maths ONLINE TEST 0% 11th Maths One Mark – Full (Based on Reduced Syllabus) Wish you all the Best ! -St. Joseph Study Centre 1 / 85 If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x- axis, then tan α tan β =? 7/6 6/7 -6/7 -7/6 2 / 85 Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is? an onto function an one-to-one function a function which is not one-to-one not a function 3 / 85 The sum up to n terms of the series √2 + √8 + √18 + √32 + ….. is? n(n + 1) / √2 2n (n + 1) 1 n(n + 1) / 2 4 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5,−4) (4, 5) (−5, 5) (−5, 4) 5 / 85 If |x + 2| ≤ 9, then x belongs to? [−11, 7] (−∞,−7) ∪ [11,∞) (−11, 7) (−∞,−7) 6 / 85 Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is? symmetric equivalence transitive reflexive 7 / 85 Which of the following equation is the locus of (at²; 2at)? y² = 4ax x²/a² + y²/b² = 1 x² + y² = a² x²/a² – y²/b² = 1 8 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? 1 89 zero -1 9 / 85 If log√x 0.25 = 4, then the value of x is? 2.5 1.25 0.5 1.5 10 / 85 If A and B are symmetric matrices of order n, where (A ≠ B), then A + B is a zero matrix A + B is symmetric A + B is skew-symmetric A + B is a diagonal matrix 11 / 85 The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. How many students take at least one of these two subjects is 1130 1120 insufficient data 1100 12 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? neither an odd function nor an even function both odd function and even function an even function an odd function 13 / 85 If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is? 1 Infinity Zero 2 14 / 85 The value of 1 – 1/2 (2/3) + 1/3 (2/3)² – 1/4 (2/3)³ + ….. is ? 5/3 log (5/3) 2/3 log (2/3) log (5/3) 3/2 log (5/3) 15 / 85 If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? 2 3 zero 1 16 / 85 The image of the point(2,3)in the line y = -x is? (3, 2) (-3, 2) (-2, -3) (-3, -2) 17 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 8 4 5 1 18 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? (−∞, 2) (0, 2) [2,∞) [0, 2] 19 / 85 The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is? 3/2 9/2 2/3 2/9 20 / 85 If the two straight lines x + (2k – 7)y + 3=0 and 3kx + 9y – 5 = 0 are perpendicular then the value of k is? k = 3 k = 2/3 k = 3/2 k = 1/3 21 / 85 The value of log₃ 1/81 is? -9 -8 -2 -4 22 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? [0,∞) (0, 1) [0, 1) [0, 1] 23 / 85 (1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) = 1 / 8 1 / √3 1 / 2 1 /√2 24 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? bijection one-to-one cannot be defined onto 25 / 85 The equation of the locus of the point whose distance from y-axis is half the distance from origin is? 3x² + y² = 0 x² -3y² = 0 x² + 3y² = 0 3x² -y² = 0 26 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? 3α + β = 9 3α + β = 11 α + 2β = 7 α + 3β = 11 27 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? 3 1 -1 -3 28 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 14 4 7 6 29 / 85 Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if α + 3β = 11 3α + 3β = 11 α + 2β = 7 3α + β = 9 30 / 85 If a is the arithmetic mean and g is the geometric mean of two numbers, then a = g a ≥ g a > g a ≤ g 31 / 85 The range of the function 1 / 1-2 sin x is? (-1, 1/3) (−∞,−1] ∪ [1/3 , ∞) (−∞,−1) ∪ (1/3 , ∞) [-1, 1/3] 32 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? 4 2 √3 √2 33 / 85 If A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains? no element only one element infinitely many elements cannot be determined 34 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? ± k³ / √2 -k³ / √3 -k³ / √2 k³ / √2 35 / 85 If a and b are the roots of the equation x² − kx + 16 = 0 and satisfy a² + b² = 32, then the value of k is? 10 -8, 8 6 -8 36 / 85 Given that x, y and b are real numbers x < y,b > 0, then? xb > yb xb ≤ yb xb < yb (x/b) ≥ (y/b) 37 / 85 The relation R defined on a set A = {0,−1, 1, 2} by xRy if |x² + y² | ≤ 2, then which one of the following is true? R⁻¹ = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)} Domain of R is {0,−1, 1, 2} Range of R is {0,−1, 1} R = {(0, 0), (0,−1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)} 38 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (7, 3) (-2, 3) (1, -1) (4, 1) 39 / 85 The line (p + 2q)x + (p – 3q)y = p – q for different values of p and q passes through the point? (3/2, 5/2) (3/5, 3/5) (2/5, 3/5) (2/5, 2/5) 40 / 85 If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is? [0, 9] R [−3, 3] [−9, 9] 41 / 85 If 3 is the logarithm of 343, then the base is? 6 9 5 7 42 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to B × B none of these A × A A ∩ B 43 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 69760 10000 90000 30240 44 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 4 + √2 9 3 + √2 45 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? [2,∞) (−2,∞) (2,∞) (−∞, 2) 46 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (−1,∞) (1,∞) (−∞, 1] R 47 / 85 If a vertex of a square is at the origin and its one side lies along the line 4x + 3y – 20 =0, then the area of the square is? 25sq.units 20sq.units 16sq.units 4sq.units 48 / 85 The number of solutions of x² + |x − 1| = 1 is ? 