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    Bscit 402

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    This document contains a practice exam for a Basic Mathematics course. It has 13 multiple choice questions across two sections. Section A has 15 compulsory short answer questions. Section B has 9 longer answer questions worth 5 marks each. The questions cover topics like sets, matrices, arithmetic progressions, trigonometry, and logic.

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    Download as PDF, TXT or read online from Scribd

    Bscit 402

    Uploaded by

    api-3782519
    35 views3 pages
    This document contains a practice exam for a Basic Mathematics course. It has 13 multiple choice questions across two sections. Section A has 15 compulsory short answer questions. Section B has 9 longer answer questions worth 5 marks each. The questions cover topics like sets, matrices, arithmetic progressions, trigonometry, and logic.

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    bscit402

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    This document contains a practice exam for a Basic Mathematics course. It has 13 multiple choice questions across two sections. Section A has 15 compulsory short answer questions. Section B has 9 longer answer questions worth 5 marks each. The questions cover topics like sets, matrices, arithmetic progressions, trigonometry, and logic.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    35 views3 pages

    Bscit 402

    Uploaded by

    api-3782519
    This document contains a practice exam for a Basic Mathematics course. It has 13 multiple choice questions across two sections. Section A has 15 compulsory short answer questions. Section B has 9 longer answer questions worth 5 marks each. The questions cover topics like sets, matrices, arithmetic progressions, trigonometry, and logic.

    Copyright:

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    Download as PDF, TXT or read online from Scribd
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    You are on page 1of 3

    Roll No...........................

    Total No. of Questions : 13] [Total No. of Pages : 03

    J-3648[S-1504] [2037]
    B.Sc. (IT) (Semester - 1st/4th)
    BASIC MATHEMATICS-I (B.Sc.(IT)- 402 / 102)
    Time : 03 Hours Maximum Marks : 75
    Instruction to candidates:
    1) Section - A is compulsory.
    2) Attempt any Nine questions from Section - B.

    Section-A

    Q1) (15 × 2 = 30)

    a) List all the elements of the set A = { x; x is an integer, x 2 ≤ 4 }.


    b) Define finite and infinite sets.
    c) Let A = {2, 4, 6, 8} and B = {2, 6, 8, 10, 12}. Find A ∩ B .Also
    draw its venn diagram.
    d) Define a connective and equivalent statement.
    e) Form conjunction and disjunction of :
    p : It is cold q : It is raining
    f) Prove that sec2 = 1 + tan2 .
    o
    g) Find cosec(– 1410 ).
    h) Define Diagonal and Upper triangular matrices.

     3 4
    i) If A =   , find all minors and cofactors of A.
     – 1 2

    1 2 3
     
    j) If A = 2 4 5 , prove that A is Symmetric matrix.
     
    3 5 6

    k) Write nth term and sum of an A.P. with first term a and common
    difference d.

    l) Find the Sum of the progression 1 + 1 + 12 + 13 + ....................∞.


    4 4 4
    P.T.O.
    m) Which term of the AP 5, 2, –1, ----- is –22?
    n) State fundamental principle of counting.
    o) In how many ways can 3 people be seated in a row containing 7
    seats?

    Section-B
    (9 × 5 = 45)
    Q2) In how many ways can a student choose a program of 5 courses if 9
    courses are available and 2 courses are compulsory for every student?

    n–1 n
    Q3) (a) Find n if P3 : P4 = 1:9.
    5
    (b) Prove that r∑ Cr = 31.
    5
    =1

    Q4) Find the sum upto n - terms of the series .7 + .77 + .777 + ------ n terms.

    Q5) Insert 6 arithmetic means between 3 and 24.

    Q6) The sum of n terms of two APs are in the ratio 5n + 4 : 9n + 6. Find the
    ratio of their 18th terms.

    12
    Q7) If cot θ = – , θ lies in second quadrant, find the volues of other
    5
    trigonometric functions.

    Q8) Use Cramer’s rule to solve 5x – y + 4z = 5, 2x + 3y + 5z = 2,


    5x – 2y + 6z = –1.

    1 3 3
     
    Q9) Find the inverse of A = 1 4 3
     
    1 3 4
    J-3648[S-1504] 2
    x x2 yz
    Q10) Prove that y y2 zx = (x – y) (y – z) (z – x) (xy + yz + zx).
    z z2 xy

    Q11) In a group of 65 people, 40 like cricket, 10 like both cricket and tennis.
    How many like tennis only and not cricket? How many like tennis?

    Q12) If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 6, 7} and B = {2, 4, 7, 9} verify


    that (A ∪ B)′ = A ′ ∩ B′ and (A ∩ B)′ = A ′ ∪ B′.

    Q13) Show that (p ∨ q) ∨ (~ p) is tautology and (p ∧ q) ∧ (~ p) is contradiction.

    ZZZ

    J-3648[S-1504] 3

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