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10th Public Exam March 2019 Important 2 Marks Questions

10th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 80
    40 x 2 = 80
  1. A sequence {an} is given by the formula an = (12 - 3n) prove that it is an A.P., find its 10th term.

  2. Show that (a - b)2, (a2+b2) and (a+b)2 are in A.P.

  3. Find the value of k so that (8k+4), (6k-2) and (2k+7) form three consecutive terms of an A.P.

  4. which term of the A.P. 5, 8, 11, ..... is 320?

  5. How many terms are there in the A.P. 10, 13, 16, ....., 43?

  6. Find the value of the unknown if the roots are equal.
    x2 - 3x + m = 0

  7. Find the nature of the equation.
    4x2+4x+1=0

  8. Find the square root of the following;x6y12

  9. Find the square root of the following by identity method.x2 +10x +25

  10. Find the GCD of the following:.x2y2,x2y,x2z

  11. Simplify: \(\frac { { x }^{ 2 }+6\sqrt { 3 } x+27 }{ { x }^{ 2 }+\sqrt { 3 } } \)

     

  12. Construct a 3x2 matrix \(A=[a_{ ij }]\) whose elements are given by \({ a }_{ ij }=\frac { { \left( i-2j \right) }^{ 2 } }{ 2 } \)

  13. Construct a 3x2 matrix \(A=[a_{ ij }]\) whose elements are given by \({ a }_{ ij }=\frac { \left| 2i-3j \right| }{ 2 } \)

  14. Find the equation of the line passing through the points (2, 3) and (5, -2).

  15. Determine x so that 2 is the slope of the line joining the points (2, 5) and (x, 3).

  16. What is the value of y so that the line through (3, 4) and (2, 7) is parallel to the line through (-1, 4) and (0, -6)?

  17. Find the slopes of PQ and RT with the points P (-1, 2), Q (-8, 2), R (4, -1) and T (-3, 5).

  18. A (2, 3), B (0, 4), C (-5, 0) are three given points. Find the slope of the line through B and the midpoint of AC.

  19. If D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD= 3 cm, DB = 4.5 cm,.AE = 4 cm and EC = 6 cm then show that DE II BC.

  20. The diagonals of a quadrilateral ABCD cut at K. If AK = 2.4 cm, KC = 1.6 cm, BK = 1.5 cm, KD = 1 cm, prove that AB II DC.

  21. If the bisector of an angle of a triangle bisects the opposite sides, prove that the triangle is isosceles.

  22. A, B, C are points on sides QR, RP and PQ respectively of Δ PQR such that PA bisects ㄥP, QB bisects ㄥQ and RC bisects ㄥR. If PQ = 6 cm, QR = 8 cm and RP = 4 cm, determine PC, QA, RB.

  23. A vertical stick 1cm long casts a shadow 8 cm long. At the same time a tower casts the shadow 30 m long. Determine the height of the tower.

  24. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.

  25. Find the volume of right circular cylinder which has a height of 21cm and base radius 5 cm.

  26. A rectangular sheet of paper 44cm x 18cm is rolled along its length and a cylinder is formed.Find the volume of the cylinder

  27. The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550cm3 Find its radius

  28. The radii of two circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5 : 4.Calculate the ratio of their C.S.A. and also the ratio of their volumes

  29. The volume of right circular cylinder is 448πcu. cm and height is 14 cm. Find its C.S.A.

  30. Compute the variance of the following observations of marks of 5 students in a tutorial class; 8, 12, 13, 15 and 22.

  31. Calculate the variance for 65, 68, 58, 44, 48, 45, 60, 62, 60, 50.

  32. Find the variance of the following data:
    2, 4, 5, 6, 8, 17.

  33. Find the variance of the following data:
    6, 7, 10, 12, 13, 4, 8,12.

  34. Find the variance of the following data:
    15, 22, 27, 11, 9, 21, 14, 9.

  35. A die is thrown twice. Find the probability of getting a total of 9.

  36. Find the probability that the birthday of a child is on a Saturday or Sunday.

  37. Find the probability of getting a multiple of 2 in the throw of a die.

  38. Find the probability that the sum of the score is odd in a throw of two dice

  39. What is the probability that a non-leap year selected at random will contain 53 Saturdays.

  40. A natural number less than or equal to 25 is chosen. Find the probability that it is a multiple of 4

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