1. Let \[y=\frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+.....}}}}\]

What is the value of y?

a) \[\frac{\sqrt{13}+3}{2}\]

b) \[\frac{\sqrt{13}-3}{2}\]

c) \[\frac{\sqrt{15}+3}{2}\]

d) \[\frac{\sqrt{15}-3}{2}\]

Explanation:

2. For which value of k does the following pair of equations yield a unique solution for x such that the solution
is positive?

\[x^{2}-y^{2}=0\]

\[\left(x-k\right)^{2}+y^{2}=1\]

a) 2

b) 0

c) \[\sqrt{2}\]

d) \[-\sqrt{2}\]

Explanation:

3. let \[x=\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-.......infinity }}}}\]

Then x equals

a) 3

b) \[\left(\frac{\sqrt{13}-1}{2}\right)\]

c) \[\left(\frac{\sqrt{13}+1}{2}\right)\]

d) \[\sqrt{13}\]

Explanation:

4. A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40
calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wages of Rs.
250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs.
10 per call she answer. To minimize the total cost, how many male operators should the service provider employ assuming he has
to employ more than 7 of the 12 female operators available for the job?

a) 15

b) 14

c) 12

d) 10

Explanation:

5. When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18
when their digits are reversed?

a) 5

b) 6

c) 7

d) 8

Explanation:

6. What values of x satisfy \[x^{2/3}+x^{1/3}-2\leq 0\]

a) \[-8\leq x\leq1\]

b) \[-1\leq x\leq8\]

c) 1 < x < 8

d) \[1\leq x\leq8\]

Explanation:

7. What are the values of x and y that satisfy both the equations?

\[2^{0.7x}.3^{-1.25y}=8\frac{\sqrt{6}}{27}\]

\[4^{0.3x}.9^{0.2y}=8.\left(81\right)^{1/5}\]

a) x = 2, y = 5

b) x = 2.5, y = 6

c) x = 3, y = 5

d) x = 5, y = 2

Explanation:

8. The number of solutions of the equation 2x + y = 40 where both x and y are
positive integers and \[x\leq y\]

a) 13

b) 14

c) 18

d) 20

Explanation:

9. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can
possibly be one of these four numbers?

a) 21

b) 25

c) 41

d) 67

Explanation:

10. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the \[n^{th}\] day of 2007 (n = 1, 2, ..., 100), and then remains
constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the \[n^{th}\] day of 2007 (n = 1, 2, ..., 365).
On which date in 2007 will the prices of these two varieties of tea be equal?

a) June 30

b) May 21

c) April 11

d) May 20

Explanation: