1. If a + b + c = 0, where \[a\neq b \neq c \] , then,
\[\frac{a^{2}}{2a^{2}+bc}+\frac{b^{2}}{2b^{2}+ac}+\frac{c^{2}}{2c^{2}+ab}\] is equal to

a) zero

b) 1

c) -1

d) abc

Explanation:

2. If one root of \[x^{2}+px+12=0\] is 4, while the equation \[x^{2}+px+q=0\] has equal roots, then the value of q is

a) 49/4

b) 4/49

c) 4

d) 1/4

Explanation:

3. Nineteen years from now Jackson will be 3 times as old as Joseph is now. Joseph is three years younger than Jackson.

I. Johnson’s age now

II. Joseph’s age now

a) I > II

b) I < II

c) I = II

d) Nothing can be said

Explanation: Let present age of Jackson be x years and present age of Joseph be y years; then present age of Joseph = x – 3

After 19 years Jackson’s age = (x + 19) years and

Joseph’s age = (y + 19) years.

According to the question:

x + 19 = 3(y + 19)

or x – 3y = 38

So only from above equation x and y cannot be found.

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

a) m < 2 or m > 5

b) m > 2

c) 2 < m < 5

d) m < 5

Explanation:

5. The value of \[\frac{55^{3}+45^{3}}{55^{2} - 55\times 45+45^{2}}\] is

a) 100

b) 105

c) 125

d) 75

Explanation:

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

a) 2

b) 8

c) -8

d) -2

Explanation:

7. Once I had been to the post-office to buy stamps of five rupees, two rupees and one rupee. I paid the clerk Rs 20, and since he
did not have change, he gave me three more stamps of one rupee. If the number of stamps of each type that I had ordered initially
was more than one, what was the total number of stamps that I bought?

a) 10

b) 9

c) 12

d) 8

Explanation: The number of stamps that were initially bought were more than one of each type. Hence, the total number of stamps

= 2(5 rupee) + 2(2 rupee) + 3(1 rupee) + 3(1 rupee)

= 10

8. Given the quadratic equation \[x^{2}-\left(A-3\right)x-\left(A-7\right)\] , for what value of A will the sum of the squares of the roots be zero?

a) -2

b) 3

c) 6

d) None of these

Explanation:

9. Which of the following values of x do not satisfy the inequality \[\left(x^{2}-3x+2>0\right)\] at all?

a) \[1\leq x\leq 2\]

b) \[-1\geq x\geq -2\]

c) \[0\leq x\leq 2\]

d) \[0\geq x\geq -2\]

Explanation:

10. Out of two-thirds of the total number of basket-ball matches, a team has won 17 matches and lost 3 of them. what is the maximum
number of matches that the team can lose and still win three-fourths of the total number of matches, if it is true that no match can
end in a tie ?

a) 4

b) 6

c) 5

d) 3

Explanation: