Points of Discontinuity

Q. a, b, c are real numbers in the polynomial p(z)=2z^4+az^3+bz^2+cz+5. If two roots of the equation p(z)=0 are 2 and i, then the value of a is

Q. $y=\frac{1}{t^2+t-2}$ where $t=\frac{1}{x-1}$ then the number of points of discontinuities of $y=f\left(x\right),xϵR$ is

1. Infinite
2. 1
3. 3
4. 2

Q.

The centre and radius of the circle x² + y² + 4x – 6y = 5 is:

1. (– 2, 3), 2√2

2. (– 2, 3), 3√2

3. (2, – 3), 2√2

4. (2, – 3), 3√2

Q. If the two feet of normals drawn from a point to the parabola x² - 6x - 4y +5 =0 be (7, 3) and (-1, 3) then the third foot is A) (1, 0) B) (-3, 8) C) (3, -1) D) (5, 0)

Q.

If the centre of the circle $2x^2+pxy+q{y}^2+2gx+2fy+3$ = 0 is (1, -3) then the radius of the circle is

1. 

2. 

3. 17

4. 

Q. $If|z|=1and\omega =\frac{z-1}{z+1}(where,z\ne -1),thenRe\left(\omega \right)is$

1. $\frac{1}{|z+1{|}^2}$
2. $\frac{\sqrt{2}}{|z+1{|}^2}$
3. $\left|\begin{array}{c}\frac{1}{z+1}\end{array}\right|.\frac{1}{|z+1{|}^2}$
4. 0

Q. Let $f:[-1,3]\to R$ be defined as

$f\left(x\right)=\{\begin{array}{c}|x|+\left[x\right],-1\le x<1\\ x+|x|,1\le x<2\\ x+\left[x\right],2\le x\le 3\end{array}$

where $\left[t\right]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at :

1. only one point
2. only two points
3. only three points
4. four or more points

Q. if f:R->R is defined by f(x)=a^x/a^x+roota, a>0, then evaluate f(x)+ f(1-x)

Q.

If the sets A and B are defined as

A = {(x, y) : y = $\frac{1}{x}$, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

1. 

2. 

3. 

4. None of these

Q.

The values of x and y for which the numbers 3+i$x^2$y and $x^2$ +y+4i are conjugate complex are

1. (-2, -1) or (2, -1)

2. (1, -2) or (-2, 1)

3. (1, 2) or (-1, -2)

4. None of these

Q. 49. The straight line joining the origin to the points of intersection of line 4x + 3y =24with the curve (x-3)square + (y-4)square =25

Q. if alpha and beta are the roots of the equation e^2.x^lnx=x^3 with alpha>beta and alpha^m=beta^n where m and n are coprime to each other then find m.n is equal to

Q. If alpha, beta and gamma are the roots of the equation x^3+4x+1=0, then (alpha+beta)^-1 + (beta+gamma)^-1 + (gamma+alpha)^-1 is

Q. The number of points at which the function $f\left(x\right)=\{\begin{array}{cc}\left[\cos \pi x\right],& 0\le x\le 1\\ |x-1|[x-2],& 1<x\le 2\end{array}$
is discontinuous, is
$\left(\right[.]$ denotes the greatest integral function $)$

1. $1$
2. $2$
3. $3$
4. $4$