1. The value of x for which the expressions 19 - 5x and 19x + 5 become equal is ______.

2. If a + b + c = 0, then the value of a3 + b3 + c3 is

3. A got married 5 years ago. A’s present age is \(1\frac{1}{4}\) times his age at the time of marriage. 4 years from now, A’ s wife will be \(1\frac{1}{2}\) times her age at the time of marriage. Difference in age between husband and wife is

4. Sum of the digits of a two-digit number is 8. If the digits of the number are inter changed, then the new number is 36 more than the original number. What is the original number?

5. If a + b = 17 and a – b = 9 then the value of (4a2 + 4b2) is,

6. A man gets Rs.40 if he works for a day, and is fined 10% of this amount if he is absent for a day. After 60 days, if he receives a total of Rs.1300, find the no. of days he was absent for work.

7. If x + y = 4, x – y = 3, find the value of 16xy (x2 + y2).

8. The value of \(\frac} \right)} \right)\; + \;0.319\left( - \; \right)} \right)} \right)}}\)

9. Find the value of \(\sqrt + 2\sqrt \), if 1 < x < 2

10. If x + y = 25 then (x – 15)3 + (y – 10)3 is :

11. If x and y are natural numbers such that x + y = 2017, then what is the value of (-1)x + (-1)y?

12. If x + (1/x) = 2, then the value of x99 + (1/x99) – 2 is

13. The expression \({\left( {27\; + \;\sqrt {756} } \right)^{1/3}}\; + \;{\left( {27 - \sqrt {756} } \right)^{1/3}}\) is equivalent to -

14. A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

15. If P + 1/P = 8, then the value of \({\left( {P - 8} \right)^{11}}\; + \;\frac{1}^{11}}}}\) is

16. If xy = - 30 and x2 + y2 = 61, then find the value of (x + y).

17. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 3 tables together is Rs. 4500. The total price of 12 chairs and 5 tables is:

18. Rs. 3450 is to be divided among X, Y and Z in such a way that if X gets Rs. 11, then Y must get Rs. 18 and if Y gets Rs. 6, then Z must get Rs. 9.50. The share of Z will exceed to that of Y by –

19. The sum of three consecutive odd natural numbers is 93. The smallest of three numbers is:

20. The equations 3x + 4y = 10 -x + 2y = 0 Have the solution (a, b). The value of a + b is

21. The grocery store parking lot will hold 2000 vehicles 2/5 of the parking spaces are for cars. When you went to buy groceries, there were 400 cars and some trucks in the parking lot. The parking lot was ¾ full. How many trucks were in it?

22. Cost of 8 pencils, 5 pens and 3 erasers is Rs. 111. Cost of 9 pencils, 6 pens and 5 erasers is Rs. 130. Cost of 16 pencils, 11 pens and 3 erasers is Rs. 221. What is the cost (in Rs) of 39 pencils, 26 pens and 13 erasers?

23. A and B together have six times the sum what B and C together have, while A, B and C together have Rs. 30 more than the sum that A has. If B has four times the sum than that of C, the sum A has, is approximately –

24. The difference between a number and 2/7th of the number is 100. The number is

25. If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?

26. If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

27. From 9.00 AM to 2.00 PM, the temperature rose at a constant rate from 26°C to 36°C, What was the temperature at noon?

28. A number is greater than twice its reciprocal by 31/4. Find the number.

29. Find the coefficient of x2 in the expansion of (x2 + x + 1) (x2 – x + 1)

30. If x + y + z = 1, \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1\) and xyz = 1, then x3 + y3 + z3 is equal to