1. State fundamental theorem of arithmetic.
2. Express 360 as product of its prime factors.
3. If a and b are two prime numbers then find HCF (a, b).
4. If a and b are two prime numbers then find LCM (a, b).
5. Find the quadratic polynomial the sum and product of whose zeroes are -2 and 3.
6. Find whether the given polynomial is quadratic or not ?
7. If one zero of the quadratic polynomial 𝑥² − 4𝑥 + 1 is 2 + √3, then the other find the
( x−4) +𝑥² =(3 x +3) +3
2 3
other zero .
8. Find the zeroes of the polynomial 2𝑥² - 3x + 1.
9. Solve the pair of linear equations by substitution method x – 7y + 42 = 0 and x – 3y – 6 =
0.
10. Find the value of k for which the following pair of linear equations have infinitely many
solutions. 2x + 3y = 7 and (k + 1)x + (2k – 1 )y = 4k + 1
11. If 51x + 23y = 116 and 23x + 51y = 106, then find the value of (x – y).
12. Find the relation between a, b, c and d for which the equations ax + by = c and cx + dy =
a have a unique solution.
13. Are the following pair of linear equations consistent? Justify your answer.
2𝑎𝑥 + 𝑏𝑦 = 𝑎; 4𝑎𝑥 + 2𝑏𝑦 – 2𝑎 = 0; , 𝑏 ≠ 0
14. Represent in the form of quadratic equation: (x – 3)(2 x+1)=x (x +5).
15. Find the roots of the equation 2 x 2 – 5 x +3=0 , by factorisation.
16. Reduce in a quadratic equation √ 6 x+ 7−( 2 x−7 )=0
17. If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the
value of its 12th term.
18. Find the common difference of the A.P whose first term is 12 and fifth term is 0.
19. Two APs have the same common difference. The first term of one of these is –1 and
that of the other is – 8. The difference between their 4th terms is
BE BC
20. In the figure, DE ∥ AC and = . Is DC ∥ AP ? Justify.
EC CP
21. In the figure, altitudes AD and CE of Δ ABC intersect each other at the point P. Show
that:
(i) ΔABD ~ ΔCBE
(ii) ΔPDC ~ ΔBEC
22. write the name of quadrant in which The point lies which divides the line segment
joining the points (7,-6) and (3,4) in ratio 1:2 internally
23. Find the midpoint of the line segment joining the points (- 5, 7) and (- 1, 3).
24. What is the distance of the point (3,4) from the origin
25. A tree breaks due to storm and the broken part bends so that the top of the tree
touches the ground making an angle 30° with it. The distance between the foot of the
tree to the point where the top touches the ground is 8 m. Find the height of the tree.
26. The angle of depression from the top of a tower to a point on the ground is 30 degrees.
If the height of the tower is 50 meters, find the horizontal distance between the tower
and the point on the ground
27. In the given figure, AB, AC and AD are tangents. If AB = 5 cm, find AD.
28. In Figure, common tangents AB and CD to the two circles with centres O 1 and
O2 intersect at E. Prove that AB = CD.
29. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
30. The length of the minute hand of a clock is 14 cm. Find the area swept by the
minute hand in 5 minutes.
31. A race track is in the form of a ring whose inner circumference is 352 m and the
outer circumference is 396 m. Find the width of the track.
32. . In the given figure, arcs have been drawn of radius 7cm each with
vertices A, B, C and D of quadrilateral ABCD as centres. Find the area
of the shaded region
33. The circumference of the base of a cylindrical vessel is 132 cm and its
height is 25 cm. How many litres of water can it hold?
34. Volume and surface area of a solid hemisphere are numerically equal.
What is the diameter of hemisphere?
35. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m
deep. If the cost of painting is at the rate of Rs 20 per m2, find radius of the base.
36. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24
cm and diameter 49 cm to cover the whole surface. Find the length of the wire.
37. The volumes of two spheres are in the ratio 64 : 27. Find the ratio of their
surface areas.
38. Find the mean of the following data:
39. Find the median class of the following data
.
40. The distribution of sale of shirts sold in a month in a departmental store is as under
Calculate the modal size of shirts sold.
41. A bag contains 2 red and 6 black balls. a ball is taken out of the bag at random. Find the
probability of getting a black ball
42. Two coins are tossed simultaneously. Find the probability of getting exactly one tail.
43. The probability that it will rain tomorrow is 0.53. what is the probability that it will not
rain tomorrow?
44. A fair dice is rolled. What is the probability of getting number ' x ' such that1 ≤ x ≤6 .
an angle of 80° .then find the measure of ∠ POA .
45. If tangents PA and PB from a point P to a circle are inclined are inclined to each other at
46. The angle of elevation of the top of a cliff from a point
on the ground, which is 50 meters away from the foot
of the cliff, is 45 degrees. Find the height of the cliff.
48. In a ∆ABC, if ∠C = 90°, prove that sin2 A + sin2 B =1.
47. If cos A = 2/5, find the value of 4 + 4 tan2A
49. If sec A = 2x and tan A = 2/x, find the value of 2(x2−1/x2) .
50. If 7 sin2 θ + 3 cos2 θ = 4, then find the value of tan θ
