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All Chapter 1 mark Impatant Question

10th Standard EM

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 80
80 x 1 = 80
1. The range of the relation R ={(x,x2) |x is a prime number less than 13} is

(a)

{2,3,5,7}

(b)

{2,3,5,7,11}

(c)

{4,9,25,49,121}

(d)

{1,4,9,25,49,121}

2. Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

(a)

{0,2,3,4,5}

(b)

{–4,1,0,2,7}

(c)

{1,2,3,4,5}

(d)

{0,1,2}

3. Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

4. If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

5. f(x) = (x+1)3 - (x-1)3 represents a function which is

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

quadratic

6. If the order pairs (a,-1) and 5,b) blongs to {(x,y)[y=2x+3}, then a and b are:

(a)

-13,2

(b)

2,13

(c)

2,-13

(d)

-2,13

7. If functionf:N⟶N,f(x)=2x then the function is, then the function is

(a)

Not one - one and not onto

(b)

one-one and onto

(c)

Not one -one but not onto

(d)

one - one but not onto

8. If(x)=mx+n,when m and n are integers f(-2)=7, and f(3)=2 then m and n are equal to :

(a)

-1,-5

(b)

1,-9

(c)

-1,5

(d)

1,9

9. If (x)=ax-2,g(x)=2x-1 and fog=gof, the value of a is

(a)

3

(b)

-3

(c)

$\cfrac { 1 }{ 3 }$

(d)

13

10. If(x)=2-3x, then f of(1-x)=?

(a)

5x+9

(b)

9x-5

(c)

5-9x

(d)

5x-9

11. Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

(a)

1 < r < b

(b)

0 < r < b

(c)

$\le$ r < b

(d)

0 < r $\le$ b

12. The sum of the exponents of the prime factors in the prime factorization of 1729 is

(a)

1

(b)

2

(c)

3

(d)

4

13. 74k $\equiv$ ________ (mod 100)

(a)

1

(b)

2

(c)

3

(d)

4

14. Given F1 = 1, F2 = 3 and Fn = Fn-1+Fn-2 then F5 is

(a)

3

(b)

5

(c)

8

(d)

11

15. The next term of the sequence $\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 }$, ..... is

(a)

$\frac { 1 }{ 24 }$

(b)

$\frac { 1 }{ 27 }$

(c)

$\frac { 2 }{ 3 }$

(d)

$\frac { 1 }{ 81 }$

16. If 3 is the least prime factor of number and 7 is least prime factor of b, then the least prime factor a+b is

(a)

a+b

(b)

2

(c)

5

(d)

10

17. The difference between the remainders when 6002 and 601 are divided by 6 is:

(a)

2

(b)

1

(c)

0

(d)

3

18. The first term of an A,P.whose 8th and 12th terms are 39 and 59 respectively is :

(a)

5

(b)

6

(c)

4

(d)

3

19. a boy saves Rs1 on the first day Rs2 on the second day, Rs4 on the third day and so on.How much did the boy will save upto 20 days?

(a)

219+1

(b)

219-1

(c)

220-1

(d)

221-1

20. In an A.P if the pth term is q and the qth term is p, then its nth term is

(a)

p+q-n

(b)

p+q+n

(c)

p-q+n

(d)

p-q-n

21. The solution of the system x + y − 3x = −6, −7y + 7z = 7 , 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = 2, z = 3

22. y2 + $\frac {1}{y^{2}}$ is not equal to

(a)

$\frac {y^{2} + 1}{y^{2}}$

(b)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }$

(c)

${ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2$

(d)

${ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2$

23. Which of the following should be added to make x4 + 64 a perfect square

(a)

4x2

(b)

16x2

(c)

8x2

(d)

-8x2

24. Graph of a linear polynomial is a

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

25. For the given matrix A = $\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right)$ the order of the matrix AT is

(a)

2 x 3

(b)

3 x 2

(c)

3 x 4

(d)

4 x 3

26. Which of the following is correct
(i) Every polynomial has finite number of multiples
(ii) LCM of two polynimials of degree 2 may be a constant
(iii) HCF of 2 polynomials may be constant
(iv) Degree of HCF of two polynomials is always less then degree of LCM

(a)

(i) and (ii)

(b)

(iii) and (iv)

(c)

(iii) only

(d)

(iv) only

27. The HCF of two polynomials p(x) and q(x) is 2x(x+2) and LCM is 24x(x+2)2 (x-2) if p(x)=8x3+32x2+32x, then q(x)

(a)

4x3-16x

(b)

6x3-24x

(c)

12x3+24x

(d)

12x3-24x

28. Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(a)

(i) and (iii) only

(b)

(iii) only

(c)

(iv) only

(d)

(ii) and (iv) only

29. If $2A+3B=\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \end{matrix} \right]$ and $A+2B=\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \end{matrix} \right]$ then B=[hint:B=(A+2B)-(2+3B)]

(a)

$\left[ \begin{matrix} 8 & -1 & -2 \\ -1 & 10 & -1 \end{matrix} \right]$

(b)

$\left[ \begin{matrix} 8 & -1 & 2 \\ -1 & 10 & -1 \end{matrix} \right]$

(c)

$\left[ \begin{matrix} 8 & 1 & 2 \\ -1 & 10 & -1 \end{matrix} \right]$

(d)

$\left[ \begin{matrix} 8 & 1 & 2 \\ 1 & 10 & 1 \end{matrix} \right]$

30. If $A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right]$ and $I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right]$ then A2=16I for:

(a)

y=4

(b)

y=5

(c)

y=-4

(d)

y=16

31. In a given figure ST||QR,PS=2cm and SQ=3 cm.
Then the ratio of the area of $\triangle$PQR to the area $\triangle$PST is

(a)

25 : 4

(b)

25 : 7

(c)

25 : 11

(d)

25 : 13

32. In a $\triangle$ABC, AD is the bisector $\angle$BAC.If AB=5cm and DC=8cm. The length of the side AC is

(a)

6 cm

(b)

4 cm

(c)

3 cm

(d)

8 cm

33. The two tangents from an external points P to a circle with centre at O are PA and PB.If $\angle APB$=70o then the value of $\angle AOB$ is

(a)

100°

(b)

110°

(c)

120°

(d)

130°

34. In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP=11 cm andBC =7 cm, then the length of BR is

(a)

6 cm

(b)

5 cm

(c)

8 cm

(d)

4 cm

35. In figure if PR is tangent to the circle at P and O is the centre of the circle, then $\angle PQR$ is

(a)

120o

(b)

100°

(c)

110°

(d)

90°

36. A line which intersects a circle at two distinct points ic called

(a)

Point of contact

(b)

sccant

(c)

diameter

(d)

tangent

37. If the angle between two radil of a circle is o, the angle between the tangents at the end of the radii is

(a)

50o

(b)

90o

(c)

40o

(d)

70o

38. In figure $\angle OAB={ 60 }^{ o }$ and OA=6cm then radius of the circle is

(a)

$\cfrac { 3 }{ 2 } \sqrt { 3 } cm$

(b)

2 cm

(c)

$3\sqrt { 3 } cm$

(d)

$2\sqrt { 3 } cm$

39. Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

(a)

$\sqrt { { a }^{ 2 }-{ b }^{ 2 } }$

(b)

$\sqrt { { a }^{ 2 }-{ b }^{ 2 } }$

(c)

$\sqrt { { a }^{ 2 }+{ b }^{ 2 } }$

(d)

$2\sqrt { { a }^{ 2 }+{ b }^{ 2 } }$

40. Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

(a)

1 cm

(b)

3 cm

(c)

5 cm

(d)

4 cm

41. The slope of the line joining (12, 3) , (4, a) is $\frac 18$The value of ‘a’ is

(a)

1

(b)

4

(c)

-5

(d)

2

42. The slope of the line which is perpendicular to line joining the points (0, 0) and (–8, 8) is

(a)

–1

(b)

1

(c)

$\frac13$

(d)

-8

43. The equation of a line passing through the origin and perpendicular to the line

(a)

7x - 3y + 4 = 0

(b)

3x - 7y + 4 = 0

(c)

3x + 7y = 0

(d)

7x - 3y = 0

44. Consider four straight lines
(i) l1 : 3y = 4x + 5
(ii) l2 : 4y = 3x - 1
(iii) l3 : 4y + 3x =7
(iv) l4 : 4x + 3y = 2
Which of the following statement is true?

(a)

l1 and l2 are perpendicular

(b)

l1 and l4 are parallel

(c)

l2 and l4 are perpendicular

(d)

l2 and l3 are parallel

45. When proving that a quadrilateral is a parallelogram by using slopes you must find

(a)

The slopes of two sides

(b)

The slopes of two pair of opposite sides

(c)

The lengths of all sides

(d)

Both the lengths and slopes of two sides

46. f the points (0,0), (a,0) and (0,b) are colllinear, then

(a)

a=b

(b)

a+b

(c)

ab=0

(d)

a≠b

47. Find the slope and the y-intercept of the line $3y-\sqrt { 3x } +1=0$ is

(a)

$\cfrac { 1 }{ \sqrt { 3 } } ,\cfrac { -1 }{ 3 }$

(b)

$-\cfrac { 1 }{ \sqrt { 3 } } ,\cfrac { -1 }{ 3 }$

(c)

$\sqrt { 3 } ,1$

(d)

$-\sqrt { 3 } ,3$

48. Find the value of 'a' if the lines 7y=ax+4 and 2y=3-x are parallel

(a)

$\cfrac { 7 }{ 2 }$

(b)

$-\cfrac { 2 }{ 7 }$

(c)

$\cfrac { 2 }{ 7 }$

(d)

$-\cfrac { 7 }{ 2 }$

49. A line passing through the point (2,2) and the axes enclose an aream ∝. The intercept on the axes made by the line are given by the roots of

(a)

x2-2-∝x+∝=0

(b)

x2+2∝x+∝=0

(c)

x2-∝x+2∝=0

(d)

none of these

50. In a right angle traiangle, right angled at B, if the side BC is parallel to x axis, then the slope of AB is :

(a)

$\sqrt { 3 }$

(b)

$\cfrac { 1 }{ \sqrt { 3 } }$

(c)

1

(d)

not defined

51. tan$\theta$cosec2$\theta$-tan$\theta$ is equal to

(a)

sec$\theta$

(b)

$cot^{ 2 }\theta$

(c)

sin$\theta$

(d)

$cot\theta$

52. A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

(a)

41.92 m

(b)

43.92 m

(c)

43 m

(d)

45.6 m

53. The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

(a)

20,10$\sqrt { 3 }$

(b)

30,5$\sqrt { 3 }$

(c)

20,10

(d)

30,10$\sqrt { 3 }$

54. Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

(a)

$\sqrt { 2 }$ x

(b)

$\frac { x }{ 2\sqrt { 2 } }$

(c)

$\frac { x }{ \sqrt { 2 } }$

(d)

2x

55. If (sin α + cosec α)+ (cos α + sec α)= k + tan2α + cot2α, then the value of k is equal to

(a)

9

(b)

7

(c)

5

(d)

3

56. The value of the expression $\left[ \frac { { sin }^{ 2 }{ 22 }^{ o }+{ sin }^{ 2 }{ 68 }^{ o } }{ { cos }^{ 2 }{ 22 }^{ 0 }+{ cos }^{ 2 }{ 68 }^{ 0 } } +{ sin }^{ 2 }{ 63 }^{ o+ }{ cos }63^{ 0 }{ sin27 }^{ 0 } \right]$is

(a)

3

(b)

2

(c)

1

(d)

0

57. If secθ + tanθ=n, and secθ-tanθ=0, then the value of mn is

(a)

2

(b)

1

(c)

土1

(d)

土2

58. (cosec2θ-cot2θ) (1-cos2θ) is equal to

(a)

cosec θ

(b)

cos2θ

(c)

sec2θ

(d)

sin2θ

59. $\cfrac { tan\theta }{ sec\theta } +\cfrac { tan\theta }{ sec\theta +1 }$ is equal to

(a)

2tanθ

(b)

2secθ

(c)

2cosecθ

(d)

2 tanθsecθ

60. A ladder of length 14m just reaches the top of a wall. If the ladder makes an angle of 60o with the horizontal, then the height of the wall is:

(a)

$14\sqrt { 3 }$

(b)

$28\sqrt { 3 }$

(c)

$7\sqrt { 3 }$

(d)

$35\sqrt { 3 }$

61. The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

(a)

60$\pi$ cm2

(b)

68$\pi$ cm2

(c)

120$\pi$ cm2

(d)

136$\pi$ cm2

62. Th e height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

(a)

12 cm

(b)

10 cm

(c)

13 cm

(d)

5 cm

63. If the radius of the base of a cone is tripled and the height is doubled then the volume is

(a)

made 6 times

(b)

made 18 times

(c)

made 12 times

(d)

unchanged

64. A spherical ball of radius r1 units is melted to make 8 new identical balls each of radius r2 units. Then r1 r2: is

(a)

2:1

(b)

1:2

(c)

4:1

(d)

1:4

65. The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(a)

$\frac{4}{3}\pi$

(b)

$\frac{10}{3}\pi$

(c)

$5\pi$

(d)

$\frac{20}{3}\pi$

66. How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

(a)

64

(b)

216

(c)

512

(d)

16

67. The ratio of the volumes of two spheres is 8:27. If r and R are the radii of sphere respectively, Then (R-r):r is

(a)

1:2

(b)

1:3

(c)

2:3

(d)

4:9

68. A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cmrespectively, then its slant height is:

(a)

15 cm

(b)

12 cm

(c)

10 cm

(d)

17 cm

69. A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is:

(a)

1:3

(b)

$1:\sqrt { 3 }$

(c)

1:1

(d)

$\sqrt { 3 } :1$

70. A floating boat having a length 3m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it.The mass of the man is (density of water is 10000 kg/m3)

(a)

50kg

(b)

60kg

(c)

70kg

(d)

80kg

71. Which of the following is not a measure of dispersion?

(a)

Range

(b)

Standard deviation

(c)

Arithmetic mean

(d)

Variance

72. The sum of all deviations of the data from its mean is

(a)

Always positive

(b)

always negative

(c)

zero

(d)

non-zero integer

73. The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

(a)

3

(b)

15

(c)

5

(d)

225

74. If the standard deviation of x, y, z is p then the standard deviation of 3x+5, 3y+5, 3z +5 is

(a)

3p+5

(b)

3p

(c)

p + 5

(d)

9p + 15

75. A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

(a)

$\frac{3}{10}$

(b)

$\frac{7}{10}$

(c)

$\frac{3}{9}$

(d)

$\frac{7}{9}$

76. which of the following is true?

(a)

0≤p(∈)≤1

(b)

p(∈)>1

(c)

p(∈)<0

(d)

$-\frac { 1 }{ 2 } \ge P(\epsilon )\le \frac { 1 }{ 2 }$

77. IF the probability of the non-happening of a event is q, then the probability of happening of that event is

(a)

1-q

(b)

q

(c)

q/2

(d)

∝q

78. The variance of 5 values is 16. If each value is doubled. them the standard deviation of new values is_______

(a)

4

(b)

8

(c)

32

(d)

16

79. The range of first 10 prime number is

(a)

9

(b)

20

(c)

27

(d)

5

80. When three coins are tossed, the probability of getting the same face on all the three coins is

(a)

$\cfrac { 1 }{ 8 }$

(b)

$\cfrac { 1 }{ 4 }$

(c)

$\cfrac { 3 }{ 8 }$

(d)

$\cfrac { 1 }{ 3 }$