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Questions >> JEEMAIN and NEET >> Mathematics >> Class11 >> Complex Numbers and Quadratic Equations

if one root of the equation 5x^2+13x+k=0 is the reciprocal of the other then k=?

answered Jun 21, 2015 by pady_1

1 answer

find all possible values of a for which the expression (ax^2-7x+5) /(5x^2-7x+a) may be capable of all values, x being any real quantity of

answered Apr 16, 2015 by sharmaaparna1

1 answer

if p>2 and p belongs to N, then the equation x cube -px+1=0 cannot have

answered Apr 16, 2015 by sharmaaparna1

1 answer

let a,b,c be non-zero real no such that integral (1+(cosx)^8)(ax^2+bx+c)dx when limits applied from 0-1=integral(1+(cosx)^8)(ax^2+bx+c)dx when limits applied from 0-2 . Then the equation ax^2+bx+c=0 has

asked Apr 13, 2015 by nimmy1357

0 answers

The value of P for which the sum of squares of roots of equation $x^2-(p-2)x-(p+1)=0$ attains the least value is :

answered Apr 15, 2014 by sreemathi.v

1 answer

Given, $(4+i)(z+\overline{z})-(3+i)(z-\overline{z})+26i=0$ then value of $\mid z\mid^2$ is

answered Apr 9, 2014 by sreemathi.v

1 answer

If $z=\sqrt{20i-21}+\sqrt{20i+21}$ ,then possible value of arg(z) equals

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z\mid=2$ ,then set of points $x+iy=z-\large\frac{1}{z}$ lie on,

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\big|z-\large\frac{4}{z}\big|$ $=2$ ,the maximum value of $\mid z\mid$ is equal to

answered Apr 9, 2014 by sreemathi.v

1 answer

If $z_1+z_2+z_3=0$ and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid=1$ then value of $z_1^2+z_2^2+z_3^2$ equals

answered Apr 9, 2014 by sreemathi.v

1 answer

Let $z,\omega$ be two comlex numbers such that $\overline{z}+i\overline{\omega}=0$ and $arg(z\omega)=\pi$ , then $arg(z)$ equal to

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z+4\mid\leq 3$ ,then maximum value of $\mid z+1\mid$ is

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z^2-1\mid=\mid z\mid^2+1$ then $z$ lies on

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\mid z\mid=1$ and $z\neq \pm 1$ then $\large\frac{z}{1-z^2}$ lie on

answered Apr 9, 2014 by sreemathi.v

1 answer

Let $z=\begin{vmatrix}1&2+3i&4+5i\\2-3i&6&7+8i\\4-5i&7-8i&-9\end{vmatrix}$ ,then

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\omega$ is a complex root of unity, one root of the equation $\begin{vmatrix}x+1 &\omega&\omega^2\\\omega&x+\omega^2&1\\\omega^2&1&x+\omega\end{vmatrix}=0$ is

answered Apr 9, 2014 by sreemathi.v

1 answer

$z=\large\frac{1}{1-\cos \theta+i\sin \theta}$ .Re(z) is equal to

answered Apr 9, 2014 by sreemathi.v

1 answer

Given $x=2+5i$ , the value of $x^3-5x^2+33x-19$ is

answered Apr 9, 2014 by sreemathi.v

1 answer

If $\omega=\large\frac{z-\perp}{z+1}$ $\quad (z\neq -\perp)$ and $\mid z\mid =\perp$ then $Re(\omega)$ equals

answered Apr 9, 2014 by sreemathi.v

1 answer

$z$ and $\omega$ are two non zero complex numbers such that $\mid z\mid=\mid \omega\mid$ and $arg(z)+arg(\omega)=\pi$ .Then $z$ equals

answered Apr 9, 2014 by sreemathi.v

1 answer

If $z\neq 0$ is a complex no having arg= $\large\frac{\pi}{4}$ ,then

answered Apr 9, 2014 by sreemathi.v

1 answer

Let $a,b$ be real numbers between $0\; and\; 1$ such that $z_1=1+bi,z_2=a+i$ and $z_3=0$ forms an equilateral triangle then

answered Apr 9, 2014 by sreemathi.v

1 answer

The complex numbers $\sin x+i\cos 2x$ and $\cos x-i\sin 2x$ are conjugate for

answered Apr 9, 2014 by sreemathi.v

1 answer

If complex numbers $z_1,z_2,z_3$ represents vertices of an equilateral triangle and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid$ then

answered Apr 9, 2014 by sreemathi.v

1 answer

If $z$ is a complex number such that $\left|\; z \;\right| \geq 2$ then the minimum value of $\large\left|\normalsize z \normalsize + \large\frac{1}{2} \right |$

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If the coefficients of $x^3$ and $x^5$ in the expansion of $(1+ax+bx^2)(1-2x)^{18}$ in powers of $x$ are both zero, then $(a,b)$ is equal to:

