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    I Pu Model Test Paper 1

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    udaymanju31
    This document is a mathematics model paper from St. Philomena PU College in Bengaluru, India. It contains multiple choice and short answer questions testing concepts in sets, trigonometry, functions, and proofs. The questions are divided into four parts - Part A contains one mark multiple choice questions, Part B contains two mark short answer questions, Part C contains three mark proof questions, and Part D contains five mark proof questions. Students are asked to show their work to earn full marks.

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    I Pu Model Test Paper 1

    Uploaded by

    udaymanju31
    49 views2 pages
    This document is a mathematics model paper from St. Philomena PU College in Bengaluru, India. It contains multiple choice and short answer questions testing concepts in sets, trigonometry, functions, and proofs. The questions are divided into four parts - Part A contains one mark multiple choice questions, Part B contains two mark short answer questions, Part C contains three mark proof questions, and Part D contains five mark proof questions. Students are asked to show their work to earn full marks.

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    I PU MODEL TEST PAPER 1

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    This document is a mathematics model paper from St. Philomena PU College in Bengaluru, India. It contains multiple choice and short answer questions testing concepts in sets, trigonometry, functions, and proofs. The questions are divided into four parts - Part A contains one mark multiple choice questions, Part B contains two mark short answer questions, Part C contains three mark proof questions, and Part D contains five mark proof questions. Students are asked to show their work to earn full marks.

    Copyright:

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

    I Pu Model Test Paper 1

    Uploaded by

    udaymanju31
    This document is a mathematics model paper from St. Philomena PU College in Bengaluru, India. It contains multiple choice and short answer questions testing concepts in sets, trigonometry, functions, and proofs. The questions are divided into four parts - Part A contains one mark multiple choice questions, Part B contains two mark short answer questions, Part C contains three mark proof questions, and Part D contains five mark proof questions. Students are asked to show their work to earn full marks.

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    ST.

    PHILOMENA PU COLLEGE
    BYALAKERE, BENGALURU-560089
    Sub: Mathematics
    Subject Code:35
    Time 1 Hour 30 minutes I PUC model paper 1 Max. Marks: 40 marks
    PART A
    One-mark questions carrying each 1*5=5
    1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } , A = {1, 2, 5}, B = {6, 7} , then A  B is
    (a) B (b) A
    (c) A (d) B
    2. If 𝐴 = {𝑎, 𝑏, 𝑐} , 𝐵 = {𝑏, 𝑐, 𝑑} 𝑎𝑛𝑑 𝐶 = {𝑎, 𝑐 , 𝑑 } then (𝐴 − 𝐵) × (𝐵 ∩ 𝐶) =
    𝑎){(𝑎, 𝑏), (𝑐, 𝑑)} (𝑏) {(𝑎, 𝑐), (𝑎, 𝑑)}
    (c){(a, c), (a, d), (b, d)} 𝑑) {(𝑐, 𝑎), (𝑑, 𝑎)}
    1 − tan 2 15
    3. The value of is
    1 + tan 2 15
    3
    a) 1 b) 3 c) d) 2
    2
    sin ( −660 ) .tan (1050 ) .sec ( −420 )
    4. =
    cos ( 225 ) .cosec ( 315 ) .cos ( 510 )
    3 3 2 4
    a) b) c) d)
    4 2 3 3
    5. The conjugate of √3𝑖 − 1 =
    a) √3𝑖 − 1 b) √3𝑖 + 1 c) − √3𝑖 − 1 d) −√3𝑖 + 1
    Fill in the blanks by choosing the appropriate answer from those given in the bracket:
    ( 7 , 16, , 0)
    6. If the set A has 4 elements then number of subsets of A is………………..
    7. The value of 𝑖 9 + 𝑖 19 is……………………
    8. If 𝐴 = {1,2,3} 𝑡ℎ𝑒𝑛 the number of non -empty subsets of A is ……………………..
    answer all the following questions
    9. Convert 540° into radian measure .
    10. Write the following set in the set builder form {2,4,8,16,32}
    Part B

    Answer any THREE questions 𝟑×𝟐 =𝟔


    11. If A={2,1} find 𝐴 × 𝐴 × 𝐴.
    12. Let U ={1,2,3,4,5,6,7,8,9} ,A={1,2,3,4} , B={2,4,6,8} find (𝐴 ∪ 𝐵)′ =𝐴′ ∩ 𝐵′.
    13. Find the radius of the circle in which a central angle of 60∘ intercepts an arc of length 37.4cm(use
    22
    𝜋= )
    7
    14. Find the value of 𝑠𝑖𝑛765°.
    15. Find the multiplication inverse of 2 + 𝑖3
    Part C
    Answer any THREE questions 𝟑×𝟑=𝟗
    2
    16. Let f(x)= 𝑥 and g(x)=2x+1 be two real functions .find
    (𝑓 + 𝑔)(𝑥), (𝑓 − 𝑔)(𝑥), (𝑓𝑔)(𝑥)
    17. 𝐿𝑒𝑡 𝐴 = {1,2,3,4, … … … … … … . .14}. 𝑑𝑒𝑓𝑖𝑛𝑒 𝑎 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑅 𝑓𝑟𝑜𝑚 𝐴 𝑡𝑜 𝐴 𝑏𝑦 𝑅 = {(𝑥, 𝑦): 3𝑥 −
    𝑦 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑥, 𝑦 ∈ 𝐴}. Write down its domain ,codomain and range.
    18. Prove that sin(3𝜃) = 3𝑠𝑖𝑛𝜃 − 4𝑠𝑖𝑛3 𝜃...
    𝜋 𝜋 𝜋 1
    19. Prove that 𝑠𝑖𝑛2 6 + 𝑐𝑜𝑠 2 3 − 𝑡𝑎𝑛2 4 = − 2.
    𝑎+𝑖𝑏
    20. 𝐼𝑓 𝑥 + 𝑖𝑦 = 𝑎−𝑖𝑏 prove that 𝑥 2 + 𝑦 2 = 1
    Part D
    Answer any THREE questions . 3× 𝟓 = 𝟏𝟓
    21. Define modulus function. Write its domain and range . also draw the graph .
    22. Define identity function . Write its domain and range . also draw the graph .
    23. Prove that geometrically that cos(x + y) = cos x . cos y − sin x . sin y
    sin 5𝑥−2 sin 3𝑥 +sin 𝑥
    24. Prove that = tan 𝑥
    cos 5𝑥−cos 𝑥
    4 tan 𝑥(1−tan2 𝑥)
    25. Prove that tan 4𝑥 =
    1−6 tan2 𝑥+tan4 𝑥

    ********************************************************************************************

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