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SHREE GURU GYAN TUTORIALS, Std 12: MATHS, Chapters :1, Total Marks:41, Date:14/02/22, PAPER 1 EXAM ORIENTED MCQ, Time: 03Hour, Section A, Choose correct answer from the given options. [Each carries 1 Mark], [41], 1., If a set A has m elements and a set B has n elements then the number of relation from A to B is, (A) 2m +n, A relation R on a finite set having n elements is reflexive. If R has m pairs then . ., (В) 2тп, (C) m + n, (D) mn, 2., (A) m 2 n, (B) т < n, (С) т %3D п, (D) Nome of these, 3., x and y are real numbers. If xRy x - y + V5 is on irrational number then R is .. relation., (A) Reflexive, (B) Symmetric, (C) Transitive, (D) None of these, 4., A = {1, 2, 3, 4}. A relation R is A is given by R = {(2, 2), (3, 3), (4, 4), (1, 2)}. Then R is . . relation., (A) Reflexive, (B) Symmetric, (C) Transitive, (D) None of these, 5., A relation R is from set A to B, and a relation S is from set B to C. Then relation SOR is from, (A) Set C to A, (B) Set A to C, (C) Does not exist, (D) None of these, 6., Relation R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)} then ROR, (В) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}, (D) None of these, (A) {(1, 1), (4, 4), (7, 4), (4, 7), (7, 7)}, (С) {(1, 5), (1, 6), (3, 6)}, 7., Which of the graphs is not a graph of function ?, (A) X', (В) Xе, (C) X'<, (D) x'<, Y', 8., If f(1) = 1. fln + 1) = 2f (n) + 1, n 2 1 then fin), (A) 2" + 1, (B) 2", (C) 2" - 1, (D) 2n-1 - 1, 1, = x2, 1, 2 (x # 0) then f(x) = . ., 9., A function y =, f(x) satisfies the condition fx +, (A) - x2 + 2, (B) – x2 - 2, (C) x2 - 2, x eR- {0}, (D) x2 - 2, |x| e 12, ), 10., If fix + ay, x- ay) = axy then f(x, y) =, (A) xy, (B) x - a²y?, (C), (D), 11., If f(x), x + -1 for fof(x) = x then a = ..., %3D, x +1, (A) V2, (В) -1, (C), (D) - 2, 12., For real valued functions f and g, flx) = 2sin, and g(x) =, Vx. then fog(4) – gof(6) = .., 1, (A) 0, (B) 5, (C) 1, (D), 2, 13., The domain of the real value function f(x) = 5-4x-x2 + x² log(x + 4) is, (A) -5 < x < 1, (B) - 5 < 4 and n 2 1, (C) - 4 < x < 1, (D) O, 14., Wish You - All The Best, 1
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The domain of sin log3, is, (A) [1, 9], (B) [-1, 9], (C) [-9, 1], (D) [-9, -1], x + x + 2, 15., The range of f(x) 3D, , x e R is, x* + x + 1, (B) (1.4), (D) |1,, ( ) «, (A) (1, ), (C), If g(x) = x + x-2 and, 1, (gof) (x) = 2x² - 5x + 2 then f(x) = . ., 16., %3D, %3D, (A) 2x - 3, (B) 2x + 3, (C) 2x2 + 3x + 1, (D) 2x2 - 3x - 1, 17., g(x) = 1 + Vx and f(g (x)) = 3 + 2 Vx + x then f(x) = . . ., (A) 1 + 2x2, (B) 2 + x, (C) 1 + x, (D) 2 + x, 18., If real function f(x) = (x + 1)2 and g(x) = x + 1 then (fog) (- 3) =, %3D, (A) 121, (B) 112, (C) 211, (D) 111, 19. fх), = cotx : R* (0, n) and g(x) = 2x - x2 : R → R then the range of f(g (x)) is, (A) (0,, (a), (B), 0,, (C), (D), 4' 2, 20., The domain of f is [-5, 7] and g(x) = | 2x + 5 then the domain of (fog) (r) is, %3D, (A) [-4, 1], (B) [-5, 1], (C) [-6, 1], (D) None of these, 21., A set A has 3 elements and a set B has 4 elements. The number of one one function defined from, set A to B is, (A) 144, (В) 12, (C) 24, (D) 64, 22. f: R → R, flx) = (x - 