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 point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? zero 3 1 2 2 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5,−4) (−5, 4) (−5, 5) (4, 5) 3 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? -1 89 1 zero 4 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (4, 1) (1, -1) (7, 3) (-2, 3) 5 / 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 only one element infinitely many elements 6 / 85 The value of (1/2!) + (1/4!) + (1/6!) + ….. Is? (e + 1)² / 2e (e -1)² / 2e e² – 1 / 2e e² + 1 / 2e 7 / 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 8 / 85 One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is? x – y cot θ = 0 x sin θ + y ( cos θ + 1) = 0 x + y tan θ = 0 x cos θ + y (sin θ + 1) = 0 9 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? α + 2β = 7 α + 3β = 11 3α + β = 11 3α + β = 9 10 / 85 Which of the following equation is the locus of (at²; 2at)? x²/a² – y²/b² = 1 y² = 4ax x² + y² = a² x²/a² + y²/b² = 1 11 / 85 The range of the function 1 / 1-2 sin x is? (-1, 1/3) (−∞,−1] ∪ [1/3 , ∞) [-1, 1/3] (−∞,−1) ∪ (1/3 , ∞) 12 / 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 and B are two matrices not necessarily of same order A = B Number of columns of A is equal to the number of rows of B 13 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? – 2 cosθ 2 sinθ 2 cosθ -2 sinθ 14 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 3/2 2/3 -4/15 4/15 15 / 85 The image of the point(2,3)in the line y = -x is? (3, 2) (-3, -2) (-2, -3) (-3, 2) 16 / 85 The sum up to n terms of the series √2 + √8 + √18 + √32 + ….. is? 1 n(n + 1) / √2 n(n + 1) / 2 2n (n + 1) 17 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 4 5 8 1 18 / 85 If y = mx + c and f (0) = f ‘(0) =1, then f (2) is -3 2 3 1 19 / 85 Let R be the universal relation on a set X with more than one element. Then R is? not reflexive none of the above not symmetric transitive 20 / 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) √(4c − k²) √(k² − 4c) √(4k² − c) 21 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 4 + √2 3 + √2 9 22 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 3/4 2/3 1/3 1/6 23 / 85 If pv = 81, then dp/dv at v = 9 is 2 1 -1 -2 24 / 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 4sq.units 25sq.units 20sq.units 25 / 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? 4 zero 2 1 26 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? (0, 1) [0, 1] [0,∞) [0, 1) 27 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 7 14 6 4 28 / 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 29 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to A × A none of these B × B A ∩ B 30 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? [2,∞) (0, 2) (−∞, 2) [0, 2] 31 / 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 + x − 7 3x² − 5x − 7 = 0 3x² − 5x+7 = 0 32 / 85 If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is? Zero Infinity 1 2 33 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? n m mn m + n 34 / 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 + 3 = 0 x+ y = 1 x – y + 3 = 0 35 / 85 The area of the triangle formed by the lines x² – 4y² = 0 and x = a is? (‘√3/2) a² (2/√3)a² (1/2) a² 2a² 36 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? -k³ / √2 ± k³ / √2 -k³ / √3 k³ / √2 37 / 85 The value of log√2 512 is? 9 18 12 16 38 / 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 a function which is not one-to-one an one-to-one function not a function 39 / 85 The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 2ⁿ – n – 1 2 ⁻ ⁿ + n – 1 1 – 2 ⁻ ⁿ 2 ⁿ ⁻ ˡ 40 / 85 The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is 2 1 4 3 41 / 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? transitive reflexive equivalence symmetric 42 / 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) 43 / 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 44 / 85 The number of relations on a set containing 3 elements is? 81 512 9 1024 45 / 85 The intercepts of the perpendicular bisector of the line segment joining(1,2)and(3,4)with coordinate axes are? 5, 3 5, -5 5, -4 5, 5 46 / 85 Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0? (1,2) (0,0) (-2,3) (0,-1) 47 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? an odd function an even function both odd function and even function neither an odd function nor an even function 48 / 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 49 / 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} Domain of R is {0,−1, 1, 2} R⁻¹ = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)} R = {(0, 0), (0,−1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)} 50 / 85 The value of log₃ 1/81 is? -2 -9 -4 -8 51 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 30240 10000 69760 90000 52 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 4 1 2 3 53 / 85 Which of the following is not true ? cos θ = -1 sec θ = 1/4 tan θ = 25 sin θ = -3/4 54 / 85 If A and B are symmetric matrices of order n, where (A ≠ B), then A + B is a diagonal matrix A + B is a zero matrix A + B is symmetric A + B is skew-symmetric 55 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? (−∞, 2) (−2,∞) (2,∞) [2,∞) 56 / 85 The number of solutions of x² + |x − 1| = 1 is ? 3 zero 1 2 57 / 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’ 58 / 85 The value of logₐ b logb c logc a is? 1 2 3 4 59 / 85 The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is? 3/2 2/9 9/2 2/3 60 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 5/12 11/5 -5/12 12/5 61 / 85 The derivative of f (x) = x | x | at x = −3 is 6 -6 does not exist Zero 62 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? cannot be defined one-to-one bijection onto 63 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (−1,∞) (−∞, 1] (1,∞) R 64 / 85 The slope of the line which makes an angle 45⁰ with the line 3x – y = -5 are? 1, 1/2 2, -1/2 1/2, -2 1, -1 65 / 85 The line (p + 2q)x + (p – 3q)y = p – q for different values of p and q passes through the point? (3/5, 3/5) (2/5, 2/5) (2/5, 3/5) (3/2, 5/2) 66 / 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 = 1/3 k = 3 k = 2/3 67 / 85 If log√x 0.25 = 4, then the value of x is? 0.5 1.25 2.5 1.5 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 x² -3y² = 0 3x² + y² = 0 69 / 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 70 / 85 If |x + 2| ≤ 9, then x belongs to? (−∞,−7) ∪ [11,∞) (−11, 7) (−∞,−7) [−11, 7] 71 / 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, 1 9, 1 1, 2 72 / 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 73 / 85 (1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) = 1 /√2 1 / 2 1 / √3 1 / 8 74 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? -1 1 3 -3 75 / 85 Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if α + 2β = 7 α + 3β = 11 3α + β = 9 3α + 3β = 11 76 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? 2 √2 4 √3 77 / 85 The rule f(x) = x² is a bijection if the domain and the co-domain are given by? (0,∞),R [0,∞), [0,∞) R, (0,∞) R,R 78 / 85 If 3 is the logarithm of 343, then the base is? 6 7 9 5 79 / 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 80 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 81 101 61 71 81 / 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 36 18 432 82 / 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) log (5/3) 3/2 log (5/3) 5/3 log (5/3) 83 / 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 S is an equivalence relation but T is not an equivalence relation T is an equivalence relation but S is not an equivalence relation Neither S nor T is an equivalence relation 84 / 85 If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is? [−3, 3] [0, 9] [−9, 9] R 85 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 – λ² / λ 1 + λ² / λ 1 + λ² / 2λ 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. Once the time is over, the test will be submitted automatically. You can verify your answers at the result page.