Mathematics
Std:
10
Max. Marks : 100
Very Short Answer Questions
- One Mark
100 * 1 = 100
1.
2. A sector with central angle 63°, cut out
from a circle, contains 19.8 cm2. Find the radius of the circle.
3. Solve for x and y:
4.
5. State whether the following are true or
false. Justify your answer.
(i) The value of tan A is always
less than 1.
(iii) cot A is a product of cot
and A.
6. D and E are the points on
the sides AB and AC, respectively of a ΔABC. If AB = 12 cm, AD = 8 cm, AE = 12
cm and AC= 19 cm, show that DE is parallel to BC.
7. If D and E are
respectively the points on the AB and AC of a ΔABC such that AB = 12 cm, AD = 8 cm, AE = 12
cm, AC = 18 cm, show that DE || BC.
8. It is known that a box of
600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random
from this box. What is the probability that it is a non-defective bulb ?
9. Find the mean of the
following data:
|
Class
Interval
|
25-35
|
35-45
|
45-55
|
55-65
|
65-75
|
|
Frequency
|
6
|
10
|
8
|
12
|
4
|
10. A circular ground whose diameter
is 35 metres, has a 1.4 m broad garden around it. What is the area of the
garden?
11. Given that L.C.M. (480, 672) =
3360, find H.C.F. (480, 672).
12. For the following
APs, write first term and common difference.
(i) 4,1,-2,-5, ... (ii) -3, 1, 1,3, ...
(iv) 0.7, 1.6, 2.5,
3.4, ...
13. Find the mean of the
following data.
|
Class
|
0-100
|
100-200
|
200-300
|
300-400
|
400-500
|
|
Frequency
|
6
|
9
|
15
|
12
|
8
|
14. Find the value of x, if the
distance between the points (x, - 1) and (3, 2) is 5.
15. Which term of the
Arithmetic Progression 3, 10, 17...., will be 84 more than its 13th
term?
16. Write down the decimal expansions of those rational
numbers in the following which have terminating, decimal expansions.
17. In the adjoining figure, if DE
||BC and AD = (4x - 3) cm, AE = (8x- 7)cm, BD=(3x-1)cm and CE = (5x - 3) cm,
find x.
18. Cards marked with
numbers 3, 4, 5, 50 are placed in a box and mixed thoroughly. One card is drawn
at random from the box. Find the probability that the number on the drawn card
is
(i) divisible by 7
(ii) a
number which is a perfect square
19. The 8th term of an
Arithmetic Progression is 37 and its 12th term is 57. Find the A.P.
20. Which term of the
sequence 36, 31, 26, 21, 16,....is the first negative term?
21. For the following system of
equations, find the value(s) of p so that the system has a unique solution.
(i) px + 2y = 5; 3x + y - 1 = 0
(ii) px + 3y - 7 = 0; 2x -y = 6
(iii) 9x + py= 1; 3x + 4y = 2.
22. Write first five
terms of an AP if
(i) a = 2, d =
3
(ii) a = 10, d =
6
(iii) a = 44, of = -4
(iv) a = 7,d
= -7
23.
24. In ΔABC ÐB = ÐC and D and E
are points on AB and AC such that BD = CE. Prove that DE||BC.
25. D and E are two points on the
sides AB and AC of ΔABC such that AD = 5cm, DB=7 cm, AE = 6cm and EC = 9cm.
Determine whether DE || BC.
26. If the radius of a sphere is
increased by 2 cm, then its surface area increases by 352 cm2. What
was the radius of the sphere before the increase ?
27. Find the point on the x-axis which
is equidistant from the points (-2, 5) and (2, -3).
28. A dice is tossed
once. What is the probability of the dice coming up with a number < 8 ? What
is the probability of the dice coming up with the number 8?
29. Which of the
following sequences are in AP.
(i) 1,2,3,4,5,6,
......
(ii) 3,6,9, 12,
......
(iii) 2,4,8, 16,
32,.....
(iv) 22, 24,
26, 28, ......
(v) 22, 32,
42, 52, ......
(vi) a0, a2,
a4, a6.......
(vii) 95, 90, 85,
80,......
30. Solve the quadratic
equation : (3x - 4) (3x - 2) = 0.
31. The volume of a right circular
cylinder is 1100 cu.cm and the radius of its base is 5 cm. Find its curved
surface area.
32. Find the first three
terms of a sequence whose nth term is given by t n =2n+ 1.
33. The circumference of the edge of
a hemispherical bowl is 132 cm. Find the capacity of the bowl. (Take p=
)
34. Fill in the blanks
using the correct word given in brackets.
(i) All circles are
... (congruent, similar)
(ii) All squares are
... (similar, congruent)
(iii)All ...
triangles are similar (equilateral, isosceles)
(iv) Two polygons of
the same number of sides are similar if (a) their corresponding angles are…
(b) their
corresponding sides are…. .....
35. In the adjoining figure, ΔABC and
ΔCPD are right angled at B and P respectively.
36. Find the 8th
term from the end of the A.P. 7, 10, 13,...., 184.
37. Show that the system
of equations 3x + 4y =7; 12x+ 16y = 28 has infinitely many solutions.
38. Find the area of a sector of a
circle with radius 14 cm and angle of sector is 60°.
39. Find the cubic polynomial with
the sum of its zeros, sum of the products of its zeros taken two at a time and
the product of its zeros as 10, 11 and - 70 respectively.
40. If one of the zeros of the
quadratic polynomial 2x2 + kx - 12 is - 4, find the value of k.
41. A horse is placed for grazing
inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope
21 m long. On how much area can it graze? How much area is left ungrazed?
42. The circumference of a circle
exceeds its diameter by 16.8 cm. Find the circumference of the circle.
43. In 56, 63, 70,......,
497 series, how many terms are there?
44. In the given figure, sectors of
two concentric circles of radii 7 cm and 3.5 cm are shown. Find the area of the
shaded region.
45.
46.
47. The height of a cylinder is 15
cm. The curved surface area is 660 sq. cm. Find its radius. (Take p=
)
48. Find the common
difference of the A.P. whose 11th term is 5 and 13th term is 79. What is the
24th term?
49. Eleven balls are
serially numbered and placed in an urn. Find the probability that a ball drawn
will be:
(i) odd
numbered ball
(ii)
even numbered ball
(iii)
prime numbered ball
50. The end points of the
diameter of a circle are (2, -1) and (5, 4). Find the co-ordinates of the
centre.
51. Check whether the
following are quadratic equations?
(iii) (x-1) (x+4) = x2 +1
52. The zeros of the quadratic
polynomial x2 + 4x + k are α
and β. Find the value of k if 5α + 2β = 1.
53. For what value of k
will the terms (2k + 1), 8 and 3 k form an A.P.?
54. Show that the points (a, b + c),
(b, c + a) and (c, a + b) are collinear.
55. The coordinates of the midpoint
of the line joining the points (2p + 2, 3) and (4, 2q +1) are (2p,2q). Find the
values of p and q.
56.
57.
58. Prove that : (sec2q -1) cot2q =1.
59.
60. If α and β are the zeros of the
quadratic polynomial p(x)=ax2 + bx + c ,then evaluate :
61. In right triangle ACB, ÐC = 90°, AB = 29
units and BC = 21 units. If ÐABC = θ, find cos2 θ - sin2
θ and sin2 θ + cos2 θ
62. A circular garden has a circumference
of 440 m. There is a 7 m wide path inside the garden along its periphery. Find
the area of the path.
63. If one of the zeros of the
polynomial 3x2 - 10x + (2k - 1) is a reciprocal of the other, then evaluate the value of k.
64. The diagonal AC of a
quadrilateral ABCD bisects both ÐA and ÐC. Prove that
65. The coordinates of two vertices A
and B of a triangle ABC are (1, 4) and (5, 3) respectively. If the coordinates
of the centroid of DABC are (3, 3), find
the coordinates of the third vertex C.
66. If 7 times the 7th
term of an A.P. is equal to 11 times the 11th term, show that its 18th
term is zero.
67. A (7, 0), B (0, - 24) and O (0,
0) are the vertices of a triangle. Calculate the length of the hypotenuse of
right angled DAOB.
68. Prove that the product of a
rational and an irrational number is irrational.
69. By distance formula, show that
the points (1, - 1), (5, 2) and (9, 5) are collinear.
70. The area of the sector of a
circle of radius 17.5 cm is 192.5 cm2. Find the central angle of the
sector.
71. Solve for x and y :
3x-2y = 4;
x+y= 3
72. Find the distance of the point
(6, -6) from the origin.
73. Prove that : (1 - sin2q) sec2
q
=1.
74. Find the length of canvas 1.1m
wide required to build a conical tent of base radius 10.5 metres and height 14
metres.
75. The 7th term
of an A.P. is 32 and its 13th term is 62. Find the A.P.
76.
77. Without plotting the graph of the
polynomials find the vertex of the following polynomials (or parabola).
(i) f(x)
= -4x2 + 4x - 1
(ii) f(x)
= 6x2 - 7x - 3
(iii) f(x)
= x2 - 12x + 35
78. Find the term of the
Arithmetic Progression 9, 12, 15, 18,.....which is 39 more than its 36th term.
79. Which term of the
arithmetic progression 5, 15, 25,.... will be 130 more than its 31st
term?
80. Find the cubic polynomial having
- 3, 2 and - 5 as its zeros.
81. Find the coordinates
of middle point of A(x1, y1) and B(x2,
y2)
82. The area of similar triangles ABC
and DEF are 64cm2 and 169cm2 respectively. If the length
of BC is 4cm, find the length of EF.
83. For what value of k,
does the quadratic equation 9x2 + 8kx +16 = 0 have equal
roots?
84. In a musical chair
game, the person playing the music has been advised to stop playing the music
at any time within 2 minutes after she starts playing. What is the probability
that the music will stop within the first half-minute after starting?
85. Use the method of Fundamental
Theorem of Arithmetic to find the H.C.F. of 630, 945 and 1470
86. If sin θ= cos θ find the value of
θ
87.
88. The 8th term of an
Arithmetic Progression is -23 and its 12th term is -39. Find the A.P.
89. A bag contains 9
black and 12 white balls. One ball is drawn at random. What is the probability
that the ball drawn is black ?
90. A wire when bent in the form of
an equilateral triangle encloses an area of 121 Ö3 cm2.
The same wire is bent to form a circle. Find the area enclosed by the circle.
91. Show that the product of two
irrational numbers is not necessarily irrational.
92. Find the ratio of the volume of a
cube to that of a sphere which will fit inside the cube.
93. If one of the zeros of the
quadratic polynomial f(x) = 3x2 - 20x+ 3p + 4 is four times the other, find the value of p
94. The wheels of a car are of
diameter 80 cm each. How many complete revolutions does each wheel make in 10
minutes when the car is travelling at a speed of 66 km per hour?
95. The probability that
it will rain tomorrow is 0.76. What is the probability that it will not rain
tomorrow ?
96. Two candidates are to
be selected from a group of 3 boys and 2 girls. Find the probability that
(i) one girl is
selected
(ii) at least
one girl is selected
97.
98. Find the [HCF x LCM] for 105 and
120.
99.
100. A dice is thrown
once. Find
(i) p (an even
number)
(ii) p (a number ³ 3)
(iii) p (a number £ 4)
(iv) p (a number < 7)
(v) p (a number > 6)
(vi) p(an ace )
ANSWERS
1.
2. 6cm
3. x =
7,y =13.
4.
5.
6.
7.
8.
9. 49.5
10. 147.84
m2
11. 96.
12. (i) a
= 4, d = -3 (ii) a = 3, d = 2
(iv) a = 0.7, d = 0.9
13. 264
14. x =7
or -1
15. 25th
16.
17. 1
18.
19. 2,7,12,17,…..
20. 9th
21. (i) p
≠ 6
(ii) p ≠ -6
(iii) p ≠ 12
22. (i) 2,
5, 8, 11, 14
(ii) 10, 16, 22. 28, 34
(iii) 44, 40, 36, 32,
28
(iv) 7,0,-7,-14,-21
23.
24.
25. No
26. 6 cm
27. (-2,0)
28. 1,0
29. (i) It
is an AP (ii) It is an AP
(iii) It is not an
AP (iv) It is not an AP
(v)It is not an AP (vi) It is not an AP
(vii)It is an AP
30.
31. 440 cm2
32. 3,5,7
33. 19404
cm3
34. (i)
similar
(ii) similar
(iii) equilateral
(iv) equal,
proportional
35.
36. 163
37.
38. 61.6
cm2
39. x3-10x2+11x+70.
40. 5.
41. 346.5
m2, 3293.5 m2
42. 24.64
cm
43. 64
44. 9.625cm2
45.
46. 2:3
47. 7cm
48. 37,486
49.
50.
51. (i) It
is not a quadratic equation.
(ii) It is not a
quadratic equation.
(iii) It is not a
quadratic equation.
52. -21
53. 3
54.
55. (p =
3, q =2)
56.
57. (3,-2)
58.
59.
60.
61. 20k
62. 2926 m2
63. k=2.
64.
65. (3,2)
66.
67. 25
units
68.
69.
70. 72°
71. x=2,y=1
72.
73.
74. 525 m
75. 2,7,12,17……..
76.
77.
78. 49th
79. 44th
80. x3+6x2-x-30.
81.
82. 6.5 cm
83. k = ±3
84.
85. 105.
86. 45°
87. 2.4 cm
88. 5,1,-1,-7……
89.
90. 346.5cm2
91.
92. 21 :
11
93.
94. 4375
95. 0.24
96.
97.
98. Given number are 150
and 120
HCF x LCM = Product of two numbers = 105 x 120 = 12600
99.
100.
(iv) 1 (v) 0
