Q. 1. Nivedita has 440 laddo and 140 barfis. She wants to sack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of burfis that can be placed for this purpose?
Q. 2. Prove 5 + 2
is an irrational number.
Q. 3. Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and product of its zeros as 2, -7, -14 respectively.
Q. 4. If the polynomial 
is divided by another polynomial 
, the remainder comes out to be x+a. Find the value of k and a.
Q. 5. Find all the zeros of 
if you know that two of its zeros are 
.
Q. 6. Find the value of k for which the pair of linear equations kx-2y=3 and 3x+y=5 has a unique solution.
Q. 7. It takes 12 hours to fill a swimming pool using 2 pipes. If the larger pipe is used for 4 hours and the smaller pipe for 9 hours, only half the pool is filed. How long would it take for each pipe alone to fill the pool?
Q. 8. Determine the nature of the roots of quadratic equation:
Q. 9. If x=2 and x=3 are the roots of the equation
, find a and b.
Q. 10. For what value of k , 2k-1, 7 and 3k will form an A.P.?
Q. 11. In the figure, if the coordinates of the points A and B are (-1,0) and (3,0) respectively. Find the Polynomial.
Q. 12. How many zeros are there of the given quadratic polynomial?
Q. 13. The cost of digging a well after every metre of digging, when it costs Rs. 150 for the first metre and rises by Rs. 50 for each subsequent metre. What will be the total cost of digging it 50 metre?
Q. 14. Show that the sequence defined by an= 5n-11 is an A.P. and find its common difference.
Q. 15. How many 3-digits numbers are divisible by 7?
Q. 16. Gopal started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Q. 17. A sum of Rs. 4000 is invested at 8% s.i. per year. Calculate the interest at the end of each year. Do these interests form an A.P.? If so, find the interest at the end of 30 years making use of this fact.
Q. 18. In figure, if TP and TQ are the two tangents to a circle with centre 0 so that angle PQR = 1300, then what is the value of the angle PTQ?
Q. 19. In figure, what is the ratio of the areas of a circle and a rectangle whose diameter and diagonal of a rectangle are respectively equal?
Q. 20. The hypotenuse of a right angled triangle is 3√10 cm. If the smaller side is tripled and the longer side doubled, new hypotenuse will be 9√5 cm. How long are the sides of the triangle?
Q. 21. ABC be aright triangle in which AB = 3cm, BC = 4 cm and angle B=900. BD is the perpendicular from B on AC. The circle through B,C and D is drawn. Construct the tangents from A to this circle.
Q. 22. Construct an isosceles triangle whose base is 8 cmand the altitude 4 cm and then another triangle whose sides are 5/6 times the corresponding sides of the isosceles triangle.
The following data gives the information on marks of 70 students in a periodical test:
Marks |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
No. of students |
3 |
11 |
28 |
48 |
70 |
Q. 23. Construct less than and more than ogives for the above distribution. Determine the median of the group.
Q. 24. Evaluate: 
Q. 25. If tan A = Cot B, prove that A+B = 900.
