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 A and B are symmetric matrices of order n, where (A ≠ B), then A + B is symmetric A + B is skew-symmetric A + B is a zero matrix A + B is a diagonal matrix 2 / 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) log (5/3) 5/3 log (5/3) 3 / 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 9, 1 1, 2 -1, 2 4 / 85 The number of constant functions from a set containing m elements to a set containing n elements is? n mn m m + n 5 / 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? 2 4 zero 1 6 / 85 If |x + 2| ≤ 9, then x belongs to? [−11, 7] (−∞,−7) ∪ [11,∞) (−∞,−7) (−11, 7) 7 / 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 cannot be determined only one element no element 8 / 85 (1 + cos π / 8) (1 + cos 3π / 8) (1 + cos 5π / 8) (1 + cos 7π / 8) = 1 / 2 1 / 8 1 / √3 1 /√2 9 / 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 equivalence symmetric reflexive 10 / 85 Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is? (−∞, 1] (1,∞) R (−1,∞) 11 / 85 The slope of the line which makes an angle 45⁰ with the line 3x – y = -5 are? 1/2, -2 1, -1 1, 1/2 2, -1/2 12 / 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 25sq.units 4sq.units 13 / 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 10 6 -8, 8 14 / 85 If π < 2θ < 3π/2, then √(2√(2 + 2 cos 4θ equals to? – 2 cosθ 2 sinθ 2 cosθ -2 sinθ 15 / 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 16 / 85 The maximum value of 4 sin² x + 3cos² x + sin x/2 + cos x/2 is? 4 + √2 3 + √2 4 9 17 / 85 If A and B are two matrices such that A + B and AB are both defined, then Number of columns of A is equal to the number of rows of B A and B are square matrices of same order A and B are two matrices not necessarily of same order A = B 18 / 85 The solution set of the following inequality |x − 1| ≥ |x − 3| is ? [2,∞) [0, 2] (−∞, 2) (0, 2) 19 / 85 The value of log√2 512 is? 12 18 9 16 20 / 85 If the point(8,-5) lies on the locus x²/16 – y²/25 = k, then the value of k is? 1 zero 2 3 21 / 85 The solution of 5x − 1 < 24 and 5x + 1 > −24 is? (−5, 4) (−5, 5) (4, 5) (−5,−4) 22 / 85 If kx / (x+2) (x-1) = 2/x+2 + 1/ x-1, then the value of k is? 4 1 3 2 23 / 85 The length of ┴ from the origin to the line x/3 – y/4 = 1 is? 12/5 5/12 11/5 -5/12 24 / 85 Which of the following is not true ? sin θ = -3/4 sec θ = 1/4 tan θ = 25 cos θ = -1 25 / 85 Straight line joining the points (2, 3) and (-1, 4) passes through the point (α, β) if α + 3β = 11 3α + 3β = 11 3α + β = 9 α + 2β = 7 26 / 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 18 432 36 108 27 / 85 The number of relations on a set containing 3 elements is? 1024 9 512 81 28 / 85 The value of the series (1/2) + (7/4) + (13/8) + (19/16) + …. is ? 6 7 4 14 29 / 85 The value of logₐ b logb c logc a is? 3 2 1 4 30 / 85 The rule f(x) = x² is a bijection if the domain and the co-domain are given by? (0,∞),R R,R R, (0,∞) [0,∞), [0,∞) 31 / 85 The y-intercept of the straight line passing through (1,3) and perpendicular to 2x – 3y + 1= 0 is? 2/9 3/2 2/3 9/2 32 / 85 One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is? x + y tan θ = 0 x sin θ + y ( cos θ + 1) = 0 x – y cot θ = 0 x cos θ + y (sin θ + 1) = 0 33 / 85 If y = mx + c and f (0) = f ‘(0) =1, then f (2) is -3 3 2 1 34 / 85 The derivative of f (x) = x | x | at x = −3 is Zero does not exist -6 6 35 / 85 If log√x 0.25 = 4, then the value of x is? 1.25 0.5 1.5 2.5 36 / 85 If tan 40⁰ = λ, then (tan 140⁰ – tan 130⁰ / 1 + tan 140⁰ tan 130⁰) = 1 + λ² / 2λ 1 – λ² / λ 1 + λ² / λ 1 – λ² / 2λ 37 / 85 If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is? [0, 9] R [−3, 3] [−9, 9] 38 / 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 1130 1100 1120 39 / 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 Neither S nor T is an equivalence relation S is an equivalence relation but T is not an equivalence relation 40 / 85 cos 1⁰ + cos2⁰ + cos3⁰ +……..+ cos179⁰ =? zero -1 89 1 41 / 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 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 +1 = 0 x + y + 3 = 0 x+ y = 1 x – y + 3 = 0 43 / 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 44 / 85 1 / cos 80⁰ – √3/sin 80⁰ = ? 4 √2 2 √3 45 / 85 If cos 28⁰ + sin 28⁰ = k³,then cos 17⁰ is equal to? ± k³ / √2 k³ / √2 -k³ / √3 -k³ / √2 46 / 85 The sum of an infinite GP is 18. If the first term is 6, the common ratio is? 1/3 3/4 2/3 1/6 47 / 85 The function f : [0, 2π] → [−1, 1] defined by f(x) = sinx is? cannot be defined bijection onto one-to-one 48 / 85 The value of log₃ 1/81 is? -4 -2 -8 -9 49 / 85 If f (x) = x + 2, then f ‘(f (x)) at x = 4 is 4 5 1 8 50 / 85 The range of the function 1 / 1-2 sin x is? (-1, 1/3) (−∞,−1) ∪ (1/3 , ∞) (−∞,−1] ∪ [1/3 , ∞) [-1, 1/3] 51 / 85 The image of the point(2,3)in the line y = -x is? (-3, 2) (3, 2) (-2, -3) (-3, -2) 52 / 85 Straight line joining the points (2, 3) and (-1 ,4) passes through the point (α, β ) if? 3α + β = 11 α + 3β = 11 α + 2β = 7 3α + β = 9 53 / 85 The function f : R → R is defined by f(x) = sinx + cos x is? an odd function both odd function and even function neither an odd function nor an even function an even function 54 / 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 x – 2y = √5 2x – y = √5 55 / 85 For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to A × A B × B none of these A ∩ B 56 / 85 The area of the triangle formed by the lines x² – 4y² = 0 and x = a is? (‘√3/2) a² 2a² (1/2) a² (2/√3)a² 57 / 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, 5 5, -4 58 / 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 1 2 59 / 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 -1/9 5/9 1/9 60 / 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 61 / 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 62 / 85 The coefficient of x⁵ in the series e⁻²ˣ is? 2/3 -4/15 3/2 4/15 63 / 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) √(4k² − c) √(k² − 4c) 64 / 85 The nᵗᵸ term of the sequence 1/2, 3/4, 7/8, 15/16, ….is? 1 – 2 ⁻ ⁿ 2 ⁿ ⁻ ˡ 2ⁿ – n – 1 2 ⁻ ⁿ + n – 1 65 / 85 1 + 3 + 5 + 7 +……. + 17 is equal to 101 61 71 81 66 / 85 If pv = 81, then dp/dv at v = 9 is 1 -1 -2 2 67 / 85 The range of the function f(x) = | [x] − x|, x ∈ R is? (0, 1) [0,∞) [0, 1) [0, 1] 68 / 85 Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ ∪[(A∩B)∪B’] is? B A A’ N 69 / 85 If A = {(x, y) : y = eˣ, x ∈ R} and B = {(x, y) : y = e⁻ˣ, x ∈ R} then n(A ∩ B) is? Infinity Zero 2 1 70 / 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 an one-to-one function not a function a function which is not one-to-one 71 / 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 72 / 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) 73 / 85 The number of solutions of x² + |x − 1| = 1 is ? 3 2 zero 1 74 / 85 The sum up to n terms of the series √2 + √8 + √18 + √32 + ….. is? 1 2n (n + 1) n(n + 1) / 2 n(n + 1) / √2 75 / 85 If |x – 2| / x – 2 ≥ 0, then x belongs to? (2,∞) (−2,∞) [2,∞) (−∞, 2) 76 / 85 The number of five digit telephone numbers having at least one of their digits repeated is 30240 69760 10000 90000 77 / 85 If 3 is the logarithm of 343, then the base is? 7 6 9 5 78 / 85 The point on the line 2x – 3y = 5 is equidistance from (1,2) and (3, 4) is? (-2, 3) (7, 3) (4, 1) (1, -1) 79 / 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 80 / 85 If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0;, then c equals to? 3 -3 1 -1 81 / 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 82 / 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 = 2/3 k = 3 83 / 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⁻¹ = {(0, 0), (0,−1), (0, 1), (−1, 0), (1, 0)} Range of R is {0,−1, 1} R = {(0, 0), (0,−1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)} 84 / 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) 85 / 85 Which of the following point lie on the locus of 3x² + 3y² – 8x – 12y + 17=0? (0,0) (-2,3) (0,-1) (1,2) 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.