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