1)(x - 2)(x - 3) then f is, (A) One-one but not onto., (B) Onto but not one-one., (C) One-one and onto., (D) Neither one one nor onto., 23. f: N → N, fin) = (n + 5)², ne N then the function f is, (A) Neither one one nor onto, (B) One one and onto, (D) Onto but not one one., (C) One one but not onto, 24. f: [0, 0) → [0, ), fix) =, then the function f is, ........., 1+ x, (A) One one and onto, (B) One one but not onto, (D) Neither one one nor onto, (C) Onto but not one one, x2, + ax + b, Vx e R. If flx) is one one function then the minimum value of a is, 2, x3, f(x) =, 3, 25., (A), 4, (B) 1, (C), (D), 8., 26., flx) = x - 2x - 1, Vx e R. f: (-00, a] → [b, ) is one one and onto function then a + b =, .........., (A) – 2, (В) - 1, (C) 0, (D) 1, ex - e*, 27., f(x) =, + 2. The inverse of f(x) is .., e* + e*, x - 1, (A) loge, (B) loge, (C) loge, (D) loge, x +, 3 - x, 28., f: (2, 4) (1, 3), flx) = x -, where [ 1 is a greatest integer function then f-(x), (A) 2x, (B) x +, (C) x + 1, (D) does not exist, 29., f: [2, 0) y, fx) = x2- 4xr + 5 is a one one and Onto function. If y e la, ) then the value of, a is, Wish You - All The Best, 2, 7/5
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(A) 2, (B) 1, (C) - 00, (D) -1, 30. f: N N, flx) = x + (-1)*-1 then f-(x), E......., (A) x, (B) x - 1, (C) x - (-1)*-1, (D) x + (-1)*-1, a > 1 is a real number f(x) = log, x2, where x > 0. If f-(x) is a inverse of f(x) and b and c are real, numbers then f-(b + c) = .. . ., 31., 1, (A) f-(b) · f-(c), (B) f-!(b) + f-(c), (C), f(b + c), (D) None of these, 32. f: R → R, flx) = 2x + cos x| then f is, function., (A) One one and onto, (B) One one but not onto, (C) Neither one one nor onto, (D) Not one one but onto, 33., The number of onto function from set {1, 2, 3, 4} to {3, 4, 7} is, (A) 18, (B) 36, (C) 64, (D) None of these, 34., Match the Section (A) with the Section (B) properly., Section (A), Section (B), (1) fx) = sin(tanx| (A) f-(x) = - log,(1 - x), (2) fx) = 1 - 2-*, |(B)fx) = (5 – x²)ž, (3) f(x) = 21, (C)fx) =, %3D, x², (4) f(x) = (5 – x²)2, (D) fx), log 2x, log 2x - 1, (A) 1 A, 2 → D, 3 B, 4 C, (C) 1 A, 2 C, 3 → B, 4 → D, (B) 1 → C, 2 → A, 3 D, 4 B, (D) 1 C, 2 B, 3 → D, 4 A, 35., f: [0, 3] → [1, 29], flx) = 2x, 15x2 + 36x + 1 then f is ., function., ......., (A) One one and onto, (B) Onto but not one one, (C) One one but not onto, 3, (D) Neither one one nor onto, 36., flx, y), = (max (x, y))min(x, y) and g(x, y) = max(x, y), min(x, y) then, /8/-1,-g(-4, -1.75)=., (A) 0.5, (В) - 0.5, (C) 1, (D) 1.5, 37., The relation S on set {1, 2, 3, 4, 5} is S = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}. Then S is, (A) Only symmetric, (C) Only transitive, (B) Only reflexive, (D) Equivalence relation, 38., The functionf: R R, flx) = 5x + 7 then the function f is, (B) One one and not onto, (A) One one and onto, (C) Onto but not one one, (D) Neither one one nor onto, 39., The number of binary operation on set {1, 2} is, (A) 8, (B) 16, (C) 2, (D) 4, 40., The function f : R* → R*, fx) = x, g : R* → R*, g(x) = x3 then (fog)(x), %3D, (A) x3, 1, (B), (C), (D) x, 41., a • b = a? + b + ab + 2 on Z then 3 * 4 =, (A) 39, (B) 40, (C) 25, (D) 41, Wish You - All The Best, 3