Solved Mathematics Notes |

## 11th Class Math MCQs Chapter 1 Punjab Board

Question 1: The possible number subsets of the set {a, {b, c}} are ?

- Zero
- 1
- 2
- 4

D

Question 2: The property of inequality used in a > b and b > c ⇒ a > c is ?

- Multiplicative property
- Transitive property
- Additive inverse
- Additive property

B

Question 3: Every real number is a complex number with zero as its ?

- None of these
- Real part
- Imaginary part
- a & b both

C

Question 4: The inverse of a linear function {(x, y) /y=mx + c} is ?

- {(x, y)|y=x+c}
- {(x, y)|y=x}
- {(x, y)|y=mx-c}
- {(x, y)|x=my+c}

D

Question 5: If A ∩ B ≠ ∅ then in (B - A) = ?

- n(B)
- n(A)
- n(B)-n(A ∩ B)
- n(A)-n(A ∩ B)

C

Question 6: (b²/b⁴ + b², -b/b⁴ + b²) is multiplicative inverse of ?

- (b, 1/b)
- (b³, b)
- (b², b)
- (b, b²)

C

Question 7: If ‘n’ is a prime number then √n is ?

- A rational number
- Prime number
- None of these
- An irrational number

D

Question 8: The solution of the equation x + a = b if a > b where a, b ε W is ?

- Rational Number
- Integers
- Whole number
- Natural number

B

Question 9: (cos θ – i sin θ)⁻ⁿ = ------------- ?

- cos nθ + i sin nθ
- cos(-n)θ + i sin(-n)θ
- Cos nθ – i sin nθ
- cosθ + i sinθ

A

Question 10: If z = a + ib then z. z̄ = ?

- a² - b²
- a + b
- a² + b²
- (a + b)²

C

Question 11: If A ⊆ B then ?

- A ∪ B = A’
- A ∩ B = A’
- A ∩ B = A
- A ∪ B = A

C

Question 12: The set N with respect to addition is a ?

- Semi group
- Monoid
- Group
- Null set

A

Question 13: ∼ (p ν q) = ?

- ∼(p ∧ q)
- None of these
- ∼p ν ∼q
- ∼p ∧ ∼q

D

Question 14: If a function f : A → B is such that range f = B then f is called an ?

- Onto function
- Into function
- 1 – 1 function
- Bijective function

A

Question 15: Number of identity elements in any group is/are ?

- 3
- 1
- 2
- None of these

B

Question 16: If (1 - 1) correspondence can be established between the sets, then they are ?

- Equivalent
- Infinite
- Equal
- Finite

A

Question 17: The figure representing one or more complex numbers on the z-plane is called ?

- Histori gram
- Argand diagram
- Histogram
- Polygon

B

Question 18: Which set does not satisfy the order axioms ?

- Q’
- N
- C
- Q

C

Question 19: π and e are ?

- Rational numbers
- Irrational number
- integers
- Natural numbers

B

Question 20: The set Z⁺ ∪ {0} is monoid w.r.t multiplication but not ?

- None
- Division
- Subtraction
- Addition

C

## 11th Class Math MCQs Chapter 2 Punjab Board

Question 1: If S and P are sum and product of roots of an equation then the equation is ?

- x² – Sx + P = 0
- x² + Sx – P = 0
- x² – Sx – P = 0
- x² + Sx + P = 0

A

Question 2: Types of rational fractions are ?

- Four
- Infinite
- Three
- Two

D

Question 3: An equation which holds good for all values of the variable is called ?

- Conditional equation
- Identity
- All of these
- Equation

B

Question 4: Equations having same solutions are called ?

- Simultaneous equation
- Exponential equation
- Reciprocal equation
- Radical equation

C

Question 5: The solutions which don’t satisfy the equation are called ?

- Extraneous roots
- Roots
- None of these
- a & b both

A

Question 6: Sum of four fourth roots of unity is ?

- -1
- 0
- 1
- i

B

Question 7: Reminder obtained when f(x) is divided by x – a is same as the value of the polynomial f(x) at ?

- x = a
- X = - a
- x = 0
- x = ± a

A

Question 8: Product of roots of equation x² – kx + k² = 0 is equals ?

- k
- –k²
- –k
- k²

D

Question 9: When x³ – 2x² + kx + 4 is divided by x – 2, the remainder is 14 then the value of k is ?

- 25
- 10
- 5
- 20

C

Question 10: The sum of a positive number and its reciprocal is 26/5. What is the number ?

- – 1/5
- – 2, – 1/2
- 2, 1/2
- 5, 1/5

D

Question 11: The fraction x²+ 7x +3/x + 1 is ?

- Equivalent
- Improper
- None of these
- Proper

B

Question 12: What is the correct (2+23)-25= ?

2n-8 2n+3 2n+1 2n-2

1st Year Islamiat Past Papers In PDF 1st Year URDU Past Papers Punjab Board 1st Year Islamiat Elective Past Papers 1st Year English Past Papers 1st Year English Chapter Wise MCQs Quiz Solved

- 50
- 25
- 12
- 0

D

Question 13: Partial fraction of 1/(a + 1)(x² - 1) will be of the form ?

- A/x + 1 + Bc+C/x²-1
- A/x+1 + B/x-1 + C/x+1
- A/x-1 + B/(x+1)² + C/x+1
- A/x-1 + Bx+C/(x+1)²

C

Question 14: The roots of the equation ax² + bx + c = 0 are rational if ?

- b² – 4ac < 0
- b² – 4ac = 0
- b² – 4ac > 0 and a perfect square
- b² – 4ac > 0

C

Question 15: cos²θ + sin²θ = 1 is a/an ?

- None of these
- Fraction
- Conditional equation
- Identity

D

Question 16: 3x + 4 = 0 is ?

- Radical equation
- Reciprocal equation
- None of these
- Exponential equation

D

Question 17: The roots of the equation 25x² – 30x + 9 = 0 are ?

- Real and equal
- Irrational and equal
- Rational and unequal
- Complex

A

Question 18: Complex cube roots of unity are ……………… of each other ?

- Square
- Inverse
- Double
- Cube

A

Question 19: Which one is the solution of the equation x1/2 - x 1/4 - 6 = 0 ?

- {2,3}
- {81}
- {16}
- {16,81}

C

Question 20: Equations having same solution are called ?

- Exponential equation
- Reciprocal equation
- Simultaneous equation
- Radical equation

C

## 11th Class Math MCQs Chapter 3 Punjab Board

Question 1: If an = (-1) n-1 (n - 7) then a₃ = ?

- None of these
- -5
- -3
- -4

D

Question 2: 1/2, 1/7, 1/12, ……………. Is a/an ?

- Geometric Progression
- Arithmetic Progression
- Harmonic Progression
- None of these

C

Question 3: The geometric means between 2 and 4 are ?

- ±3√2
- ±8√2
- ±2√2
- ±4√2

C

Question 4: 3 + 6 + 9 + ………….. 3n = ?

- 3n(n + 1)/2
- 3n(n - 1)/2
- 2n(n + 1)/3
- 2n(n - 1)/3

A

Question 5: 2.23 = ?

- 220/99
- 220/199
- 221/99
- 221/89

C

Question 6: ∑n k=1 K = ----------- ?

- kⁿ
- n(n + 1)/2
- k(k + 1)/2
- K

B

Question 7: Infinite geometric series is convergent if ?

- |r|= 1
- |r| > 1
- |r| < 1
- All of these

C

Question 8: Write the next two terms of the sequence 7, 9, 12, 16, -------- ?

- 21, 25
- 21, 27
- 20, 23
- 20, 26

B

Question 9: The sum of first n – terms of an A.P is ?

- Sn = a₁ + an
- Sn = n +1/2 (a₁ + an)
- Sn = n(a₁ - an)
- Sn = n/2(a₁ - an)

D

Question 10: If 1/K, 1/2K + 1 and 1/4k – 1 are in H.P. them the value of K is ?

- 3
- 1
- 0
- 2

A

Question 11: If 1/a ,1/b and 1/c are in A.P them b = ?

- a – c/2a
- a – c/ac
- Ac/a + c
- 2ac/ a + c

D

Question 12: If Sn increases indefinitely as n becomes very large, the series is ?

- None of these
- Convergent
- Divergent
- Does not exist

C

Question 13: For what value of n, is an + bn/an-1 + bn-1 the G.M. between a and b ?

- 1/2
- -1/2
- 0
- none of these

A

Question 14: The 5th term of the G.P 3,6,12, ----------- is ?

- 15
- 2
- 48
- 3

C

Question 15: A sequence is a special type of function form subset of N to ?

- R
- b & c both
- Q
- C

A

Question 16: If Sn = a(1 – rn )/ 1- r and if Sn → a as n → ∞ then the series is ?

- Divergent
- None of these
- Convergent
- Does not exist

C

Question 17: If an = (n + 1) an₋₁, a₁ = 1 then a₂ is ?

- 2
- 3
- -3
- -2

B

Question 18: ∑n k=1 [(km – (k – 1)m] = ---------- ?

- nm
- nⁿ
- mm
- Mⁿ

A

Question 19: The general term of H.P. is ?

- 1/a₁ + (n - 1)d
- a₁ rⁿ⁻¹
- a₁ + (n-1)d
- 1/ a₁ rⁿ⁻¹

B

C

## 11th Class Math MCQs Chapter 4 Punjab Board

Question 1: What is the probability that a slip of numbers divisible by 4 are picked from the slips bearing numbers 1, 2, 3, ……………. 10 ?

- 2/5
- - 1/5
- 1/5
- 5/2

B

Question 2: How many signals can be given by 5 flags of different colours, using 3 flags at a time ?

- 50
- 40
- 70
- 60

D

Question 3: There are 5 green and 3 red balls in a box. One ball is taken out, the probability that the ball drawn is yellow is ?

- 3/8
- Zero
- 5/8
- 1

B

Question 4: For an event E which one is true ?

- 0 ≤ P(E) ≤ 1
- -1 ≤ P(E) ≤ 1
- 0 ≥ P(E) ≤ 1
- 1 ≤ P(E) ≤ 2

A

Question 5: If¹¹ Pn = 11.10.9, what is the value of n ?

- -1
- 1
- 2
- 3

D

Question 6: N different objects can be arranged taken all at time is ?

- (n - 1) Ways
- n! ways
- (n + 1)! Ways
- None of these

B

Question 7: In how many ways of 5-digit numbers that can be formed from the digit 1, 2, 4, 6, 8 when the digits 2 and 8 are next to cach-other ?

- 96
- 72
- 24
- 48

D

Question 8: ⁿCr x r! = ?

- None of these
- ⁿ⁺¹Cr
- ⁿPr
- ⁿCr₊₁

C

Question 9: The probability of getting an add number in throwing a die once is ?

- 6
- 1/2
- 1/6
- 2

B

Question 10: ⁿC₈ = ⁿC₁₂ then n is ?

- 20
- 8
- 0
- 12

A

Question 11: Generally, Permutation of n different objects taken r ≤ n at a time is denoted by: ?

- n!/r!(n-r)!
- n!/(n-r)!
- (n+1!)/r!(n-r+1)!
- (n –1)!/(n-r)!r!

B

Question 12: The letters of the word “FASTING” taken all at a time can be written in ?

- 40320
- 504
- 50
- 5040

D

Question 13: If (n + 1)!/3! (n – 2)! and (n + 1)!/5!(n – r)! are in ratio 10 : 3, then n = ?

- 2
- 3
- 5
- 4

C

Question 14: 5-Person can be seated at a round table in: ?

- 20ways
- 24ways
- None of these
- 25ways

B

Question 15: What are the numbers of diagonals of a 6-sided figure ?

- 7
- 8
- 9
- 6

C

Question 16: The factorial of a positive integer n is n! = ?

- (n+1)(n)(n-1) …….. 3. 2.1
- (n-2)(n-3)…………3. 2. 1
- n(n-1)(n-2) ………….. 3. 2. 1
- (n-1)(n-2)……….. 3. 2. 1 >

C

Question 17: The number of 3-digit numbers formed by using each of the digits 2, 3, 5, 7, 9 only once is: ?

- 120
- 360
- 60
- 10

C

Question 18: If A and B are disjoint events, then P (A ∪ B) = ------------ ?

- P(A)\P(B)
- P(A) + P(B) = P(A ∩ B)
- P(A) + P(B)
- P(A) – P(B)

C

Question 19: (n + 1)!/(n - 1)! = ----------- ?

- n + 1
- n²(n + 1)
- None of these
- n² + n

D

Question 20: If A₁, A₂, A₃, ……………… An are independent events then P (A₁ ∩ A₂ ∩ A₃ ∩ --------- ∩ An = -------- ?

- P(A₁) + P(A₂) + ………… P(An)
- P(A₁) . P(A₂) ………… P(An)
- P(A₁ . A₂ . A₃ ……… An)
- None of these

B

## 11th Class Math MCQs Chapter 5 Punjab Board

Question 1: The 6th –term of the expansion (x² - 3/2x)¹⁰ is ?

- 15309/8 x⁵
- 15309/8 x⁴
- -15309/8 x⁵
- - 15309/8 x⁴

C

Question 2: (1 - 2x)³ is valid if: ?

- |x| = 1
- |x| < 1/2
- |x| < 2
- None of these

B

Question 3: Binomial theorem holds if ?

- a or x is complex
- a and x is both real
- a or x is real
- All of above

D

Question 4: n² - n + 41 represents a prime number for n ε N where ?

- n≤5
- n≤40
- n≤20
- n≤10

A

Question 5: The number of terms in the expansion (a + x) n is one greater that’s its ?

- Power
- Index
- Base
- None

B

Question 6: The first three terms in the expansion of (1 - x)³ are ?

- 1 - 3x + 3x²
- 1 - 3x + 6x²
- 1 - 3x - 6x²
- 1 + 3x + 6x²

A

Question 7: The inequality n! > 2ⁿ - 1 is valid if ?

- n ≥ 4
- n < 4
- n = 3
- n ≤ 3

A

Question 8: Sigma notation of binomial theorem is ?

- ∑ⁿ r=0 (n/r)aⁿ⁻r xr
- ∑ⁿ r=0 (n/r)aⁿ xr⁻¹
- ∑ ⁿ⁻¹r=0 (n/r)aⁿ xr
- ∑ⁿ r =0 (n/r)aⁿ⁺r xr

A

Question 9: The general term the expansion (a + x)ⁿ is ?

- T r ₊₁ = (n/2 -1)th term
- T r ₊₁ = (n+1/r) aⁿ⁺¹⁻r xγr
- T r ₊₁ = (n/2 +1)th term
- T r ₊₁ = (n/r) aⁿ xr

D

Question 10: If n is even, the only middle term of the expansion is ?

- n/2th term
- (n +1/2)th term
- (n/2 -1)th term
- (n/2 +1)th term

D

Question 11: If n is any positive integer then 3 + 6 + 9+ ……… + .+ 3n = ?

- 3n(n + 1)/2
- 3n(n + 1)
- 3n(n + 1)/4
- 2n(n + 1)/3

A

Question 12: (n/0),(n/1),……….,(n/n) are called ?

- Binomial co-efficient
- None
- Constant
- a & b both

A

Question 13: If n is any positive integer then 4ⁿ > 3ⁿ + 4 is true for all ?

- n ≤ 2
- n < 2
- n > 2
- n ≥ 2

D

Question 14: The number of terms in the expansion of (a + x)¹⁰ are ?

- 10
- 12
- 13
- 11

D

Question 15: The coefficient of the last term in (a – b)⁵ is ?

- -1
- 1
- None of these
- 0

A

Question 16: Number of terms in the expansion of (1/x - x²/2)¹² are ?

- 14
- 12
- 11
- 13

D

Question 17: Second term in the expansion of (a – 2x)¹/³ is ?

- x/3
- x/2
- - 2x/3
- 2x/3

C

Question 18: The middle term of (a + x)¹² is ?

- 1288a⁶x⁶
- 1297x⁶
- 110880a⁶x⁶
- 11088a⁶x

C

Question 19: The binomial co-efficient from beginning and end of the expansion are ?

- Equal
- Unique
- Not equal
- None of these

A

Question 20: The inequality 3ⁿ < n! holds for positive integral values of n if ?

- n > 6
- n > 3
- n > 2
- n > 4

D

## 11th Class Math MCQs Chapter 6 Punjab Board

Question 1: If cosθ = 12/13 and the terminal side of the angle is not in the I quadrant then cosecθ= ?

