1. Below question consists of two equations. On the basis of these two equations you have to find out the relation between p and q. I. \(p = \frac\) II. 9q2 – 12q + 4 = 0

2. On a school’s Annual Day, apples were to be equally distributed amongst 112 children. But on that particular day 32 children were absent. Thus, the remaining children got 6 extra apples. How many apples was each child originally supposed to get?

3. In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark correct answer. I. \(\frac}{6} = {x^3}\) II. 4y3 = - (589 ÷ 4) + 5y3

4. A polynomial f(x) = x4 – 11x3 + 31x2 – 46x + 20 is defined. When it is divided by x2 – 3x + n, the remainder left is q. Find the product of n and q.

5. In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer I. x2 + 11x + 30 = 0 II. y2 + 12y + 36 = 0

6. The number of solutions of x2 + 4|x| + 5 = 0 is

7. In the following question, one or two equation(s) is/are given. On their basis, you have to determine the relation between p and q and then give answer I. 2p2 = 23p – 63 II. 2q (q-8) = q-36

8. The sum of three consecutive multiples of 4 is 444. Find the products of these three multiples.

9. A boy was asked to find 8/9th of a fraction. He made a mistake of dividing the fraction by 8/9 and so got an answer which exceeds the correct answer by 17/54. Find the original fraction?

10. In the following question two equations are given. You have to solve these equations and determine relation between a and b. \(\begin{array}{l} {\rm{I}}.{a^2} + 3 = - \frac\\ {\rm{II}}.10{b^2} + {\rm{\;}}\frac{6} + 41 = - \frac \end{array}\)

11. Mr. Arun is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. For how many days is Mr. Arun out on tour?

12. Direction: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly. I. \(\frac{5} + \frac = \frac{9}\) II. \(\frac - \frac{1} = \sqrt y \)

13. Find the largest positive integer n such that n3 + 1000, is divisible by n + 10. n3 + 100 is also divisible by (n + 10).

14. A library has a fined charge for the first 3 days and an additional charge for each day thereafter Avanshi paid Rs. 27 for a book kept for seven days if fined charges are Rs. x and thereafter charges are Rs. y per day. Write the linear equation representing the above information.

15. Two hackers planned to hack a bank account which had debit card pin code in such a format that if a fraction could be made using the first two digits as numerator and last two digits as denominator, then if the numerator of the fraction was increased by 200% and the denominator by 300%, the fraction becomes 12/15. What was the pin of the debit card?

16. In the following question two equations numbered I and II are given. You have to solve both the equations and give the answer: I. 2x2 – 11x + 15 = 0 II. 21y2 – 23y + 6 = 0

17. I: x - √121 = 0 II: y2 - 121 = 0

18. In following question, two equations are given, you have to solve them and choose the correct option: x2 – 3x – 4 = 0, y2 – 4 = 0

19. The age of Mr. Ramesh is four times the age of his son. After ten years the age of Mr. Ramesh will be only twice the age of his son. Find the present age of Mr. Ramesh’s son.

20. On multiplying the polynomials x2 + px + q and x2 + mx + n with each other, we get a polynomial whose zeroes are 1, 2, 3 and 4. What will be the value of (p + m)(q + n)?

21. Raman has some 50-paisa coins, some 2-rupee coins, some 1-rupee coins and some 5-rupee coins. The value of all the coins is Rs. 50. Number of 2-rupee coins is 5 more than that of the 5 rupee coins. 50 paisa coins are double in number than 1 rupee coins. Value of 50-paisa coins and 1-rupee coins is Rs. 26. How many 2-rupee coins does he have?

22. In the following question two equations numbered I and II are given. You have to solve both the equations and give the answer: I. 3x2 + 13x + 12 = 0 II. y2 + 9y + 20 = 0

23. Direction∶ In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer. I. √1024 x + √4096 = 0 II. (16)1/4 y + (512)1/3 = 0

24. If \({P^2} + {1 \over } = 7\), then find the value of \({P^2} - {1 \over }.\)

25. In the following question two equations are given in variables ‘x’ and ‘y’. On the basis of these equations you have to decide the relation between ‘x’ and ‘y’ and give answer. I. 2x2 - (4 + √13)x + 2√13 = 0 II. 10y2 - (18 + 5√13)y + 9√13 = 0