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Punjab (PTB) · Half book test (board pattern) · Free

1st Year Mathematics First half Book Paper

100 marks · 3 hours · 62 questions. Covers: 7 chapters (UNIT 1: Complex Numbers to UNIT 7: Permutations and Combinations).

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1st Year Mathematics First half Book Paper

1st Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 100Time: 3 hours

Q1. Multiple choice questions (Attempt all · 20 × 1 = 20)

  1. Multiplicative inverse of (1,0) is:

    1. (-1,0)

    2. (0,1)

    3. (0,-1)

    4. (1,0)

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

    1. Addition

    2. Subtraction

    3. Multiplication

    4. Division

  3. nCn-r is equal to:

    1. rpn

    2. rCn

    3. npr

    4. nCr

  4. To solve absolute value quadratic function we must illuminate roots which are:

    1. Real

    2. Imaginary

    3. Extraneous

    4. Double

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

  6. If f:  is a function such that rang , then f is called a/an ...... function:

    1. Onto

    2. Injective

    3. Bijective

    4. Into

  7. The (0,0) solution of the system a1x+b1y=0 and a2x+b2y=0 is called ......:

    1. Consistent

    2. Inconsistent

    3. Non-trivial

    4. Trivial

  8. If 

    1. -2-3

    2. 2-3

    3. -2+3

    4. 2+3

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

    1. x=3

    2. x=-3

  10. nCr+nCr-1=?

    1. nCr

    2. n+1Cr

    3. n+1Cr+1

    4. None

  11. Inverse of a quadratic function should be:

    1. Into

    2. Onto

    3. One to one

    4. Not to one

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

  13. Point of intersection f(x)=2x+5 and g(x)= -x+5 is a point which satisfies:

    1. f(x)

    2. g(x)

    3. Both f(x) and g(x)

    4. None

  14. For homogeneous linear equations, system AX=0 non-trivial solution is possible if IAI = ......:

    1. Non-zero

    2. Zero

    3. Negative

    4. Positive

  15. If Z is complex number, then  is:

    1. Z2

  16. 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

  17. 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!

  18. Name the type of equation .

    1. Radical

    2. Reciprocal

    3. Rational

    4. None of these

  19. A.M between  is:

    3. 10

  20. A bijective function is ......:

    1. Both one-one and onto

    2. One-one but not onto

    3. Onto, but not one-one

    4. Neither one-one nor onto

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

  1. If then find: z1+z2

  2. Find the domain and range of .

  3. Solve the following:

  4. If then find the following and express the result into x+y form: z1+z2

  5. Given f(x)=x3-2x2+4x-1 find: f(-2)

  6. Solve the following:

  7. Find the product of .

  8. Given f(x)=x3-2x2+4x-1 find: f(0)

  9. Find the inverse of . Also find its domain and range.

  10. Solve the following equation: z3-5z2+z-5=0

  11. Find the point (s) of intersection of the following function graphically: f(x) =2x-4, g(x)=3x-1

  12. Solve the following:

Q3. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. Resolve into partial fractions.

  2. Without expansion show that: =0

  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. Resolve into partial fraction.

  5. If them compute A2B.

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

  7. Without expansion show that:

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

  9. Solve the matrix equation A2-5A+4I-X=0 if

  10. Sum the series: 3+5-7+9+11-13+15+17-19+... to 3n terms.

  11. Verify that (AB)t=BtAt if:

  12. If the 5th term of an A.P is 13 and 17th term is 49, find an, and a13,.

Q4. Short questions (Attempt any 9 of 13 · 9 × 2 = 18)

  1. If nPr = 120 and nCr=20, find r.

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

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

  4. Evaluate the following: 10p5

  5. How many 4 digit number can be formed, with distinct digits, with each digit odd?

  6. Find the number of possible arrangements of vowel letters from the English alphabet?

  7. How many arrangements of the letters of the following word, taken all together can be made? PROBABILITY

  8. How many arrangements of the letters of the following word, taken all together can be made? CURRICULUM

  9. In a school, a class consist of 12 girls and 8 boys. The teacher wants to select 5 students for an activity. In how many ways can the student be selected including? (i) 2 girls (ii) 5 boys (iii) 2 boys.

  10. How many words can be formed from the letters of the following word using all letters when no letter is to be repeated: PYTHON

  11. Write the following in factorial form: n3-n

  12. In how many ways can five subjects be selected out of eight subjects to select a course programme?

  13. How many words can be formed from the letters of the following word using all letters when no letter is to be repeated: COMPUTER.

Q5. Long questions (Attempt any 3 of 5 · 3 × 10 = 30)

  1. A building's height over time is modeled by H(t)=100+20t which is in metres and t is the time in months. The height of a growing tree nearby is given by T(t)=50+10t+t2. (i) At what time will the building and tree have the same height? (ii) What will be the height be?. Sketch the graph of both functions and determine the time when the tree will overtake the height of the building.

  2. Find the maximum and minimum point by sketching the following quadratic function. Also find their domain and range:

  3. Evaluate:

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

  5. Resolve the following into partial fraction: