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