- – 13/5
- – 5/13
- 5/13
- 13/5

B

Question 2: Which angle is quadrantal angle ?

- 45˚
- 270˚
- 60˚
- 120˚

B

Question 3: Sec (- 9/2 π) = ?

- ∞
- None of these
- 0
- 1

A

Question 4: θ +360k where k ε Z is conterminal with ?

- 2θ
- θ
- πθ
- 2kπ

B

Question 5: Cos θ + Sin θ tan θ = ?

- csc θ
- sec2 θ
- sec² θ
- sec θ

D

Question 6: (22 1/2)⁰ = ?

- π rad
- π/2 rad
- π/8 rad
- π/4 rad

C

Question 7: If a cot θ + bcsc θ =x² bcot θ + acsc θ=y² then x⁴ - y⁴ = ?

- b² – a²
- b – a
- a² + b²
- a² – b²

A

Question 8: If cot θ > 0 and sin θ< 0 then terminal arm of θ lies in ?

- 2nd Quad
- 3rd Quad
- 1st Quad
- 4th Quad

B

Question 9: 2tan θ/1+tan² θ = ?

- cos2 θ
- sin2
- cos θ
- sin θ

B

Question 10: One radian is equal to: ?

- 50˚
- 45˚
- 57.296˚
- 58.296˚

C

Question 11: The 60th part of one degree is called one ?

- Radian
- Degree
- Minutes
- Second

C

Question 12: Which one is true ?

- 1 rad < 1˚
- 5 rad = 2˚
- 1 rad > 1˚
- 1 rad = 1˚

C

Question 13: The vertex of an angle in standard form is at ?

- (1,0)
- (1, 1)
- (0, 0)
- (0,1)

C

Question 14: Cos(-1980˚) = ?

- – 1/2
- –1
- 0
- √3/2

C

Question 15: Cot⁴θ + cot²θ = ---------- ?

- None of these
- cosec²θ – cot²θ
- cosec⁴θ + cosec²θ
- cosec⁴θ – cosec²θ

D

Question 16: If cot θ= 15/8 and θ ∉ 1st –quadrant then Cos θ = ?

- 15/7
- - 5/17
- - 15/17
- 8/5

C

Question 17: If cos 2θ = a sin²θ – 2/a then a = ?

- 1
- -1
- 2
- -2

D

Question 18: 5- person can be seated at a round table in ?

- 25 ways
- 24 ways
- 20 ways
- None of these

B

Question 19: In 30 min, the hour hand of a clock turns through ?

- π rad
- π/6 rad
- π/12 rad
- π/24 rad

B

Question 20: Sin² π/6 + sin² π/3 + tan² π/4 = ?

- 1
- 3
- 2
- 0

B

## 11th Class Math MCQs Chapter 7 Punjab Board

Question 1: Cos α= ?

- ±√1 + Cos α/2/2
- ±√1 - Cos α/2/2
- ±√1 + Cos 2α/2
- ±√1 - Cos2α/2

C

Question 2: Sin α = ?

- Sin α/2 cos α/2
- 1
- 2Sin α/2 cos α/2
- cos² α/2 - sin² α/2

C

Question 3: Sin3 α= ?

- 4 Sin³ α + 3Sin α
- 4 Sin³ α – 3Sin α
- 3 Sin α + 4Sin³ α
- 3 Sin α – 4Sin³ α

D

Question 4: sinP + sinQ = ?

- None of these
- - 2 sin P+Q/2 cos P – Q/2
- 2 cos P+Q/2 cos P – Q/2
- 2 sin P+Q/2 cos P – Q/2

D

Question 5: If Cos α = 3/5, 0 < a < π/2 then tan2α = ?

- 24/29
- - 24/7
- 7/25
- - 7/24

B

Question 6: The angles 90˚ ± θ, 180˚ ± θ, 270˚ ± θ,360˚ ± θ are called ---------angles ?

- Composite
- Allied
- Half
- Quadrantal

D

Question 7: 2cos 5θ . sin 3θ = ?

- cos8θ + cos 2θ
- Sin8θ – sin 2θ
- sin4θ – sinθ
- sin8θ + sin 2θ

B

Question 8: secθ ≠ ?