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If $\large\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P., then the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has

answered Aug 8, 2013 by rvidyagovindarajan_1

1 answer

If the ratio of the roots of $ax^2+bx+c=0$ is equal to the roots of the equation $x^2+x+1=0$ , then $a,b,c$ are in ?

answered Aug 8, 2013 by rvidyagovindarajan_1

1 answer

If $\alpha$ is the fifth root of unity, then the value of $log_2 |1+\alpha+\alpha^2+\alpha^3-\large\frac{1}{\alpha}$ $|=?$

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If for any complex number $z$ , $|z-1|=1$ , then $\large\frac{z-2}{z}=?$

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $|z+\overline z|+|z-\overline z|=8$ then $z$ lies on ?

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $z_r(r=1,2,......7)$ are the roots of $(z_r+1)^7+z_r^7=0$ , then $\sum\limits_{r=1}^{7} Re(z_r)=?$

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $p,q\in \{1,2,3,4\},$ then the number of equations of the form $px^2+qx+1=0$ having real roots is?

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $3+\sqrt 2 i$ is a root of of $x^2+px+q=0$ , then $(p,q)=?$

answered Aug 6, 2013 by rvidyagovindarajan_1

1 answer

If $z$ is a complex number having non zero imaginary part and $z^2+z+1=a$ where $a$ is real, then $a$ cannot take which of the following values?

answered Aug 5, 2013 by rvidyagovindarajan_1

1 answer

The value of $b$ for which the eqns., $x^2+bx-1=0,\:x^2+x+b=0$ have one common root is

answered Aug 5, 2013 by rvidyagovindarajan_1

1 answer

If the eqns., $x^2-6x+a=0$ and $x^2-5x+6=0$ have one root in common and the other roots are in the ratio 4:3, then the common root is

answered Aug 5, 2013 by rvidyagovindarajan_1

1 answer

If $\cos\theta+2\cos\alpha+3\cos\beta=\sin\theta+2\sin\alpha+3\sin\beta=0$ , then $\sin\;3\theta+8\sin\;3\alpha+27\sin\;3\beta=?$

answered Aug 2, 2013 by rvidyagovindarajan_1

1 answer

If $(\cos\alpha+i\sin\alpha)(\cos2\alpha+i\sin2\alpha)....(\cos n\alpha+i \sin n\alpha)$ = 1, then $\alpha$ = ?

answered Aug 2, 2013 by rvidyagovindarajan_1

1 answer

The common roots to the equations $z^3+2z^2+2z+1=0\:\:and\:\:z^{149}+z^{100}+1=0$ are

answered Aug 2, 2013 by rvidyagovindarajan_1

1 answer

For any complex number $z$ , the minimum value of $|z|+|z-1|=?$

answered Aug 1, 2013 by rvidyagovindarajan_1

1 answer

The cube roots of $-1$ are?

answered Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $z_r=cos(\large\frac{\pi}{3^r})$ $+isin(\large\frac{\pi}{3^r})$ , where $r=1,2,3...........then \:\:z_1.z_2.z_3.....................\infty=?$

answered Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $a=\cos\alpha+i \sin\alpha$ , $b=\cos\beta+i \sin\beta$ , $c=\cos\gamma+i\sin\gamma$ and $\large\frac{b}{c}+\frac{c}{a}+\frac{a}{b}$ = 1, then $\cos(\beta-\gamma)+\cos(\gamma-\alpha)+\cos(\alpha-\beta)$ = ?

answered Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $R_e\bigg(\large\frac{z-8i}{z+6}\bigg)$ $=0$ , then $z$ lies in the curve

answered Aug 1, 2013 by rvidyagovindarajan_1

1 answer

If $n$ is a positive integer, then $(1+i)^n+(1-i)^n=?$

answered Jul 31, 2013 by rvidyagovindarajan_1

1 answer

$\large\frac{(cosx+isinx)(cosy+isiny)}{(cotu+i)(1+itanv)}=?$

answered Jul 31, 2013 by rvidyagovindarajan_1

1 answer

If $\large\frac{3}{2+\cos\theta+i\sin\theta}=$ $x+iy$ , then $(x-1)(x-3)=?$

answered Jul 31, 2013 by rvidyagovindarajan_1

1 answer

If $\omega$ is cube root of $1$ and $\alpha,\beta,\gamma$ are cube roots of $p$ , then for any real numbers $x,y,z$ the value of $\large\frac{x\alpha+y\beta+z\gamma}{x\beta+y\gamma+z\alpha}$ is ?

answered Jul 28, 2013 by rvidyagovindarajan_1

1 answer

For any integer $n$ , the argument of $z=\large\frac{(\sqrt 3+i)^{4n+1}}{(1-\sqrt 3 i)^{4n}}$ is ?

answered Jul 28, 2013 by rvidyagovindarajan_1

1 answer

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