maths ONLINE TEST 0% 11th Maths One Mark – Full (Based on Reduced Syllabus) Wish you all the Best ! -St. Joseph Study Centre 1 / 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 2 / 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? √(k² − 4c) √(k − 8c) √(4k² − c) √(4c − k²) 3 / 85 The area of the triangle formed by the lines x² – 4y² = 0 and x = a is? (2/√3)a² (1/2) a² 2a² (‘√3/2) a² 4 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? [0, 1] [0, 1) [0,∞) (0, 1) 5 / 85 The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is? 2x – y = √5 2x – y = 5 x – 2y – 5 = 0 x – 2y = √5 6 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 4 6 14 7 7 / 85 Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ ∪[(A∩B)∪B’] is? A B N A’ 8 / 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) (2/5, 2/5) (2/5, 3/5) (3/5, 3/5) 9 / 85 The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is? 9/2 2/9 2/3 3/2 10 / 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 11 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? neither an odd function nor an even function an even function an odd function both odd function and even function 12 / 85 The equation of the locus of the point whose distance from y-axis is half the distance from origin is? x² + 3y² = 0 3x² -y² = 0 3x² + y² = 0 x² -3y² = 0 13 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? 3 1 -1 -3 14 / 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? 1 2 zero 4 15 / 85 The value of 1 – 1/2 (2/3) + 1/3 (2/3)² – 1/4 (2/3)³ + ….. is ? 2/3 log (2/3) 5/3 log (5/3) log (5/3) 3/2 log (5/3) 16 / 85 If A and B are symmetric matrices of order n, where (A ≠ B), then A + B is skew-symmetric A + B is a zero matrix A + B is symmetric A + B is a diagonal matrix 17 / 85 The number of relations on a set containing 3 elements is? 512 81 9 1024 18 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 3 4 2 1 19 / 85 The range of the function 1 / 1-2 sin x is? (−∞,−1] ∪ [1/3 , ∞) (-1, 1/3) [-1, 1/3] (−∞,−1) ∪ (1/3 , ∞) 20 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to none of these A ∩ B A × A B × B 21 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? cannot be defined bijection one-to-one onto 22 / 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 one-to-one function a function which is not one-to-one an onto function not a function 23 / 85 If A and B are two matrices such that A + B and AB are both defined, then A and B are square matrices of same order A = B Number of columns of A is equal to the number of rows of B A and B are two matrices not necessarily of same order 24 / 85 The value of log₃ 1/81 is? -8 -4 -2 -9 25 / 85 The rule f(x) = x² is a bijection if the domain and the co-domain are given by? (0,∞),R R,R [0,∞), [0,∞) R, (0,∞) 26 / 85 The image of the point(2,3)in the line y = -x is? (-3, -2) (-2, -3) (3, 2) (-3, 2) 27 / 85 The intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are? 5, 3 5, -4 5, 5 5, -5 28 / 85 (1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) = 1 /√2 1 / √3 1 / 2 1 / 8 29 / 85 If pv = 81, then dp/dv at v = 9 is -1 -2 2 1 30 / 85 The value of logₐ b logb c logc a is? 1 2 4 3 31 / 85 The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 2 ⁻ ⁿ + n – 1 2ⁿ – n – 1 1 – 2 ⁻ ⁿ 2 ⁿ ⁻ ˡ 32 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? m + n m mn n 33 / 85 The value of (1/2!) + (1/4!) + (1/6!) + ….. Is? (e + 1)² / 2e e² – 1 / 2e e² + 1 / 2e (e -1)² / 2e 34 / 85 Which of the following is not true ? cos θ = -1 sec θ = 1/4 sin θ = -3/4 tan θ = 25 35 / 85 The value of log√2 512 is? 9 16 18 12 36 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? 2 √3 4 √2 37 / 85 The sum up to n terms of the series √2 + √8 + √18 + √32 + ….. is? n(n + 1) / √2 n(n + 1) / 2 2n (n + 1) 1 38 / 85 If 3 is the logarithm of 343, then the base is? 7 9 6 5 39 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 4/15 2/3 3/2 -4/15 40 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? -2 sinθ 2 sinθ – 2 cosθ 2 cosθ 41 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 5 8 1 4 42 / 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 + y + 3 = 0 x +1 = 0 x – y + 3 = 0 x+ y = 1 43 / 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? equivalence transitive reflexive symmetric 44 / 85 If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is? [−3, 3] [−9, 9] R [0, 9] 45 / 85 The number of solutions of x² + |x − 1| = 1 is ? zero 1 3 2 46 / 85 If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is? 2 Infinity 1 Zero 47 / 85 The derivative of f (x) = x | x | at x = −3 is 6 does not exist -6 Zero 48 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (−∞, 1] (−1,∞) R (1,∞) 49 / 85 If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? 3 1 zero 2 50 / 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 51 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 30240 69760 10000 90000 52 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 + λ² / λ 1 – λ² / 2λ 1 + λ² / 2λ 1 – λ² / λ 53 / 85 Given that x, y and b are real numbers x < y,b > 0, then? (x/b) ≥ (y/b) xb < yb xb > yb xb ≤ yb 54 / 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 =? -6/7 6/7 7/6 -7/6 55 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 11/5 5/12 -5/12 12/5 56 / 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? 4sq.units 25sq.units 20sq.units 16sq.units 57 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5, 5) (−5, 4) (4, 5) (−5,−4) 58 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? α + 3β = 11 α + 2β = 7 3α + β = 9 3α + β = 11 59 / 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 6 -8, 8 60 / 85 Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if 3α + β = 9 α + 2β = 7 α + 3β = 11 3α + 3β = 11 61 / 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 36 108 432 18 62 / 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) 63 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 81 61 71 101 64 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? zero 1 89 -1 65 / 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 ? -1/9 1/9 1 5/9 66 / 85 If |x + 2| ≤ 9, then x belongs to? (−∞,−7) ∪ [11,∞) [−11, 7] (−11, 7) (−∞,−7) 67 / 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 68 / 85 One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is? x cos θ + y (sin θ + 1) = 0 x sin θ + y ( cos θ + 1) = 0 x – y cot θ = 0 x + y tan θ = 0 69 / 85 Let R be the universal relation on a set X with more than one element. Then R is? not symmetric transitive not reflexive none of the above 70 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (1, -1) (-2, 3) (7, 3) (4, 1) 71 / 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? Range of R is {0,−1, 1} R⁻¹ = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)} Domain of R is {0,−1, 1, 2} R = {(0, 0), (0,−1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)} 72 / 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 73 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? [0, 2] (−∞, 2) [2,∞) (0, 2) 74 / 85 If y = mx + c and f (0) = f ‘(0) =1, then f (2) is -3 1 3 2 75 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? (−2,∞) [2,∞) (2,∞) (−∞, 2) 76 / 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 1120 1130 1100 insufficient data 77 / 85 The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is 3 2 4 1 78 / 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? -1, 2 1, 2 -1, 1 9, 1 79 / 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 = 3/2 k = 3 k = 1/3 k = 2/3 80 / 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 81 / 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 82 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 + √2 3 + √2 9 4 83 / 85 If log√x 0.25 = 4, then the value of x is? 0.5 2.5 1.25 1.5 84 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 3/4 1/3 1/6 2/3 85 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? -k³ / √3 -k³ / √2 ± k³ / √2 k³ / √2 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.