Monday, 16 April 2018

Some Important Four Marks Questions For 10Th Class Students in Mathematics Paper-1


Some Important Four Marks Questions For 10Th Class Students in Mathematics Paper-1

1. Cost of 4 chairs and 3 tables is Rs.2100; Cost of 5 chairs and 2 tables is Rs.1750. Write the pairs of linear equations in two variables and find the value of chairs and tables by using graph method
2. Draw the graph of p(x) = x23x 10 and write the zeroes.
3. Is A(2, 2), B(8, 4), C(5, 7), D(1, 1) are vertices of rectangle? If vertices of rectangle then find the area
4. 6th term, 13th terms of a Geometric progression are 24, 3/16 respectively. Then find the G.P. and also find first term and ratio
5. Solve (57/x+y) + (6/x-y) =5; (38/x+y) + (21/x-y) =9
6. Solve (1/x+1) + (2/x+2) = (4/x+4)
7. If A = {x/x factors of 35}, B = {x/x prime numbers, x < 15} then find AB, AB, AB and B A.
8. A rectangular plot length is 8 m excess of its breadth. Its area is 308 m2 then finds length, breadth and its perimeter.
9. Draw the graph of the polynomial p(x) = 2x27x + 6 and find its zeros from the graph.
10. Draw the graph of pair of linear equations in two variables 2x + y = 5 and 3x 2y = 4 and find their solutions from the graph.
11. Find the coordinates of the points of trisection of the line segment joining the points (5, 0) and (2, 3)
12. Solve the Quadratic equation 9x29x + 2 = 0 by the method of completing the square.
13. "The diagonals of the Quadrilateral ABCD where A (1, 1), B (2, 1), C (2, 2) and D (1, 2) divides it into four congruent triangles". Do you agree? Justify
14. There are 49 cards numbered in serial order from 1 to 49 placed on a table in the same order Shriya has to pick a card such that the sum of the numbers on all the cards preceding it must be equal to the sum of the numbers on all the cards following it. Find the number on the card she has to pick.
15. Prove that 5 + 3 7 is an Irrational number
16. A = {x / x is the zero of the polynomial x2 5x + 6}; B = {x / x is a factor of 42}
Find (i) AB (ii) AB (iii) AB (iv) B A
17. Prove that 5 + 7 is an irrational.
18. Verify that 3, 1, 1/3 are the zeroes of the cubic polynomial p(x) = 3x35x211x 3 and then verify the relationship between the zeroes and the coefficients.
19. If A = {x : x is a letter in the word eenadu}, B = {x :x is a letter in the word prathibha} then find i) AB ii) AB iii) AB iv) B A
20. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
21. Spherical marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, which contains some water. Find the number of marbles that should be dropped into the beaker, so that the water level rises by 5.6 cm.
22. How many silver coins, 1.75 cm in diameter and thickness 2 mm need to be melted to form a cuboid of dimensions 5.5 cm ×10 cm ×3.5 cm?
23. Find the zeroes of the polynomial p(x) = x2x 6 by using graph.
24. Solve the equations graphically 2x + y = 5, 3x 2y = 4.
25. Prove that 3 -2 is irrational number. Is (3 + 2)(3 + 2) is Rational or Irrational number?
26. If x2+ y2= 34 xy then show that 2 log(x + y) = 2 (log 3 + log 2) + log x + log y.
27. If A = {x : x N, x < 10}, B = {x: x prime, x < 10}, C = {x: x even number, x < 10},D = {x: x prime number, x < 10} find i) A-C ii) A-B iii) B -C iv) which are the disjoint sets
28. Draw the graph of p(x) = x2+ x -12 and find zero's.
29. Draw the Venn diagrams of
i) AB ii) AB = φ iii) A-B iv) B -A
30. -8 + 7x -2x2+ 14x3+ 8x4 is divided by 4x2+ 3x -2 remainder is ax + b, then find a, b.
31. Write 2 examples of p(x), g(x) if p(x) = g(x) × q(x) + r(x) & r(x) = 0
32. Mid points of a triangle is D (2, 2) E (2, -3) & F (3, 4) then find the vertices of a triangle.
33. If sum of 7 terms is 49 & sum of 17 terms is 289 in a Arithmetic Progression, then find the sum of 'n' terms.
34. Draw the graph of Linear equations 3x -y = 7 & 2x + 3y = 1.
35. Draw the graph of the polynomial and find the zeros of p(x) = x2x 12.
36. If the roots are equal in a quadratic equation ax2+ (a + b) x + b = 0 then show that a = b.
37. The sum of the digits of a two digit number is 8 and the difference between the numbers and that formed by reversing the digits is 18. Find the number.
38. If α, β are the zero's of the quadratic polynomial f(x) = Kx2+ 4x + 4 such that α2+ β2= 24 find the value of K?
39. Find the zeros of a quadratic polynomial x2+ 2x 3 by using graph
40. By using graph, solve 2x y = 5 & 3x + 2y = 11
41. Midpoint of (1, 2) (3, 4) is A, Midpoint of (2, 4) (4, 8) is B. Find the coordinates of line segment of AB internally with 2 : 3.
42. Find the multiples of 3 in between 1 to 500. With this find their sum
43. Verify that 1, 1 & 2 are the zeros of the cubic polynomial p(x) = x32x2x + 2 and then verify the relationship between the zeros and its coefficient
44. Show that P(1, 4), Q(1, 2), R(2, 2) is a right angled triangle and find in which vertices is right angle.
45. Write three quadratic equations, satisfy the discriminate b24ac = 0, b24ac >0 & b24ac <0
46. Use Euclid division lemma, to show that square of any positive integer is of the form 5p or 5p + 1 or 5p + 4.
47. Use Euclid division lemma to show that cube of any positive integer is of the form 8p or 8p + 1 or 8p + 3 or 8p + 5 or 8p +7 for any integer p.
48. A hemispherical bowl of internal radius 15 cm. contains a liquid is to be filled into cylindrical bottles of diameter 5 cm. and height 6 cm. How many bottles are needed to empty the bowl?
49. The sum of the 5th and 10th terms of an A.P. is 75 and 8th and 10th terms is 135. Find first four terms of the A.P.
50. A motor boat whose speed is 18 km/hr in still water if takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream?
51. Solve the pair of equations graphically 2x + y 6 = 0, 4x 2y 4 = 0.
52. A cottage industry produces certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs.90, find the number of articles produced and the cost of each article.

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