maths ONLINE TEST 0% 10th Maths One Mark Questions – (FULL) Based on Reduced Syllabus – St. Joseph Study Centre Wish you all the Best ! 1 / 85 If Δ > 0? Real and Equal roots No Real root None of these Real and Unequal roots 2 / 85 A shuttle cock used for playing badminton has the shape of the combination of? A hemisphere and a cone A sphere and a cone A cylinder and a sphere Frustum of a cone and a hemisphere 3 / 85 The number of divisors of any prime number is _____? 4 3 2 1 4 / 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 _______? G.P none of these Both A.P and G.P A.P 5 / 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? (D×A) ⊂ (B×A) (B×D) ⊂ (A×C) (A×B) ⊂ (A×D) (A×C)⊂ (B×D) 6 / 85 If Δ = 0? Real and Equal roots Real and Unequal roots None of these No Real root 7 / 85 P(A ∪ B) + P(A ∩ B) is ________? P(A) – P(B) P(A) + P(B) 8 / 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? Into function Identity function Many-one function One-to-one function 9 / 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? 60˚ 90˚ 30˚ 45˚ 10 / 85 Is x² + 4x + 4 a perfect square? yes no 11 / 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 x x / 2√2 x / √2 2x 12 / 85 If slope of the line PQ is 1/√3 then slope of the perpendicular bisector of PQ is? 1/ √3 -√3 zero √3 13 / 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? 3πr² sq. units 6πr² sq. units 4πr² sq. units 8πr² sq. units 14 / 85 The sum of the exponents of the prime factors in the prime factorization of 1729 is? 4 3 2 1 15 / 85 Which of the following should be added to make x⁴ + 64 a perfect square? -8x² 4x² 8x² 16x² 16 / 85 The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is? p + r / (p +q +r) q / (p +q +r) p + q / (p +q +r) p / (p +q +r) 17 / 85 The HCF of numbers of the form 2 ͫ and 3 ᶯ is ____? 3 2 1 18 / 85 The total surface are of a hemi – sphere is how much times the square of its radius? 4π 2π π 3π 19 / 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? y = 0 y = 10 x = 0 x = 10 20 / 85 Fill in the blanks for the following sequences 2, _____, 10, 17, 26,…? 2 9 4 5 21 / 85 A system of three linear equations in three variables is inconsistent if their planes? do not intersect intersect only at a point coincides with each other intersect in a line 22 / 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? 5 15 10 20 23 / 85 The point of intersection of 3x −y = 4 and x +y = 8 is? (4, 4) (3, 5) (5, 3) (2, 4) 24 / 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 8cm 6cm 4cm 3cm 25 / 85 When a positive integer is divided by 3, What are the possible remainders? 0, 1, 2 2, 1, 0 1, 0, 2 26 / 85 If Δ < 0? None of these No Real root Real and Unequal roots Real and Equal roots 27 / 85 A = {a,b, p}, B = {2, 3}, C = {p,q,r,s} then n[(A U C)×B] is? 16 12 8 20 28 / 85 If the radius of the base of a cone is tripled and the height is doubled then the volume is? Made 12 times Made 18 times unchanged Made 6 times 29 / 85 How many tangents can be drawn to the circle from an exterior point? two infinite zero one 30 / 85 Complete the quadratic equation x² + 14x + ____? 7 -49 49 14 31 / 85 The solution of (2x – 1)² = 9 is equal to? -1, 2 None of these -1 2 32 / 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? 12.8m 15m 13m 14m 33 / 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? 8x −5y = 40 x = 8 y = 5 8x + 5y = 40 34 / 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? 0 < r ≤ b 1 < r < b 0 ≤ r < b 0 < r < b 35 / 85 The solution of the system x +y −3z = −6 , −7y + 7z = 7 , 3z = 9 is? x = 1, y = −2, z = 3 x = −1, y = 2, z = 3 x = 1, y = 2, z = 3 x = −1, y = −2, z = 3 36 / 85 Find q and r for the following pairs of integers a and b satisfying a =bq +r, a = 13, b = 3? 1, 4 4, 2 4, 1 2, 4 37 / 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? 4 : 1 2 : 1 1 : 2 1 : 4 38 / 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? mᶰ nᵐ 2ᵐᶰ 2ᵐᶰ – 1 39 / 85 If n(A×B) = 6 and A = {1, 3} then n(B) is? 2 3 6 1 40 / 85 (2, 1) is the point of intersection of two lines.? x −y −3 = 0; 3x −y −7 = 0 x +y = 3; 3x +y = 7 x + 3y −3 = 0; x −y −7 = 0 3x +y = 3; x +y = 7 41 / 85 Is 1 a prime number? Yes No 42 / 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 1.4cm 8cm 3cm 4cm 43 / 85 What will be the probability that a non – leap year will have 53 Saturdays? 1/7 1/8 1/9 1/5 44 / 85 The slope of the line which is perpendicular to a line joining the points (0,0) and (–8,8) is? -1 1/3 1 -8 45 / 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? 3 / 10 1 / 5 4 / 5 2 / 3 46 / 85 Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of 340 and 412? 3 2 4 1-Jan 47 / 85 If the ordered pairs (a +2, 4) and (5,2a +b)are equal then (a,b) is? (2, –2) (3, –2) (5,1) (2,3) 48 / 85 The range of the relation R = {(x,x²) | x is a prime number less than 13} is? {2,3,5,7,11} {2,3,5,7} {1,4,9,25,49,121} {4,9,25,49,121} 49 / 85 Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are? 1, 3, 5 0, 1, 3 0, 1, 8 1, 4, 8 50 / 85 If (5,7), (3,p) and (6,6) are collinear, then the value of p is? 9 12 9 3 51 / 85 The area of triangle formed by the points (−5,0) , (0,−5) and (5,0) is? 0 sq.units 5 sq.units 25 sq.units none of these 52 / 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? 1 : 2 1 : 6 1 : 8 1 : 4 53 / 85 If A and B are mutually exclusive events then P(A∩ B) = _______. Zero 3 4 5 54 / 85 Euclid’s division algorithm is a repeated application of division lemma until we get remainder as ____? 1 4 3 55 / 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? 3/9 3/10 7/9 7/10 56 / 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? 3600π cm³ 11200π cm³ 56π cm³ 5600π cm³ 57 / 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? 2 x cm x cm 3 x cm 4 x cm 58 / 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? 45.6 m 43.92 m 41.92 m 43 m 59 / 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? 5 π (20 / 3) π (10 / 3) π (4 / 3) π 60 / 85 The ratio of the volumes of a cylinder, a cone and a sphere , if each has the same diameter and same height is? 2:1:3 1:3:2 3:1:2 1:2:3 61 / 85 Which of the following is incorrect? P(A)> 1 P(A)+P(Ā) = 1 0 ≤ P(A) ≤ 1 P(Ø) = 0 62 / 85 The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is? 136π cm² 60π cm² 68π cm² 120π cm² 63 / 85 The values of a and b if 4x⁴ −24x³ + 76x² +ax +b is a perfect square are? -120 ,100 100, 120 10 ,12 12, 10 64 / 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? b / 2 b /√3 b / 3 √3 b 65 / 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? h(1+ tan β) / 1 – tan β h(1- tan β) / 1 + tan β h tan (45˚ – β) none of these 66 / 85 The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be ? 12 cm 5 cm 13cm 10 cm 67 / 85 The number of points of intersection of the quadratic polynomial x²+ 4x + 4 with the X axis is? Zero or 1 1 zero 2 68 / 85 The HCF of two equal positive integers k, k is ____? m k k² n 69 / 85 Two positive integers are said to be relatively prime or co prime if their Highest Common Factor is? 0:00 7 1 8 70 / 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? 20, 10 20, 10 √3 30, 5 √3 30, 10 √3 71 / 85 The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is? 2025 2520 5220 5025 72 / 85 The total surface area of a cylinder whose radius is 1/3 of its height is? 9 π h² / 8 sq. units 8 π h² / 9 sq. units 56 π h² / 9 sq. units 24πh² sq. units 73 / 85 If the HCF of 65 and 117 is expressible in the form of 65m -117 , then the value of m is ? 4 2 3 1 74 / 85 Fill in the blanks for the following sequences 7, 13, 19, _____ , …? 15 35 11 25 75 / 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? 3340π cm³ 3228π cm³ 3328π cm³ 3204π cm³ 76 / 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? 1 : 2 3 : 1 1 : 3 2 : 1 77 / 85 The straight line given by the equation x = 11 is? parallel to Y axis passing through the point (0,11) passing through the origin parallel to X axis 78 / 85 Find q and r for the following pairs of integers a and b satisfying a =bq +r, a = 18, b = 4? 4, 3 3 ,4 4, 2 0, 4 79 / 85 If (x -6) is the HCF of x² -2x -24 and x² -kx -6 then the value of k is? 6 5 3 8 80 / 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 2 3 8 81 / 85 The slope of the line joining (12, 3) , (4,a) is 1/8. The value of ‘a’ is? 4 -5 2 1 82 / 85 Graph of a linear equation is a _______? straight line parabola circle hyperbola 83 / 85 The remainder when 7 x 13x 19x 23x 29 x31 is divided by 6 is ________? 9 7 2 1 84 / 85 A tangent is perpendicular to the radius at the point of contact centre infinity chord 85 / 85 The nth term of the sequence 0,2,6,12,20,… can be expressed as _____? n – n n² n² – n n Your score is Note: Once you start the test, you are not allowed to go back. Results won’t be generated if you quit the test. Complete the test within the given time. Once the time is over, the test will be submitted automatically. You can verify your answers at the result page.