1
###
Largest value of min(2 + x^2, 6 - 3x), when x > 0, is

Largest value of min(2 + x^{2}, 6 - 3x), when x > 0, is

- 1
- 2
- 3
- 4

2
###
A quadratic function f(x) attains a maximum of 3 at x = 1

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

- -180
- -159
- -110
- -119

3
###
If both a and b belong to the set {1, 2, 3, 4}, then the number of equations

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax^{2}+ bx + 1 = 0 having real roots is

- 6
- 7
- 10
- 12

4
###
Let p and q be the roots of the quadratic equation x^2 - (α-2)x - α - 1 = 0

Let p and q be the roots of the quadratic equation x^{2} - (α - 2)x - α - 1 = 0. What is the minimum possible value of p^{2} + q^{2}?

- 0
- 3
- 4
- 5

5
###
The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0

The number of roots common between the two equations x^{3} + 3x^{2} + 4x + 5 = 0 and x^{3} + 2x^{2} + 7x + 3 = 0 is

- 0
- 1
- 2
- 3

6
###
One root of x^2 + kx - 8 = 0 is square of the other. Then the value of k is

One root of x^{2} + kx - 8 = 0 is square of the other. Then the value of k is

- 2
- -2
- 8
- -8

7
###
What is the value of m which satisfies 3m^2 - 21m + 30

What is the value of m which satisfies 3m^{2} - 21m + 30 < 0?

- m < 2 or m > 5; 2 < m < 5
- 2 < m < 5
- m < 2 or m > 5
- m > 2

8
###
Which of the following values of x do not satisfy the inequality x^2 - 3x + 2 > 0 at all

Which of the following values of x do not satisfy the inequality x^{2} - 3x + 2 > 0 at all?

- 0 ≥ x ≥ –2
- 0 ≤ x ≤ 2
- –1 ≥ x ≥ –2
- 1 ≤ x ≤ 2

9
###
The minimum possible value of the sum of the squares of the roots

The minimum possible value of the sum of the squares of the roots of the equation x^{2} + (a + 3)x - (a + 5) = 0 is

- 1
- 2
- 3
- 4