Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 3 views

    Class 12 WT1 (12363)

    Uploaded by

    moiiifitbituser

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Class 12 WT1 (12363)

    Uploaded by

    moiiifitbituser
    3 views2 pages

    Original Title

    Class 12 WT1[12363]

    Copyright

    © © All Rights Reserved

    Available Formats

    DOCX, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    Copyright:

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

    Class 12 WT1 (12363)

    Uploaded by

    moiiifitbituser

    Copyright:

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

    Fahaheel Al-Watanieh Indian Private School, Ahmadi, Kuwait

    First Term Weekly Test (08-May-2022)


    MATHEMATICS (041)
    Class XII

    Time: 60 Minutes Maximum Marks: 30

    1) Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then the relation R is
    a) Reflexive and Symmetric b) Symmetric and transitive c) Equivalence relation d) Symmetric
    2) Let f : Z → Z be defined by f ( x )=x 3 , then fis
    a) One-one and onto b) many-one onto c) one-one but not onto d) neither one-one nor onto
    3) Evaluate tan−1 √ 3−¿ sec −1 (−2) ¿
    2π π −π
    a) b) c) d) π
    3 3 3
    −1 5π −1
    4) If α =tan (tan )∧β=tan ¿ ¿ then
    4
    7π
    a ¿ 4 α=3 β b)3 α =4 β c) α −β= d) none of these
    12
    5) If A and B are square matrices of same order then ( A+B)(A – B) is
    a) A2- B2 b) A2−BA− AB−B2 c¿ A2−B2 + BA− AB d) A2−BA+ B2 + AB
    6) If A and B are symmetric matrices of same order then ABT- BAT is a
    a) Skew symmetric matrix b) Null matrix c) symmetric matrix d) none of these
    SECTION B
    7) Show thar the relation R in the set of real numbers defined as R={( a , b ) : a≤ b 3 , a , b ∈ R }
    is neither reflexive , nor symmetric and nor transitive.
    OR
    If A = { 1 , 2, 3 } define a relation on A which is reflexive and symmmetric but not transitive.
    x−2
    8) Let A = R−{ 3 } and B = R −{ 1 }.Let f: A→ B be defined by f(x) = for all x∈ A . Show that f is
    x−3
    bijective.
    9) Prove that sec 2 (tan-13) + cosec2 (cot-14) = 27
    OR
    33 π
    Find sin-1(cos ¿
    5
    10) Find the values of a and b if A = B

    [ ] [ ]
    2
    a+ 4 3 b 2 a+2 b +2
    A= B=
    8 −6 8 b2−5 b
    11) If A is a square matrix such that A2 = A, show that ( I + A )3 = 7 A+ I

    [ ][ ]
    −1 0 −1 1
    12) If [ 2 1 3 ] −1 1 0 0 = A, find A.
    0 1 1 −1
    SECTION C

    XII 1st Term Weekly Test 2022-23 Page 1/2 Subject: Mathematics (041)
    13) Prove that tan-1
    √ 1+ x 2 + √ 1−x 2 =¿ π 1
    + cos ( x )
    −1 2

    √1+ x 2− √1−x 2 4 2

    14) Show that f: N → N given by f ( x )= {


    x+1 if x is odd
    x−1 if x is even
    is both one-one and onto.

    OR

    Let A = { 1 , 2, 3 … … … 9 } and A be the relation in A × A defined by (a,b) R (c,d)


    if a+ d=b+ c , for (a,b) ,(c,d) ∈ A × A . Prove that R is an equivalence relation.
    Also find the equivalence class { (2 ,5) } .

    15) If A= [−12 −12 ] and I the identity matrix of order 2 then show that A =4 A−3 I .
    2

    Hence find A−1.

    XII 1st Term Weekly Test 2022-23 Page 2/2 Subject: Mathematics (041)

    You might also like