 has equal roots
  • 1
  • 3
  • A and B both
  • none of these
Number of complex numbers z satisfying \left| 2z \right| =\left| 2z-1 \right| =\left| 2z+1 \right| is equal to-
  • 0
  • 1
  • 2
  • 3
If both a and b belong to the set \displaystyle \left\{ 1,2,3,4 \right\} then the number of equations of the form ax^{2}+bx+1=0 having real roots is :
  • 10
  • 7
  • 6
  • 12
If 0 \leq argz \leq \displaystyle \frac{\pi}{4}, then the least value of \sqrt 2 |2z - 4| is
  • 6
  • 1
  • 4
  • 2
If \displaystyle z= (i)^{(i)^{(i)}} where i = \sqrt{-1}, then z is equal to
  • -i
  • -1
  • 1
  • i
The roots of the equations \displaystyle x^{2}-x-3=0 are
  • Imaginary
  • Rational
  • Irrational
  • None of these
If the roots of the equation \displaystyle \left ( a^{2}+b^{2} \right )x^{2}-2b\left ( a+c \right )x+\left ( b^{2}+c^{2} \right )=0 are equal then
  • 2b = ac
  • \displaystyle b^{2}=ac
  • \displaystyle b=\frac{2ac}{a+c}
  • b = ac
The value (s) of k for which the quadratic equation \displaystyle kx^{2}-kx+1=0 has equal roots is
  • k = 0 only
  • k = 4 only
  • k = 0, 4
  • k = -4
Let z = x + iy & amp (e^{z^2}) = amp (e^{(z+i)}). If y = (x) is a function, then y(3) is equal to 
  • \displaystyle \frac{1}{2}
  • \displaystyle \frac{1}{3}
  • \displaystyle \frac{1}{4}
  • \displaystyle \frac{1}{5}
The quadratic equations \displaystyle x^{2}-5x+3=0 has 
  • no real roots
  • two distinct real roots
  • two equal real roots
  • more than two real roots
Find the value of 
arg\left ( \left ( 1+i \right )^{i} \right )
  • \displaystyle \dfrac{1}{4}ln\left ( 2 \right )
  • \displaystyle \dfrac{1}{2}ln\left ( 2 \right )
  • \displaystyle \dfrac{1}{2}ln\left (\dfrac{1}{ 2} \right )
  • \displaystyle ln\left ( 2 \right )
Find the value of k for which the equation (k+1){x}^{2}-2(k-1)x+1=0 has real and equal roots
  • 1,-2
  • 0,4
  • -1,3
  • 0,3
If the roots of the equation \displaystyle x^{2}+px-6=0 are 6 and -1 then the value of p is
  • 2
  • 3
  • -5
  • 5
The roots of the equation, where \displaystyle a\: \: \epsilon \: \: R  are 
\displaystyle x^{2}+ax-4=0
  • Real and distinct
  • Equal
  • Imaginary
  • Real
If the roots of the equation \displaystyle (a^{2}+b^{2})x^{2}-2b(a+c)x+(b^{2}+c^{2})=0 are equal then =
  • 2b = ac
  • \displaystyle b^{2}=ac
  • \displaystyle b=\frac{2ac}{a+c}
  • b = ac
If the equation \displaystyle x^{2}-2kx-2x+k^{2}=0 has equal roots the value of k must be
  • zero
  • either zero or \displaystyle -\frac{1}{2}
  • \displaystyle -\frac{1}{2}
  • either \displaystyle \frac{1}{2} or \displaystyle -\frac{1}{2}
For what value of k will \displaystyle x^{2}-\left ( 3k-1 \right )x+2k^{2}+2k=11 have equal roots?
  • 9, -5
  • -9, 5
  • 9, 5
  • -9, -5
If the equation \displaystyle 16x^{2}+6kx+4=0 has equal roots, then the value of k is 
  • \displaystyle \pm 8
  • \displaystyle \pm \frac{8}{3}
  • \displaystyle \pm \frac{3}{8}
  • 0
Which of the following equation has two equal real toots ?
  • \displaystyle 3x^{2}+14x-5=0
  • \displaystyle 4x^{2}+2x-1=0
  • \displaystyle 9x^{2}-6x+1=0
  • \displaystyle x^{2}-5x+4=0
For what values of k will the quadratic equation : \displaystyle { 2x }^{ 2 }-kx+1=0 have real and equal roots?
  • \displaystyle \pm 2\sqrt { 2 }
  • \displaystyle \pm \sqrt { 2 }
  • \displaystyle \pm 3\sqrt { 2 }
  • \displaystyle \pm \sqrt { 3 }
The roots of 2{x}^{2}-6x+3=0 are
  • rational
  • equal
  • irrational
  • imaginary
Given that kx(x-2)+6=0 has real and equal roots, the root is
  • 2
  • -1
  • 1
  • \cfrac{1}{2}
Find the value of 'm' so that the equation \displaystyle { 9x }^{ 2 }-8mx-9=0 has one root as the negative of the other. 
  • 0
  • 1
  • 2
  • None of these
The value of k for which 4{x}^{2}-4\sqrt {3}x+k=0 is satisfied by only one real value of x is
  • \sqrt 6
  • -3
  • 3
  • \cfrac{1}{\sqrt {3}}
kx^2-2\sqrt 5x +4 = 0
For what value of k will the quadratic equation have real and equal roots ?
  • \displaystyle \frac { 2 }{ 3 }
  • \displaystyle \frac { 4 }{ 5 }
  • \displaystyle \frac { 5 }{ 4 }
  • \displaystyle \frac { 3 }{ 2 }
For what value of 'k' the equation \displaystyle \left( k+3 \right) { x }^{ 2 }-\left( 5-k \right) x+1=0 has coincident roots ?
  • 1, 13
  • 1, 12
  • 3, 13
  • None of these
For what value of k will the quadratic equation \displaystyle { 2x }^{ 2 }+3x+k=0 have real equal roots ?
  • \displaystyle \frac { 3 }{ 8 }
  • \displaystyle \frac { 8 }{ 3 }
  • \displaystyle \frac { 9 }{ 8 }
  • \displaystyle \frac { 8 }{ 9 }
Find the value of k for which the equation
{x}^{2}+kx+81=0 and {x}^{2}-6\sqrt {2}x+k=0 has both real roots, k> 0
  • k=9
  • k=18
  • k=3\sqrt {2}
  • No such value
Find the value of k for which the equation {x}^{2}-6x+k=0 has distinct roots.
  • k> 9
  • k=6,7 only
  • k<9
  • k=9
The values of b for which the equation \displaystyle { 2bx }^{ 2 }-40x+25=0 has equal root is :
  • 5
  • 6
  • 7
  • 8
For what value of k will the quadratic equation:  \displaystyle { kx }^{ 2 }+4x+1=0 have real and equal roots ?
  • 2
  • 3
  • 4
  • 1
If z_1, z_2 and z_3 are complex numbers such that |z_1| = |z_2| = |z_3| = \left | \displaystyle \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right | = 1, then |z_1 + z_2 + z_3| is
  • equal to 1
  • less than 1
  • greater than 3
  • equal to 3
If k be the ratio of the roots of the equation  \displaystyle x^{2}-px+q=0     , the value of  \displaystyle \frac{k}{1+k^{2}}    is
  • \displaystyle \frac{q^{2}-2p}{p}
  • \displaystyle \frac{q}{p^{2}-2q}
  • \displaystyle \frac{p}{q^{2}-2p}
  • \displaystyle \frac{p}{p^{2}-2q}
For what values of k, will quadratic equation \displaystyle { 9x }^{ 2 }+3kx+4=0 have real and equal roots? 
  • \displaystyle \pm 4
  • \displaystyle \pm 3
  • \displaystyle \pm 2
  • \displaystyle \pm 1
For what values of k will the quadratic equation :  \displaystyle { 3x }^{ 2 }+kx+3=0 have real equal roots? 
  • \displaystyle \pm \sqrt { 3 }
  • \displaystyle \pm \sqrt { 6 }
  • \displaystyle \pm 6
  • \displaystyle \pm 3
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