#### Question - 1

For the equation 3x2 + px + 3 = 0,p > 0; if one of the roots is square of the other,then p is equal to

• A $\frac{1}{2}$
• B 1
• C 3
• D $\frac{ 2 }{ 3 }$

#### Question - 2

If 1,a1,a2,a3,....an-1 are the nth roots of unity,then value of (1 - a1) (1 - a2)(1 - a3)...(1 - an-1),is

• A n
• B n2
• C n3
• D 0

#### Question - 3

The equation $\sqrt { x+1 }$- $\sqrt { x-1 }$  = $\sqrt { 4x-1 }$, has

• A no solution
• B one solution
• C two solutions
• D more than two solutions

#### Question - 4

The number of the real roots of the equation |x2| + 3|x| + 2 = 0, is

• A 4
• B 3
• C 2
• D 0

#### Question - 5

If b > a,then the equation (x-a)(x-b)-1 = 0,has

• A both roots in [a,b]
• B both roots in (-$\alpha$,a)
• C both roots in (b,$\infty$)
• D one root in (- $\infty$,a) and other in (b, $\infty$)

#### Question - 6

Let $\alpha,\beta$ be the roots of x2 - x + p = 0 and $\gamma,\delta$ be roots of x2 - 4x + q.If $\alpha,\beta,\gamma,\delta$ are in G.P., then the integral values of p and q respectively,are

• A -2,-32
• B -2,3
• C -6,3
• D -6,-32

#### Question - 7

The real roots of the equation 7log7(x2-4x+5) = x-1,are

• A 1 and 2
• B 2 and 3
• C 3 and 4
• D 4 and 5

#### Question - 8

If a,b,c are real numbers.such that a2+b2+c2 = 1,then ab +bc + ca lies in the interval

• A $[\frac{1}{2},2]$
• B [-1,2]
• C $[-\frac{1}{2},1]$
• D $[-{1},\frac{1}{2}]$

#### Question - 9

If the roots of the equation x2 -2ax+a2+a-3 = 0 are real and less than 3,then

• A a < 2
• B  $2 \le a \le 3$
• C $3 < a \le 4$
• D a > 4

#### Question - 10

If $\alpha$ and $\beta$ ($\alpha < \beta$) are the roots of the equation x2 + bx + c = 0,where c < 0

• A 0< $\alpha$< $\beta$
• B $\alpha$ <0< $\beta$ <| $\alpha$ |
• C $\alpha$ < $\beta$ <0
• D $\alpha$<0<| $\alpha$|< $\beta$