2 3 zero 1 49 / 85 Find a so that the sum and product of the roots of the equation 2x² + (a − 3)x + 3a − 5 = 0 are equal is? 2 4 zero 1 50 / 85 Which of the following is not true ? sin θ = -3/4 sec θ = 1/4 tan θ = 25 cos θ = -1 51 / 85 Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ ∪[(A∩B)∪B’] is? A’ N B A 52 / 85 The equation whose roots are numerically equal but opposite in sign to the roots of 3x² − 5x − 7 = 0 is? 3x² − 5x+7 = 0 3x²+ 5x − 7 = 0 3x² − 5x − 7 = 0 3x² + x − 7 53 / 85 The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is? x – 2y = √5 2x – y = 5 x – 2y – 5 = 0 2x – y = √5 54 / 85 The value of log√2 512 is? 12 18 9 16 55 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? m + n m mn n 56 / 85 The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 2 ⁿ ⁻ ˡ 1 – 2 ⁻ ⁿ 2 ⁻ ⁿ + n – 1 2ⁿ – n – 1 57 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 1 4 2 3 58 / 85 If y = mx + c and f (0) = f ‘(0) =1, then f (2) is 3 1 -3 2 59 / 85 The value of (1/2!) + (1/4!) + (1/6!) + ….. Is? e² + 1 / 2e (e -1)² / 2e e² – 1 / 2e (e + 1)² / 2e 60 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 81 101 71 61 61 / 85 Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer } Then which of the following is true? S is an equivalence relation but T is not an equivalence relation Neither S nor T is an equivalence relation Both S and T are equivalence relation T is an equivalence relation but S is not an equivalence relation 62 / 85 Let R be the universal relation on a set X with more than one element. Then R is? none of the above transitive not symmetric not reflexive 63 / 85 The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is 108 18 432 36 64 / 85 The number of relations on a set containing 3 elements is? 81 1024 512 9 65 / 85 If pv = 81, then dp/dv at v = 9 is -1 -2 2 1 66 / 85 If 8 and 2 are the roots of x² +ax+c = 0 and 3, 3 are the roots of x² +dx+b = 0, then the roots of the equation x² + ax + b = 0 are? 9, 1 -1, 2 1, 2 -1, 1 67 / 85 The intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are? 5, 5 5, 3 5, -5 5, -4 68 / 85 The value of logₐ b logb c logc a is? 1 4 2 3 69 / 85 θ is acute angle between the lines x² – xy – 6y² = 0, then (2 cos θ + 3 sin θ / 4 sin θ + 5 cos θ) is ? 5/9 1/9 -1/9 1 70 / 85 The derivative of f (x) = x | x | at x = −3 is 6 Zero -6 does not exist 71 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? -2 sinθ 2 cosθ – 2 cosθ 2 sinθ 72 / 85 One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is? x sin θ + y ( cos θ + 1) = 0 x cos θ + y (sin θ + 1) = 0 x + y tan θ = 0 x – y cot θ = 0 73 / 85 The coordinates of the four vertices of a quadrilateral are (-2,4), (-1,2), (1,2) and (2,4)taken in order. The equation of the line passing through the vertex(-1,2) and dividing the quadrilateral in the equal areas is? x +1 = 0 x+ y = 1 x + y + 3 = 0 x – y + 3 = 0 74 / 85 The rule f(x) = x² is a bijection if the domain and the co-domain are given by? R,R R, (0,∞) [0,∞), [0,∞) (0,∞),R 75 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 2/3 4/15 3/2 -4/15 76 / 85 The slope of the line which makes an angle 45⁰ with the line 3x – y = -5 are? 1, 1/2 1, -1 1/2, -2 2, -1/2 77 / 85 The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is 4 1 2 3 78 / 85 Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0? (1,2) (-2,3) (0,-1) (0,0) 79 / 85 Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 +2√2 is? x + y – √2 = 0 x + y – 2 = 0 x + y + √2 = 0 x + y + 2 = 0 80 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 1/6 3/4 2/3 1/3 81 / 85 If a and b are the real roots of the equation x² − kx + c = 0, then the distance between the points (a, 0) and (b, 0) is? √(4c − k²) √(4k² − c) √(k − 8c) √(k² − 4c) 82 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 11/5 5/12 12/5 -5/12 83 / 85 The area of the triangle formed by the lines x² – 4y² = 0 and x = a is? (1/2) a² (‘√3/2) a² 2a² (2/√3)a² 84 / 85 If A and B are two matrices such that A + B and AB are both defined, then Number of columns of A is equal to the number of rows of B A and B are square matrices of same order A = B A and B are two matrices not necessarily of same order 85 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 + λ² / λ 1 – λ² / 2λ 1 – λ² / λ 1 + λ² / 2λ 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. 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