Squaring an Inequality

Q. If alpha and beta be the real roots of the equation x square minus (m minus 2)x plus (m square plus 3m plus 5) equal to 0 the the maximum value of alpha square plus beta square is

Q.

If $z\ne 0$ is a complex number, then

1. $\mathrm{Re}\left(z\right)=0\Rightarrow \mathrm{Im}\left(z^2\right)=0$

2. $\mathrm{Re}\left(z^2\right)=0\Rightarrow \mathrm{Im}\left(z^2\right)=0$

3. $\mathrm{Re}\left(z\right)=0\Rightarrow \mathrm{Re}\left(z^2\right)=0$

4. None of these

Q.

If the square root of $-7+24i$is $x+iy$ then $x$ is equal to

1. $\pm 1$

2. $\pm 2$

3. $\pm 3$

4. $\pm 4$

Q. If alpha and beta be the real roots of the equation x square minus (m minus 2)x plus (m square plus 3m plus 5) equal to 0 the the maximum value of alpha square plus beta square is

Q.

All possible values of expression $x^2-4x+9$ is

1. ($-\infty$, 9]

2. ($-\infty$, -9]

3. (5, $\infty$)

4. [5, $\infty$)

Q. The values of $x^2$ for $x>-3$ is a set of real numbers.

1. positive
2. negative
3. non-positive
4. non-negative

Q. If tan Alpha Banten beta be the roots of x square - 3 x + 2 is equal to zero then find cos 2 (alpha + beta)

Q.

If x is real, then the maximum and minimum values of expression $\frac{x^2+14x+9}{x^2+2x+3}$will be

1. 4, - 5

2. 5, - 4

3. - 4, 5

4. - 4, - 5

Q. If one real root of the quadratic equation 81x square+kx+256=0 is cube of the other root. Then the value of k is ?

Q. If $a,b,c$ are the integral values of $x(a<b<c)$ satisfying $\sqrt{-x^2+10x-16}<x-2,$ then which of the following statements is (are) FALSE?

1. The minimum value of $|x-a|+|x-b|+|x-c|$ is $2$
2. The quadratic equation whose roots are $a$ and $b$ is $x^2-15x+56=0$
3. $2a+3b-4c=0$
4. $2b=a+c$

Q.

If I < x < I +1, Find [-x], where I is an integr

1. I-1

2. -I

3. -I-1

4. -I+1

Q.

Solve: $\sqrt{x-2}$ ≥ -1

1. [2, 3)

2. [3, )

3. [2, )

4. (, 3]

Q. If equation X square + bx + ca is equals to zero and X square + c X + ab is equals to zero have a non zero common root prove that a + b + c is equals to zero and their other Roots satisfy X square + a x + b c = 0

Q.

The values of $x^2$ for x > -3 is set of

1. All negative real numbers

2. All positive real numbers

3. All non-positive real numbers

4. All non-negative real numbers

Q. x > y>0 and n > 0. Then the value of $x^n-y^n$ is

1. Positive
2. Negative

Q.

A woman has m $\$20$ notes and n $\$50$ notes. The total amount of money in her possession cannot be less than $\$800$. Represent this as an inequality.

1. $20m+50n>800$

2. $20m+50n\ge 800$

3. $20m+50n<800$

4. $20m+50n\le 800$

Q. If $3<p<7$ and $-9<q<-4$, then what is the range of p - q?

1. (-16, -7)
2. (16, 7)
3. (7, 16)
4. (-7, -16)

Q. If tan Alpha Banten beta be the roots of x square - 3 x + 2 is equal to zero then find cos 2 (alpha + beta)

Q. Match the given expressions with the intervals in which their values could lie in

1. 0, 14
2. [-7, ∞)
3. 3, ∞
4. $(0,\frac{1}{3}]$

Q. Ifx, y, z are positive integers then minimum value of 3x+5y+z+1/15x + 25/y + 1/36z is?

Q. If alpha beeta and gama are the roots of equation x^3-3x^2+x+5=0 then y=sigma alpha square+alpha beeta gama satisfies the equation

Q.

If $(x^2-9)\sqrt{x^2-1}<0$, then what are the possible values of $x$?

1. $x\in (-3,3)$

2. $x\in (-3,-2]\cup [2,3)$

3. $x\in (-\infty ,-1]\cup [1,\infty )$

4. $x\in (-3,-1)\cup (1,3)$

Q. The valuesof $x^2+4x-3\forall x\in R$ lie in the interval

1. $(-7,\infty )$
2. $[-3,\infty )$
3. $[-7,\infty )$
4. $(-3,\infty )$

Q. Which of the following numbers is NOT a solution of the inequality $3x-5\ge 4x-3$ ?

1. -1
2. -2
3. -3
4. -5

Q.

Tell whether the given value is a solution of the inequality.

$-\frac{3}{7}\mathrm{m}<1+\mathrm{m};\mathrm{m}=-7$

Q. Write each of the following sets as intervals :
1. {x belongs to R : 1 > 2x - 3 > 0 }
2. {x belongs to R : 3/2 < 2 + 3x < 5 }

Q. Let a, b be integers such that all the roots of the equation (x^2 + ax+ b)(x^2 + 17x + b) = 0 are negative integers, then the smallest possible value of a + b is

Q. If one real root of the quadratic equation 81x square+kx+256=0 is cube of the other root. Then the value of k is ?

Q. If $\sqrt{x+6}<x-6$, then

1. $x\in (6,\infty )$
2. $x\in (10,\infty )$
3. $x\in (6,10)$
4. $x\in (-6,\infty )$

Q. The value of a for which the sum of the squares of the roots of the equation x ^ 2 - (a - 2) * x - a - 1 = 0assumes the least value is