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Punjab (PTB) · Quarter book test · Free

1st Year Mathematics 2nd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: 4 chapters (UNIT 5: Partial Fractions to UNIT 8: Mathematical induction and Binomial Theorem).

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1st Year Mathematics 2nd Quarter Book Paper

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. : (or sum of first n term):

  2. nCn-r is equal to:

    1. rpn

    2. rCn

    3. npr

    4. nCr

  3. The expansion of  is valid if ......:

    1. IxI<1

    2. IxI< 1/3

    3. IxI>1

    4. None of these

  4. The improper fraction can be changed into proper fraction by:

    1. Addition

    2. Subtraction

    3. Multiplication

    4. Division

  5. Sum of a term of G.P with first term "a" common ration 'r' is ......:

  6. nCr+nCr-1=?

    1. nCr

    2. n+1Cr

    3. n+1Cr+1

    4. None

  7. The inequality 4n>3n+2n-1 is true for integral values of n if ......:

    1. n>0

    2. n>1

    3. n>2

    4. n<2

  8. Conditional equation 3x-1=0 is truly only is ......:

    1. x=3

    2. x=-3

  9. A.M between  is:

    3. 10

  10. In how many ways a cricket team of 11 players out 15 can be selected if the captain must include in each ways:

    1. 15!

    2. 14C10

    3. 15C11

    4. 11!

  11. 1-x+x2-x3+.... is expansion equals:

    1. (1+x)-2

    2. (1-x)-2

    3. (1+x)-1

    4. (1-x)-1

  12. A realtion in which the equality is true for all finite values of unknowns is called an ......:

    1. Identity

    2. Equation

    3. Trigonometric equation

    4. Algebraic equation

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Resolve into partial fractions.

  2. If nPr = 120 and nCr=20, find r.

  3. A sum of Rs. 10400 is paid off in 40 installment such that each installment is Rs. 10 more than the preceding installment. Calculate the value of the first installment.

  4. Using the binomial theorem, show that 11n-10n leaves a remainder 1 when divided by 100 for all positive integers n.

  5. Resolve into partial fraction.

  6. In how many ways can 5 couples sit around a round table if no two women are sitting together?

  7. Write down the nth term of the following sequence:

  8. Suppose you aim to lose weight by reducing your calories intake by 50 calories each week. If you start at 2500 calories, prove that after n weeks, your daily intake is 2500-50n calories.

  9. Write the following in factorial form: n(n-1)(n-2)...(n-r+1)

  10. If 6,11,16 are three A.Ms between a and b, find a and b.

  11. Expand the following upto 4 term, taking the values of x such that the expansion in the following case valid:

  12. Evaluate the following: 10p5

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. Find the sum of the series 13+33+53+... to n terms.

  2. Use mathematical induction to prove that whenever n is non-negative integer.

  3. Find the number of the diagonals of a 6-sided figure.

  4. Resolve the following into partial fraction: