## maths ONLINE TEST

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10th Maths One Mark Questions – (FULL) Based on Reduced Syllabus – St. Joseph Study Centre

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1 / 85

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?

2 / 85

A shuttle cock used for playing badminton has the shape of the combination of?

3 / 85

If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is?

4 / 85

The ratio of the volumes of a cylinder, a cone and a sphere , if each has the same diameter and same height is?

5 / 85

The area of triangle formed by the points (−5,0) , (0,−5) and (5,0) is?

6 / 85

If the roots of the equation q²x² + p²x +r² = 0 are the squares of the roots of the equation qx² + px +r = 0 , then q, p, r are in _______?

7 / 85

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is 1 / 9, then the number of tickets bought by Kamalam is?

8 / 85

How many tangents can be drawn to the circle from an exterior point?

9 / 85

Find q and r for the following pairs of integers a and b satisfying a =bq +r, a = 13, b = 3?

10 / 85

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is?

11 / 85

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be ?

12 / 85

If the ratio of the height of a tower and the length of its shadow is √3: 1, then the angle of elevation of the sun has measure?

13 / 85

When a positive integer is divided by 3, What are the possible remainders?

14 / 85

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

15 / 85

In in a triangle ABC, BE is parallel to BC. AB = 3.6cm, AC = 2.4cm and AD = 2.1 cm then the length of AE is

16 / 85

The point of intersection of 3x −y = 4 and x +y = 8 is?

17 / 85

The number of points of intersection of the quadratic polynomial x²+ 4x + 4 with the X axis is?

18 / 85

In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is?

19 / 85

(2, 1) is the point of intersection of two lines.?

20 / 85

If A = {1,2}, B = {1,2, 3, 4},C = {5,6} and D = {5, 6, 7, 8} then state which of the following statement is true?

21 / 85

If the HCF of 65 and 117 is expressible in the form of 65m -117 , then the value of m is ?

22 / 85

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

23 / 85

What will be the probability that a non – leap year will have 53 Saturdays?

24 / 85

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

25 / 85

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1 : 2 the r₂ : r₁ is?

26 / 85

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

27 / 85

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is?

28 / 85

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?

29 / 85

If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is?

30 / 85

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are?

31 / 85

The electric pole subtends an angle of 30˚ at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the tower is 60˚. The height of the tower (in ,metres) is equal to?

32 / 85

P(A ∪ B) + P(A ∩ B) is ________?

33 / 85

The angle of elevation of a cloud from a point h metres above a lake is β. The angle of depression of its reflection in the lake is 45˚. The height of location of the could from the lake is?

34 / 85

If slope of the line PQ is 1/√3 then slope of the perpendicular bisector of PQ is?

35 / 85

Complete the quadratic equation x² + 14x + ____?

36 / 85

Is x² + 4x + 4 a perfect square?

37 / 85

Fill in the blanks for the following sequences 7, 13, 19, _____ , …?

38 / 85

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 building (in metres) is?

39 / 85

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?

40 / 85

If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is?

41 / 85

Two positive integers are said to be relatively prime or co prime if their Highest Common Factor is?

42 / 85

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?

43 / 85

If Δ < 0?

44 / 85

The HCF of two equal positive integers k, k is ____?

45 / 85

The total surface area of a cylinder whose radius is 1/3 of its height is?

46 / 85

If Δ = 0?

47 / 85

A = {a,b, p}, B = {2, 3}, C = {p,q,r,s} then n[(A U C)×B] is?

48 / 85

The straight line given by the equation x = 11 is?

49 / 85

If A and B are mutually exclusive events then P(A∩ B) = _______.

50 / 85

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?

51 / 85

The values of a and b if 4x⁴ −24x³ + 76x² +ax +b is a perfect square are?

52 / 85

A frustum of a right circular cone is of height 16 cm with radii of its ends as 8cm and 20cm. Then, the volume of the frustum is?

53 / 85

A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is?

54 / 85

The sum of the exponents of the prime factors in the prime factorization of 1729 is?

55 / 85

In a triangle ABC, AD is the the bisector of Angle BAC, if AB= 8cm, BD = 6cm and DC = 3cm. The length of the side AC is

56 / 85

Fill in the blanks for the following sequences 2, _____, 10, 17, 26,…?

57 / 85

The remainder when 7 x 13x 19x 23x 29 x31 is divided by 6 is ________?

58 / 85

The slope of the line joining (12, 3) , (4,a) is 1/8. The value of ‘a’ is?

59 / 85

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

60 / 85

Two poles of heights 6m and 11m stands vertically on a plane ground. If the distance between their feet is 12m, what is the distance between their tops?

61 / 85

Find q and r for the following pairs of integers a and b satisfying a =bq +r, a = 18, b = 4?

62 / 85

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is?

63 / 85

Is 1 a prime number?

64 / 85

The number of divisors of any prime number is _____?

65 / 85

The range of the relation R = {(x,x²) | x is a prime number less than 13} is?

66 / 85

Let A = {1,2, 3, 4} and B = {4, 8,9,10}. A function f : A→ B given by f = {(1, 4),(2, 8),(3,9),(4,10)} is a?

67 / 85

The nth term of the sequence 0,2,6,12,20,… can be expressed as _____?

68 / 85

The solution of (2x – 1)² = 9 is equal to?

69 / 85

The total surface are of a hemi – sphere is how much times the square of its radius?

70 / 85

A tangent is perpendicular to the radius at the

71 / 85

Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of 340 and 412?

72 / 85

If Δ > 0?

73 / 85

Graph of a linear equation is a _______?

74 / 85

If the ordered pairs (a +2, 4) and (5,2a +b)are equal then (a,b) is?

75 / 85

If n(A×B) = 6 and A = {1, 3} then n(B) is?

76 / 85

Euclid’s division algorithm is a repeated application of division lemma until we get remainder as ____?

77 / 85

If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is?

78 / 85

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

79 / 85

Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is?

80 / 85

Which of the following is incorrect?

81 / 85

If (5,7), (3,p) and (6,6) are collinear, then the value of p is?

82 / 85

A system of three linear equations in three variables is inconsistent if their planes?

83 / 85

A purse contains 10 notes of ₹2000, 15 notes of ₹500, and 25 notes of ₹200. One note is drawn at random. What is the probability that the note is either a ₹500 note or ₹200 note?

84 / 85

If (x -6) is the HCF of x² -2x -24 and x² -kx -6 then the value of k is?

85 / 85

The HCF of numbers of the form 2 ͫ and 3 ᶯ is ____?