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    1. The document contains 10 multiple choice questions related to mathematics. The questions cover topics like functions, equations, permutations, and matrices. 2. Question 1 involves evaluating an expression involving even, odd, and polynomial functions. Question 2 requires solving a quadratic equation to find the sum of roots. Question 3 asks to identify true statements about a piecewise defined function. 3. The remaining questions cover additional topics like periodic functions, graph analysis, one-to-one functions, matrix matching, and solving systems of equations. Questions 8-10 are subjective questions involving equations, arrangements, and word ranks.

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    Enthusiast Course

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    30 views2 pages
    1. The document contains 10 multiple choice questions related to mathematics. The questions cover topics like functions, equations, permutations, and matrices. 2. Question 1 involves evaluating an expression involving even, odd, and polynomial functions. Question 2 requires solving a quadratic equation to find the sum of roots. Question 3 asks to identify true statements about a piecewise defined function. 3. The remaining questions cover additional topics like periodic functions, graph analysis, one-to-one functions, matrix matching, and solving systems of equations. Questions 8-10 are subjective questions involving equations, arrangements, and word ranks.

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    1. The document contains 10 multiple choice questions related to mathematics. The questions cover topics like functions, equations, permutations, and matrices. 2. Question 1 involves evaluating an expression involving even, odd, and polynomial functions. Question 2 requires solving a quadratic equation to find the sum of roots. Question 3 asks to identify true statements about a piecewise defined function. 3. The remaining questions cover additional topics like periodic functions, graph analysis, one-to-one functions, matrix matching, and solving systems of equations. Questions 8-10 are subjective questions involving equations, arrangements, and word ranks.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    30 views2 pages

    Enthusiast Course

    Uploaded by

    RUDRA PATEL
    1. The document contains 10 multiple choice questions related to mathematics. The questions cover topics like functions, equations, permutations, and matrices. 2. Question 1 involves evaluating an expression involving even, odd, and polynomial functions. Question 2 requires solving a quadratic equation to find the sum of roots. Question 3 asks to identify true statements about a piecewise defined function. 3. The remaining questions cover additional topics like periodic functions, graph analysis, one-to-one functions, matrix matching, and solving systems of equations. Questions 8-10 are subjective questions involving equations, arrangements, and word ranks.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    JEE (Main + Advanced) 2022

    JEE (Main + Advanced) 2022


    ENTHUSIAST COURSE
    ENTHUSIAST COURSE
    RACE # 09 MATH EMATI CS
    Straight Objective Type
    1. Statement-1 : ƒ is an even function, g and h are odd functions, all 3 being polynomials. Given ƒ(1) = 0,

    ƒ(2) = 1, ƒ(3) = –5, g(1) = 1, g(–3) = 2, g(5) = 3,h(1) = 3, h (3) = 5 and h(5) = 1.
    The value of ƒ(g(h(1))) + g(h(ƒ(3))) + h(ƒ(g(–1))) is equal to zero.
    Statement-2 : If a polynomial function P(x) is odd then P(0) =0.
    (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
    (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
    (C) Statement-1 is true, statement-2 is false.
    (D) Statement-1 is false, statement-2 is true.
    4 log x
    2. If 25 625  5x  6  0 is satisfied for 2 values of x (say x1 & x2), then x1 + x2 is equal to -
    (A) 2 (B) 3 (C) 5 (D) 7
    Multiple Correct Answer Type
    2
    3. Let f(x) = [x] + [x + 1] – 3, where [x] denotes greatest integer less than or equal to x, then which of the
    following statement(s) is/are CORRECT ?
    (A) f(x) is many one function (B) f(x) vanishes for atleast three values of x.
    (C) f(x) is neither even nor odd function. (D) f(x) is aperiodic.
    4. Which of the following(s) is(are) correct ?
    (A) The fundamental period of the function
    x x x x x x
    ƒ(x)  cosec    sec    cot    tan    cos    sin   is 420.
    2 3 4 5 6 7
    (B) If ƒ is a function such that ƒ(s) = ƒ(t) then s = t.
    (C) A vertical line intersect the graph of a function atmost once.

    x 2 , x  0
    (D) If h(x)   then h(h(x)) = h(x) x  R.
     x, x  0
    y
    5. The figure illustrate graph of the function y = f(x) 2

    defined in [–3,2]. Identify the correct statement(s) ?


    x
    –3 –2 1(0,0) O 1 2 3
    (A) Range of y = f(–|x|) is [–2,2]
    –1
    (B) Domain of y = f(|x|) is [–2,2] –2

    (C) Domain of y = f(|x| + 1) is [–1,1]

    (D) Range of y = f(|x| + 1) is [–1,0]

    MATHEMATICS / R # 09 E-1 / 2
    JEE (Main + Advanced) 2022

    ENTHUSIAST COURSE
    Matrix Match Type
    6. Column-I Column-II

     1
    x tan 1 , if x0
    (A) f(x)   x (P) even

     0, if x0

     x cot 1 x, if x0
    (B) g(x)   (Q) odd
     0 if x0

     2 1
     x tan 1 , if x0
    (C) h(x)  x (R) neither even nor odd

     0, if x0

     x cot 1 x 2 , if x0
    (D) k(x)   (S) even as well as odd
     0, if x0

    7. Column-I Column-II
    (A) Let f : R  R be defined as f(x)  3 x  tan 1 x , then f(x) is (P) one-one
    (B) Let f : (–,)  {–1,0,1} be defined as (Q) into
    f(x) = sin3(sgn (x2 + 3x + 5)) then f(x) is
    (where sgn x denotes signum function of x.)
    x2
    (C) Let f : [–2,2]  (0,e2] be defined as f(x)  e , then f(x) is (R) odd

    (D) Let f : (–1,5)  [0,3] be defined as f(x)  5  4x  x 2 , (S) non-invertible


    then f(x) is (T) aperiodic
    Subjective Type Questions
    8. The system of equationy + z = a + 2x
    x + z = b + 2y
    x + y = c + 2z, where a,b,c  0

    is consistent & b  4a  c , then absolute value of sum of roots of equation ax2 + bx + c = 0 is


    4
    9. Out of 10 pens, 3 are identical of black colour, some are identical of blue colour and rest are different.
    If they can be arranged in 840 ways, then the number of blue colour pens is equal to
    10. The letters of the word PINTU are permuted such that vowels are not together and all the permutations
    are arranged in alphabetical order as in an English dictionary . If rank of the word 'PINTU' is 'k', then
    sum of digits of 'k' is

    RACE # 08 MATHEMATICS
    1. C 2. D 3. D 4. C 5. C 6. D 7. B
    8. C 9. A 10. A
    E-2 / 2 MATHEMATICS / R # 09

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