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    01 # Quiz

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    01 # Quiz

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    01 # Quiz

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    JEE(Main

    JEE (Main++Advanced)
    Advanced)2024
    2024
    ENTHUSIASTCOURSE
    ENTHUSIAST COURSE
    TED01

    MATH EM ATI CS QUIZ # 01

    1. (
    The complete set of values of x in the domain of function f ( x ) = log x + 2{x} [ x ] - 5 [ x ] + 7
    2
    )
    (where [.] denote greatest integer function & {.} denote fraction part function) is

    æ 1 ö æ1 ö
    (A) ç - ,0 ÷ È ç ,1÷ È ( 2, ¥ ) (B) ( 0,1) È (1, ¥ )
    3
    è ø 3 è ø

    æ 2 ö æ1 ö æ 1 ö æ1 ö
    (C) ç - ,0 ÷ È ç ,1÷ È (1, ¥ ) (D) ç - ,0 ÷ È ç ,1÷ È (1, ¥ )
    è 3 ø 3 è ø è3 ø 3è ø

    2. A family of lines is given by (1 + 2 l ) x + (1 - l )y + l = 0; l being a real parameter, the line belonging


    to this family and the maximum distance from the point (1, 4) is :
    (A) 12x + 33y - 7 = 0 (B) 12 x - 33y - 7 = 0
    (C) 4x + y - 7 = 0 (D) 33x - 12y + 7 = 0

    3. If the equation ( x - 1) 2 + 2l ( x - 1)( y - 1) + 4 ( y - 1)2 = 0 represent real lines in x - y plane, then smallest
    positive value of l is
    (A) 1 (B) 2 (C) 4 (D) 16

    æ 1 1 ö 3x - x 3
    4. f
    Let ç: - , ÷ ® R defined by ( )
    f x = , then f(x) is
    è 3 3ø 1 - 3x 2
    (A) one-one and into (B) many-one and into
    (C) many-one and onto (D) one-one and onto

    5. Let 'r' be the radius of the smallest circle which cuts the two circles
    x2 + y2 = 1 and x2 + y2 + 8x + 8y - 33 = 0 orthogonally. Then the value of r2
    (A) 9 (B) 36 (C) 64 (D) 7

    6. The function f : (-¥, -1] ® (0, e5 ] defined by f(x) = ex3 -3x + 2 is :


    (A) Many one & onto (B) Many one & into
    (C) One to one & onto (D) One to one & into

    7. If f ( x ) = 3 x - x - 2 and g(x) = sin x, then domain of fog(x) is :

    7p 11p ù
    U êë2np +
    ì pü é
    (A) í2np + ý ,n Î I (B) , 2np +
    î 2þ nÎI 6 6 úû

    p 7p 11p ù
    (D) í( 4m + 1) 2 ; m Î I ý U ê 2np + 6 ,2np + 6 ú
    ì pü ì ü é
    (C) í2np + ý ,n Î I
    î 6þ î þ nÎI ë û

    Quiz # 01 E-1/1
    JEE (Main + Advanced) 2024
    ENTHUSIAST COURSE

    8. The perpendicular distances P1, P2, P3 of the points (a2, 2a), (ab, a + b) and (b2, 2b) respectively from
    the straight line x + y tan q + tan 2 q = 0 are in
    (A) A.P. (B) G.P. (C) H.P. (D) None

    9. If a, b, c are distinct positive real numbers such that


    c > b > a. If 2 log (c - a), log (c2 - a2), log (a2 + 2b2 + c2) are in A.P., then
    (A) a , b, c are in A.P. (B) a, b, c are in A.P.
    (C) a, b, c are in G.P. (D) a, b, c are in H.P.

    æ1 1ö æ 1ö
    10. If f : R - {0} ® R, be a function satisfy f ( x ) f ( y ) = f ( xy ) + 3 ç x + y ÷ , then f ç - ÷ can be equal to
    è ø 2è ø

    5 3
    (A) - (B) - (C) -1 (D) 2
    2 2
    Comprehension (Q. 11 to Q. 12)
    Let f : ( 0, ¥ ) ® ( 0, ¥ ) satisfy f(xf(y)) = x2 ya, where a is a real constant.
    n

    11. The value of n, n Î N for which å(


    r =1
    n
    )
    C r f ( r ) = 240 is equal to

    (A) 4 (B) 5 (C) 6 (D) 7

    12. The number of real solutions of equation 4f(x) = ex is


    (A) 1 (B) 2 (C) 3 (D) none of these

    Comprehension (Q. 13 to Q.15)

    x3 x 2
    Let f ( x ) = + + ax + b " x Î R
    3 2

    13. Least value of 'a' for which f(x) is injective function, is


    1 1 1
    (A) (B) 1 (C) (D)
    4 2 8

    14. If a = -1, then f(x) is


    (A) bijective (B) many-one and onto (C) one-one and into (D) many-one and into

    15. f(x) is invertible if

    é1 ö é1 ö æ 1ù æ 1ù
    (A) a Î ê , ¥ ÷ , b Î R (B) a Îê , ¥ ÷ , b Î R (C) a Î ç -¥, ú ,b Î R (D) a Î ç -¥, ú ,b Î R
    ë4 ø ë8 ø 4è û 4è û

    E-2/1 Quiz # 01

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