Some
Important Four Marks Questions For 10

^{Th}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) = x

^{2}−3x −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. 6

^{th}term, 13^{th}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 A∪B, A∩B, A−B and B −A.

8. A rectangular plot length is 8 m
excess of its breadth. Its area is 308 m

^{2}then finds length, breadth and its perimeter.
9. Draw the graph of the polynomial
p(x) = 2x

^{2}−7x + 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 9x

^{2}−9x + 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 x

^{2}−5x + 6}; B = {x / x is a factor of 42}
Find (i) A∪B (ii) A∩B (iii) A−B (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) = 3x

^{3}−5x^{2}−11x −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) A∪B ii) A∩B iii) A−B 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) = x

^{2}−x −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 x

^{2}+ y^{2}= 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) = x

^{2}+ x -12 and find zero's.
29. Draw the Venn diagrams of

i) A∪B ii) A∩B = φ iii) A-B iv) B -A

30. -8 + 7x -2x

^{2}+ 14x^{3}+ 8x^{4}is divided by 4x^{2}+ 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) = x

^{2}−x − 12.
36. If the roots are equal in a
quadratic equation ax

^{2}+ (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) = Kx

^{2}+ 4x + 4 such that α^{2}+ β^{2}= 24 find the value of K?
39. Find the zeros of a quadratic
polynomial x

^{2}+ 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) = x

^{3}−2x^{2}−x + 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 b

^{2}−4ac = 0, b^{2}−4ac >0 & b^{2}−4ac <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 5

^{th}and 10^{th}terms of an A.P. is 75 and 8^{th}and 10^{th}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.