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 y = mx + c and f (0) = f ‘(0) =1, then f (2) is -3 1 2 3 2 / 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 5/9 1/9 1 3 / 85 The area of the triangle formed by the lines x² – 4y² = 0 and x = a is? 2a² (‘√3/2) a² (2/√3)a² (1/2) a² 4 / 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 reflexive transitive equivalence 5 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 101 71 81 61 6 / 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,∞) 7 / 85 The value of log₃ 1/81 is? -9 -8 -4 -2 8 / 85 The image of the point(2,3)in the line y = -x is? (-3, -2) (-3, 2) (-2, -3) (3, 2) 9 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 10000 30240 90000 69760 10 / 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 11 / 85 The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 2 ⁿ ⁻ ˡ 2 ⁻ ⁿ + n – 1 2ⁿ – n – 1 1 – 2 ⁻ ⁿ 12 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 + √2 3 + √2 9 4 13 / 85 The value of logₐ b logb c logc a is? 4 2 3 1 14 / 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) 15 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? (2,∞) [2,∞) (−2,∞) (−∞, 2) 16 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 2/3 4/15 -4/15 3/2 17 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? -2 sinθ 2 sinθ 2 cosθ – 2 cosθ 18 / 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) 19 / 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 20 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 5 1 4 8 21 / 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 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 22 / 85 The number of points in R in which the function f (x) =| x −1| + | x − 3| +sin x is not differentiable, is 3 4 2 1 23 / 85 The equation of the locus of the point whose distance from y-axis is half the distance from origin is? x² + 3y² = 0 x² -3y² = 0 3x² -y² = 0 3x² + y² = 0 24 / 85 If A and B are two matrices such that A + B and AB are both defined, then A = B A and B are square matrices of same order 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 25 / 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 26 / 85 The number of solutions of x² + |x − 1| = 1 is ? 1 3 2 zero 27 / 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 28 / 85 If |x + 2| ≤ 9, then x belongs to? (−∞,−7) [−11, 7] (−11, 7) (−∞,−7) ∪ [11,∞) 29 / 85 The number of relations on a set containing 3 elements is? 1024 512 9 81 30 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? 3 1 -1 -3 31 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? √2 2 4 √3 32 / 85 If log√x 0.25 = 4, then the value of x is? 1.25 0.5 1.5 2.5 33 / 85 If 3 is the logarithm of 343, then the base is? 6 5 7 9 34 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? cannot be defined onto bijection one-to-one 35 / 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 36 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? (0, 2) [0, 2] (−∞, 2) [2,∞) 37 / 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 2 1 38 / 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 39 / 85 Which of the following is not true ? sin θ = -3/4 sec θ = 1/4 cos θ = -1 tan θ = 25 40 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? 3α + β = 11 α + 2β = 7 3α + β = 9 α + 3β = 11 41 / 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, 1 1, 2 -1, 2 42 / 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)} Range of R is {0,−1, 1} R⁻¹ = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)} 43 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? m + n n mn m 44 / 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 6/7 7/6 45 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (1,∞) (−1,∞) R (−∞, 1] 46 / 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 47 / 85 If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is? [0, 9] [−3, 3] R [−9, 9] 48 / 85 If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? 3 2 1 zero 49 / 85 The equation whose roots are numerically equal but opposite in sign to the roots of 3x² − 5x − 7 = 0 is? 3x² + x − 7 3x² − 5x − 7 = 0 3x²+ 5x − 7 = 0 3x² − 5x+7 = 0 50 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (7, 3) (1, -1) (4, 1) (-2, 3) 51 / 85 The value of log√2 512 is? 9 16 18 12 52 / 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 53 / 85 If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is? 1 2 Infinity Zero 54 / 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 55 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 11/5 12/5 5/12 -5/12 56 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 3 4 2 1 57 / 85 Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0? (1,2) (0,-1) (-2,3) (0,0) 58 / 85 If A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains? infinitely many elements no element only one element cannot be determined 59 / 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 60 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to B × B A ∩ B A × A none of these 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 108 18 432 36 62 / 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 63 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 1/3 2/3 1/6 3/4 64 / 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 65 / 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? 6 -8 10 -8, 8 66 / 85 (1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) = 1 / √3 1 / 2 1 / 8 1 /√2 67 / 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 cot θ = 0 x sin θ + y ( cos θ + 1) = 0 x + y tan θ = 0 68 / 85 The value of 1 – 1/2 (2/3) + 1/3 (2/3)² – 1/4 (2/3)³ + ….. is ? log (5/3) 5/3 log (5/3) 3/2 log (5/3) 2/3 log (2/3) 69 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? -k³ / √2 k³ / √2 -k³ / √3 ± k³ / √2 70 / 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 insufficient data 1120 1100 1130 71 / 85 The derivative of f (x) = x | x | at x = −3 is does not exist Zero 6 -6 72 / 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 A’ B 73 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 + λ² / 2λ 1 – λ² / 2λ 1 – λ² / λ 1 + λ² / λ 74 / 85 The range of the function 1 / 1-2 sin x is? (−∞,−1] ∪ [1/3 , ∞) (-1, 1/3) [-1, 1/3] (−∞,−1) ∪ (1/3 , ∞) 75 / 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 20sq.units 25sq.units 16sq.units 76 / 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 77 / 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 78 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 14 4 6 7 79 / 85 If pv = 81, then dp/dv at v = 9 is 2 -1 1 -2 80 / 85 Which of the following equation is the locus of (at²; 2at)? x²/a² – y²/b² = 1 x²/a² + y²/b² = 1 y² = 4ax x² + y² = a² 81 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5,−4) (−5, 4) (−5, 5) (4, 5) 82 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? [0, 1) [0,∞) [0, 1] (0, 1) 83 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? neither an odd function nor an even function an odd function both odd function and even function an even function 84 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? -1 zero 89 1 85 / 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 an onto function an one-to-one function a function which is not one-to-one 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.