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 nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 2 ⁿ ⁻ ˡ 2 ⁻ ⁿ + n – 1 1 – 2 ⁻ ⁿ 2ⁿ – n – 1 2 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? onto one-to-one cannot be defined bijection 3 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (7, 3) (-2, 3) (4, 1) (1, -1) 4 / 85 The intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are? 5, 5 5, -5 5, 3 5, -4 5 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 30240 90000 69760 10000 6 / 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 7 / 85 The number of relations on a set containing 3 elements is? 1024 9 512 81 8 / 85 Which of the following equation is the locus of (at²; 2at)? y² = 4ax x² + y² = a² x²/a² + y²/b² = 1 x²/a² – y²/b² = 1 9 / 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? Both S and T are equivalence relation T is an equivalence relation but S is not an equivalence relation S is an equivalence relation but T is not an equivalence relation Neither S nor T is an equivalence relation 10 / 85 Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ ∪[(A∩B)∪B’] is? N A B A’ 11 / 85 The number of solutions of x² + |x − 1| = 1 is ? 2 zero 1 3 12 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 81 101 61 71 13 / 85 The derivative of f (x) = x | x | at x = −3 is Zero 6 -6 does not exist 14 / 85 The rule f(x) = x² is a bijection if the domain and the co-domain are given by? (0,∞),R R, (0,∞) R,R [0,∞), [0,∞) 15 / 85 If A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains? only one element cannot be determined no element infinitely many elements 16 / 85 If y = mx + c and f (0) = f ‘(0) =1, then f (2) is 2 1 3 -3 17 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? -1 -3 1 3 18 / 85 Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if 3α + β = 9 α + 3β = 11 3α + 3β = 11 α + 2β = 7 19 / 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 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 20 / 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 9, 1 1, 2 -1, 1 21 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? (0, 1) [0, 1) [0, 1] [0,∞) 22 / 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 23 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (1,∞) (−∞, 1] (−1,∞) R 24 / 85 Which of the following is not true ? sin θ = -3/4 sec θ = 1/4 cos θ = -1 tan θ = 25 25 / 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 26 / 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 27 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 5/12 12/5 -5/12 11/5 28 / 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 29 / 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 2 Zero 30 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 3 1 2 4 31 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 5 1 8 4 32 / 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 = 2/3 k = 3/2 k = 3 k = 1/3 33 / 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 reflexive transitive symmetric 34 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? ± k³ / √2 -k³ / √3 -k³ / √2 k³ / √2 35 / 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 36 / 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 7/6 -7/6 6/7 37 / 85 If pv = 81, then dp/dv at v = 9 is 2 1 -2 -1 38 / 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 4 1 2 39 / 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? Domain of R is {0,−1, 1, 2} 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)} Range of R is {0,−1, 1} 40 / 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 16sq.units 20sq.units 25sq.units 41 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? [2,∞) (0, 2) (−∞, 2) [0, 2] 42 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 + λ² / 2λ 1 – λ² / λ 1 – λ² / 2λ 1 + λ² / λ 43 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? 3α + β = 9 α + 3β = 11 α + 2β = 7 3α + β = 11 44 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? 1 -1 zero 89 45 / 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) 46 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? an odd function neither an odd function nor an even function both odd function and even function an even function 47 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? – 2 cosθ 2 sinθ -2 sinθ 2 cosθ 48 / 85 The value of log√2 512 is? 18 16 12 9 49 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 3 + √2 9 4 + √2 50 / 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 51 / 85 The value of log₃ 1/81 is? -8 -4 -2 -9 52 / 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 -1/9 1/9 53 / 85 If 3 is the logarithm of 343, then the base is? 9 5 7 6 54 / 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 55 / 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 56 / 85 If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? 1 zero 3 2 57 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? n m m + n mn 58 / 85 If log√x 0.25 = 4, then the value of x is? 0.5 1.5 1.25 2.5 59 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 1/6 3/4 1/3 2/3 60 / 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) √(k − 8c) √(k² − 4c) √(4k² − c) 61 / 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 62 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 4 6 14 7 63 / 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] 64 / 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 x – 2y – 5 = 0 2x – y = √5 x – 2y = √5 65 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? [2,∞) (−2,∞) (−∞, 2) (2,∞) 66 / 85 The value of logₐ b logb c logc a is? 2 1 3 4 67 / 85 If |x + 2| ≤ 9, then x belongs to? (−∞,−7) ∪ [11,∞) [−11, 7] (−11, 7) (−∞,−7) 68 / 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 + y + 3 = 0 x+ y = 1 x +1 = 0 69 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5, 4) (4, 5) (−5,−4) (−5, 5) 70 / 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) (3/5, 3/5) (3/2, 5/2) 71 / 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 72 / 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 1100 insufficient data 1130 1120 73 / 85 The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is? 9/2 2/3 3/2 2/9 74 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to none of these B × B A ∩ B A × A 75 / 85 The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is 1 3 2 4 76 / 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? not a function a function which is not one-to-one an onto function an one-to-one function 77 / 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) 3/2 log (5/3) 5/3 log (5/3) log (5/3) 78 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 4/15 3/2 2/3 -4/15 79 / 85 Let R be the universal relation on a set X with more than one element. Then R is? transitive none of the above not symmetric not reflexive 80 / 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 + y tan θ = 0 x – y cot θ = 0 x sin θ + y ( cos θ + 1) = 0 81 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? 2 √2 √3 4 82 / 85 The image of the point(2,3)in the line y = -x is? (-3, -2) (-2, -3) (3, 2) (-3, 2) 83 / 85 The range of the function 1 / 1-2 sin x is? [-1, 1/3] (−∞,−1) ∪ (1/3 , ∞) (−∞,−1] ∪ [1/3 , ∞) (-1, 1/3) 84 / 85 Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0? (0,-1) (-2,3) (1,2) (0,0) 85 / 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? -8 6 10 -8, 8 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.