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

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- 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