- cosec θ /√cosec² θ – 1
- 1/√1 – sin² θ
- √1 + cot² θ/cot θ
- √cosec² θ – 1

D

Question 9: Sec(3π/2 + α) = ?

- -cot α
- sec α
- -csc α
- csc α

D

Question 10: If α, β, γ are angles of triangle then cos (α + β) = --------- ?

- sin γ/2
- Cos γ
- -cos γ
- sin γ

C

Question 11: Fundamental law of trigonometry is--------- where α, β are any two angles ?

- Cos(α – β) = cosα cosβ + sinα sinβ
- Cos(α + β) = cosα cosβ – sinα sinβ
- sin(α + β) = sinα cosβ + cosα sinβ
- sin(α – β) = sinα cosβ – cosα sinβ

A

Question 12: Cos 315˚= ?

- √3/2
- 1/√2
- 1
- 1/2

B

Question 13: The distance between the points (3, 8) and (5, 6) is ?

- 2√2
- 1
- √2
- 3√2

A

Question 14: Tan(- α +π/2 – β) = ?

- cot(α - β)
- tan (α - β)
- cot(α + β)
- tan(α + β)

C

Question 15: If r cosθ =3 , r sinθ=4 then r is ?

- -25
- -5
- 5
- 25

C

Question 16: 2sin 12˚ sin46˚ equals ?

- Cos 34˚– cos 58˚
- sin 34˚– sin 58˚
- Cos 34˚ + cos 58˚
- sin 34˚ + sin 58˚

A

Question 17: If x > y > 0 then point P(x, y) lies in quadrant ?

- IV
- II
- I
- III

C

Question 18: 2sinα cosβ = ?

- None of these
- Sin(α + β) – sin (α – β)
- Sin(α + β) + cos (α – β)
- Sin(α + β) + sin (α – β)

D

Question 19: Tan 15˚ = ?

- √3 + 1
- √3 + 1/√3 – 1
- √3 – 1
- √3 – 1 /√3 + 1

D

Question 20: Sin (α + β) + Sin (α - β) = ?

- 2Cos α Cos β
- 2Cos α Sin β
- -2Sin α Sin β
- 2Sin α Cos β

D

## 11th Class Math MCQs Chapter 8 Punjab Board

Question 1: If R is the radius of circum-circle the R = ?

- All of these
- b/2sinα
- c/2sinα
- a/2sinα

A

Question 2: If b = 3, c = 5 and α = 120˚ then a = ?

- 6
- 7
- 5
- 8

B

Question 3: cos γ/2 = ?

- None of these
- √S(S – b)/ca
- √S(S – c)/ab
- √S(S – a)/ab

C

Question 4: When a = 37.34, b = 3.25, C = 35.06. what will be the smallest angle ?

- 3˚40’
- 3˚39’
- 4˚41’
- 3˚

B

Question 5: The angle made by an object at a lower position is called ?

- Right angle
- Angle of elevation
- None of these
- Angle of depression

D

Question 6: At the top of a Cliff of 80m high, the angle of depression of a boat is 12˚. How far is the boat from the Cliff ?

- 376m
- 400m
- 200m
- 276m

A

Question 7: The point of intersection of the right bisectors of the sides of a triangle is called ?

- None of these
- Circum-centre
- Ex-center
- In-center

B

Question 8: c + a/c – a = ?

- None of these
- tan α + γ/2/tan α – γ/2
- tan γ + α/2/tan γ – α/2
- tan α + β/2/tan α – β/2

C

Question 9: Sum of opposite angles of a cyclic quadrilateral ?

- 360˚
- 90˚
- 180˚
- 270˚

C

Question 10: If a = 319, b = 168 and γ = 110˚ 22’ then α + β = ?

- 89˚40’12”
- 60˚45’
- 69˚38’
- 91˚10’

C

Question 11: In a ∆ABC, Law of cosine is ?

- a/sin A = b/sin B = c/sin C
- cosC = a² + b² - c²/2ab
- a – b/a + b = ran(α –β/2)/tan(α + β/2)
- 1/2 ab sinγ

B

Question 12: The greatest angle is opposite to ?

- Greatest side
- Same side
- Smallest side
- Right side

A

Question 13: abc/4∆ = ?

- r₁
- r
- R
- r₂

C

Question 14: A circle passing through the vertices of a triangle is called ?

- Circum-circle
- Escribed-circle
- None of these
- In-circle

A

Question 15: If ∆ = 2437, a = 79 and c = 79 then β = ?

- 45˚12’
- 39˚30’
- 36˚10’
- 30˚

B

Question 16: A triangle can be constructed if: ?

- One side is given
- Three angle are given
- 2side are given
- Three sides are given

B

Question 17: The circle passing through the vertices of a triangle is ?

- Circum-circle
- In-circle
- e-circle
- None of these

A

Question 18: We use first law of cosine (tangent) then law of sine when measure of ……. are given ?

- One side & two angle
- One side and one angle
- Tow sides and one angle
- All three sides

C

Question 19: When measure of one side and two angles are given then we use law of ?

- Sine
- None of these
- Tangent
- Cosine

A

Question 20: With usual notation, the value of a – b + c is ?

- 2S – b
- S + b
- 2(S – b)
- S – b

C

## 11th Class Math MCQs Chapter 9 Punjab Board

Question 1: The domain of y = csc⁻¹ x is ?

- x ≥ - 1 or x ≤ 1
- x ≥ - 1
- -1 ≤ x ≤ 1
- x ≤ 1

A

Question 2: The value of sin⁻¹ √3/2 is ?

- π/2
- π/6
- π/4
- π/3

D

Question 3: Range of y = Secx is ?

- - ∞ < x < ∞
- - 1 ≤ y ≤ 1
- x > + ∞
- Y ≥ 1 or y ≤ - 1

D

Question 4: The reference angle of tanθ = -1 equals ?

- π/4
- - π
- π
- - π/4

A

Question 5: The graphs of trigonometric function will be ?

- None of these
- Line segments
- a & b both
- Smooth curve

D

Question 6: Which one is the example of trigonomentric equation ?

- X + 1/x = 0
- x² + 2m – 3 = 0
- Sinx + 1/2
- None of these

C

Question 7: Domain of y = sin⁻¹ x is ?

- (0, π)
- (-π/2 , π/2)
- [-π/2 , π/2]
- - ∞ < x < + ∞

C

Question 8: θ = (2n + 1) π/2 , n ε Z is a solution of ?

- tan θ = 0
- sin θ = 0
- cos θ = 0
- cot θ =0

C

Question 9: θ = nπ where n ε z is the solution of ?

- cos2 θ
- sin2 θ = 0
- Cos θ = 0
- sin θ = 0

D

Question 10: 2tan⁻¹ A = ?

- tan⁻¹ (2A/1 + A)
- tan⁻¹ (A/1 – A)
- tan⁻¹ (2A/1 – A²)
- tan⁻¹ (1 – A² /2A)

C

Question 11: The inverse of a function is function if ?

- All of these
- The function is into
- The function is onto
- The function is one to one

D

Question 12: The represents the function from -180 to +180 ?

- tan x
- cos x
- cot x
- Sin x

D

Question 13: Solution of the equation 1 + cosθ = 0 is in quadrant ?

- II
- III
- I
- None of these

D

Question 14: Sec (cos⁻¹ 1/2) is equal to ?

- π/6
- π/3
- 1/2
- 2

D

Question 15: Every horizontal line between the lines y = ± 1 intersects the graph ?

- Twice
- Finitely many times
- Once
- infinitely many times

D

Question 16: Domain of principal cot function y = cot x is ?

- - π/2 ≤ x ≤ π/2
- 0 < x < π
- -∞ < x < ∞
- - π/2 < x < π/2

B

Question 17: Sin x = ½ then x = ?

- - π/6
- π/6 , 5 π/6
- - π/6 , -5 π/6
- - 5 π/6

B

Question 18: 2cos⁻¹ A is equal to ?

- sin⁻¹ (2A² - 1)
- cos⁻¹ (A² - 2)
- cos⁻¹ (2A² - 1)
- sin² (A² - 2)

C

Question 19: The period of 3cos x/5 is ?

- 2π
- 10 π
- 5 π
- π

B

Question 20: Cos⁻¹ x = ?

- π/2
- sin⁻¹ x – π/2
- π/2 + sin⁻¹ x
- π/2 –sin⁻¹ x

D

## 0 comments:

## Post a Comment