Download 5. Simplify: ∛2 × ∜3 - Colonel Child Bloom School

CLASS-IX MATHS (2017-18)
1. Which of the following rational numbers have terminating decimal representation?
3
2
40
23
(II) 13 (III) 27
(IV) 7
(I) 5
2. How many rational numbers can be found between two distinct rational numbers?
(i)Two (ii) Ten (iii) Zero
(IV) Infinite
3. The value of (2 + √3)(2 − √3) is
(i)1
(ii)-1
(iii) 2
(iv) none of these
−2
4. 27 3 is equal to
(i) 9
(ii) 1/9 (iii) 3
(iv) none of these
5. Simplify: ∛2 × ∜3
6. Find the two rational numbers between
1
2
and
7. Find two irrational numbers between 2 and 3.
8. Multiply (3− √5) by (6 + √2 )
9. Express 0.8888… in the form p/q.
10. Simplify by rationalizing denominator of
−1
2
1
.
3
7+3√5
7−3√5
11. Simplify {[625
12. Visualize 3.76 on the number line using successive magnification.
13. Prove that:
]1/4 }2
1
−
1+
+
−
+ 1+
1
−
−
+
+ 1+
1
−
+
−
=1
14. Evaluate (i ) ∛125 (ii) ∜1250
15. Find rationalizing factor of √300
1
16. Rationalize the denominator
and subtract it from √5 − √2
√2
√5+
17. Represent √3 on number line.
18. Simplify (3√2 + 2√3)2 (3√2 − 2√3)2
19. Express 2.4178 in the form of .
20. Simplify (27)−2/3 ÷ 91/2 × 3−3/2
21. If √5 = 2.236 and √3 =1.732. Find the value of
2
√5+√3
+
7
√5−√3
22. 1. Which of the following expression is a polynomials?
1
(b) √x + 2
(c) 2- 2
(d) √t + 5t - 1
(a) x3 −1
23. A polynomial of degree 3 in x has at most
(a) 5 terms
(b) 3 terms
(c) 4 terms
(d) 1 term
24. The coefficient of x2 in the polynomial 2x3 + 4x2 + 3x + 1 is
(a) 2
(b) 3
(c) 1
(d) 4
25. The monomial of degree 50 is
(b) 2x50
(c) x+50
(d) 50
(a) x50 + 1
26. The value of K for which x – 1 is a factor of the polynomial 4x3 + 3x2 – 4x + K is
(a) 0
(b) 3
(c) – 3
(d) 1
27. The factors 12x2 – x – 6
(a) (3x – 2) (4x + 3)
(b) (12x + 1) (x – 6)
(c) (12x – 1) (x + 6)
(d) (3x + 2) (4x – 3)
28. x3 + y3 + z3 – 3xyz is
(a) (x + y – z)3
(b) (x – y + z)3
3
(c) (x + y + z) – 3xyz
(d) (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
29. The expended form of (x + y – z)2 is
(a) x2 + y2 + z2 + 2xy + 2yz + 2zx
(b) x2 + y2 – z2 + 2xy – 2yz – 2xz
(c) x2 + y2 + z2 + 2xy – 2yz – 2zx
(d) x2 + y2 + z2 + 2xy + 2yx + 2xz
30. Divide f(x) by g(x) & verify that the remainder f(x) = x3 + 4x2 – 3x – 10, g(x) = x + 4
31. Find the value of K it x – 2 is factor of 4x3 + 3x2 – 4x + K
32. Factorise the polynomial x3 + 8y3 + 64 z3 – 24xyz
33. Without actually Calculating the cubes, find the value of (-12)3 + (7)3 + (5)3
1
34. If x – 3 and x - are both factors of px2 + 5x + r, then show that P = r
3
5
3
35. Using suitable identify expand(4 x + 4)3
36. Using factor theorem factorise f(x) = x2 – 5x + 6
37. Without actual division, prove that the polynomial 2x3 + 4x2 + x – 34 is exactly divisible by (x – 2)
38. If x2 – bx + c = (x + p) (x – q) then factorise x2 – bxy + cy2
39. Find the integral zeroes of the polynomial x3 + 3x2 – x – 3
40. Check whether 7+ 3x is a factor of 3x2 + 7x
2
4
41. Factorise 3 x2 – x - 3
42. Evaluate (101)2 by using suitable identify
43. Find m and n it x – 1 and x – 2 exactly divide the polynomial x3 + mx2 – nx + 10
44. Using identify (a + b)3 = a3 + b3 + 3ab (a + b) drive the formula a3 + b3 = (a + b)(a2 – ab + b2)
45. Factorise (i) 64y3 + 125z3 (ii) 27m3 – 343n3
46. Without actually calculating the cubes. Find the value of (26)3 + (-15)3 + (11)3
47. Factorise: 12(y2 + 7y)2 – 8 (y2 + 7y) (2y – 1) – 15(2y – 1)2
48. The point of intersection of X and Y axes is called (a) zero point (b) origin (c) null point (d) none of these
49. The distance of the point (-3, -2) from x-axis is (a) 2units (b) 3units (c) 5units (d) 13 units
50. The distance of the point (-6, -2) from y-axis is (a) 6units (b) 38 units(c) 2units (d) 8units
51. The abscissa and ordinate of the point with Co-ordinates (8, 12) is
(A) abscissa 12 and ordinate
(B) abscissa 8 and ordinate 12
(C) abscissa 0 and ordinate 20
(D) none of these
52. Write the name of each part of the plane formed by Vertical and horizontal lines.
53. Write the Co-ordinates of a point which lies on the x-axis and is at a distance of 4units to the right of origin. Draw its
graph.
54. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.
55. Write the Co-ordinates of a point which lies on y-axis and is at a distance of 3units above x-axis.
Represent on the graph.
56. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5) and (6, 1) in the Cartesian plane.
57. Take a triangle ABC with A (3, 0), B (-2, 1), C (2, 1). Find its mirror image.
58. In fig. write the Co-ordinates of the points and if we join the points write the name of fig. formed. Also write Coordinate of point of AC and BD.
59. In which quadrant or on which axis do each of the points (-2, 4), (2, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your
answer by locating them on the Cartesian plane.
60. See fig. and write the following
(i) The Co-ordinates of B
(ii) The Co-ordinates of C
(iii) On which axes point L lies.
(iv) The abscissa of the point D
(v) The Co-ordinates of point L (vi) In which axes point M lies.
(vii) The ordinate of the point H
(Viii) The Co-ordinates of the point M
(ix) The point identified by the Co-ordinate (2, -4)
(x) The point identify by the Co-ordinates (-3, -5)
61. The distance of the point (3, 5) from x- axis is (a) 3 units (b) 4 units
(c) 5 units (d) 6 units
62. The point (0, -5) lies on (a) +ve x- axis (b) +ve y- axis (c) –ve x- axis (d) –ve y-axis
63. The point (-2, 5) lies in (a) 1st quadrant (b) 2nd quadrant (c) 3rd quadrant (d) 4th quadrant
64. The distance of the point (3, 0) from x- axis is (a) 3 units (b) 0 units (c) 9 units (d) none of these
65. Name the points of the plane which do not belong to any of the quadrants.
66. Which of the following points belong to the x- axis? (a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)
67. Which of the following points belongs to 1st quadrant? (a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)
68. Which of the following points belongs to 3rd quadrant (a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)
69. Take a rectangle ABCD with A (-6, 4), B (-6, 2), C (-2, 2) and D (-2, 4). Find its mirror image with respect to x- axis.
70. The following table gives measures (in degrees) of two acute angles of a right triangle
Plot the point and join them.
X
10
20
30
40
50
60
70
80
Y
80
70
60
50
40
30
20
10
71. Plot each of the following points in the Cartesian Plane (a) (3, 4) (b) (-3, -4) (c) (0, -5) (d) (2, -5) (e) (2, 0)
72. The following table given the relation between natural numbers and odd natural numbers
X
1
2
3
4
5
6
7
Y
3
5
7
9
11
13
15
Plot the points and join them. Do you get a straight line by joining these points?