12th Class Mathematics Lectures MCQs Notes |

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## 12th Class Math MCQs Chapter 1 Functions & Limits Punjab Board

Question 1: Limx→0 tan x⁰/x = ?

- 1
- 180 π
- 180/π
- π/180

D

Question 2: x = at², y = 2at represents ------ ?

- Hyperbola
- Parabola
- Ellipse
- Circle

B

Question 3: If f(x) + f(- x)/2 = 0, then f(x) is ----- ?

- Even
- Explicit
- Odd
- Periodic

C

Question 4: The range of function f(x) = |x|/x is ?

- R
- [–1, 1]
- R – {0}
- - 1 and 1

D

Question 5: If f(x) = ex, then f⁻¹(x) = ?

- lnx
- cosx
- ex
- Sinx

A

Question 6: Explicit form of y – x² - 2x + 1 = 0 is -------- ?

- None
- 2x + x² = y + 1
- y = x² + 2x – 1
- y – x² = 2x – 1

C

Question 7: If f(x) = sinx and g(x) = 1/tan x, then gof(x) = ?

- sin(cotx)
- cos(tanx)
- Cot (sinx)
- sin(tanx)

C

Question 8: Equation x = 9 Cost and y = 9Sint represents the equations of ?

- Parabola
- Hyperbola
- Circle
- Line

C

Question 9: x² + y² = 16 is ?

- Function
- Ellipse
- Line
- Not function

D

Question 10: Limx→∞ 2 – 3x/√3 + 4x² = ------- ?

- 1
- -3/2
- 3/2
- ∞

B

Question 11: The function f(x) = ax + b is an identity function if ?

- a = 1, b = 1
- a = 0, b = 1
- a = 0, b = 0
- a = 1, b = 0

D

Question 12: x →Lim 0 2³x - 1/x = ------ ?

- ln3
- ln8
- ∞
- ln27

B

Question 13: The value of K for which the function f(x) = {sinx/x k x ≠ 0 x = 0 is continuous is ?

- - 1
- 1
- 0
- - 2

B

Question 14: Limx→0 (1 +2x)1/x = ?

- e⁻¹
- e²
- e³
- e

B

Question 15: The linear function f(x) = ax + b is constant function if ?

- a ≠ 0, b = 1
- a = 0 = b
- a = 1 = b
- a = 1, b = 0

B

Question 16: f(x) = sin x + cos x is -------- function ?

- Even
- Odd
- None of these
- Neither even nor odd

D

Question 17: If a function f(x) is not continuous at x = c, then it is is called ------- at c ?

- Explicit
- Linear
- None
- Discontinous

D

Question 18: Cosh⁻¹ x = ?

- In(x + √x² + 1)
- 1/2 ln(x +1/x - 1)
- 1/2 ln(1 + x/1 - x)
- ln(x + √x² - 1)

D

Question 19: θ→Lim0 1-cos9θ/1-cos3θ = -------- ?

- 12
- 0
- 9
- 3

C

Question 20: θ→Lim0 sin 7θ/θ = -------- ?

- 1/7
- 7
- None
- 1

B

## 12th Class Math MCQs Chapter 2 Differentiation Punjab Board

Question 1: If f(x) = cos x, then slope of normal at x = 0 is--------- ?

- 1
- undefined
- -1
- Zero

B

Question 2: Limx→a f(x) – f(a)/x – a = -------- ?

- integral of f(x)
- f(a)
- f’(a)
- f’(x)

C

Question 3: 1/x d/dx (sinx²) = ?

- cosx²
- 2cosx²
- 2xcosx²
- 2x cos²x

C

Question 4: d/dx (tan⁻¹x – Cot⁻¹x)= ?

- x/1 + x²
- 2/1 + x²
- 1/1 + x²
- 0

B

Question 5: If y = sin x then ?

- y₄ = y₂
- y₄ = y₁
- y₄ ≠ y
- y₄ = y

D

Question 6: d/dx(axm + bxn) = ?

- (m - 1)xm-2 + (n – 1)xⁿ⁻²
- maxm-1 + nbxⁿ⁻¹
- a(m – 1) xm-2 + b (n – 1)xⁿ⁻²
- mxm-1 + nxⁿ⁻¹

B

Question 7: Notation used by Cauchy for the derivative of f(x) is ?

- df/dx
- f’(x)
- f”(x)
- Df(x)

D

Question 8: d/dx sin x - d²/dx² (cos x) = -------- ?

- 2 sin x
- 2 cos x
- 0
- - 2 sin x

B

Question 9: If f(x) = 3x² + 1 and f(2) = f(x) – f(2)/x – 2, then f’(2) = ?

- 6x
- 12
- 0
- 6

B

Question 10: f(x) = 1/x – 1 ⇒ f’(2) = ?

- 1
- 0
- -2
- -1

D

Question 11: d/dx[cot(sec⁻¹ √cot² x + 1/cot² x)] = ?

- -cotx
- cotx
- sec²x
- - cosec²x

B

Question 12: If f(x) = 3 + x, then ?

- f’(0) < f’(1)
- f’(0) ≠ f’(1)
- f’(0) > f’(1)
- f’(0) = f’(1)

D

Question 13: The function f(x) = ax² + bx + c has maximum value if ?

- a > 0
- a > 0
- a > 1
- a > 2

B

Question 14: For a function f(x), if f’ (c) = - & f’’(c) > 0 then f(x) has, at x = c ?

- Stationary point
- Relative minima
- Point of inflection
- Relative maxima

B

Question 15: d/dx log₃ x = ?

- 1/x1n3
- 1/x1na
- 1/x
- 1n3/x

A

Question 16: if y = e¹⁰x then ys = ?

- None of these
- 100 e¹⁰x
- e¹⁰x
- 100000e¹⁰x

D

Question 17: d/dx xⁿ = nxⁿ⁻¹ where ?

- n є C
- n є R
- n є Q
- n є Q’

B

Question 18: d/dx sec⁻¹ (x/a)= ?

- a/x√x² - a²
- a/x√a² - x²
- None of these
- x/a√x² - a²

A

Question 19: da³/dx = ? where a is a constant ?

- 2a
- None
- 0
- a

C

Question 20: Function f(x) = sin x for domain (- π, π) is increasing in interval -------- ?

- [- π/2, π/2]
- [- π, π/2]
- [- π/2, π]
- [π/2, π]

A

## 12th Class Math MCQs Chapter 3 Integration Punjab Board

Question 1: ∫ 2x (ln2) dx = ?

- 2x /ln 2 + c
- 1/2x ln2
- ln 2/2x + c
- 2x+ c

D

Question 2: ∫ e x[Co sec⁻¹ x – 1/x√x² - 1]dx = ?

- e x Cosec⁻¹ x + c
- Cosec⁻¹ x + c
- Cosec⁻¹/e⁺ x + c
- e x/ Cosec⁻¹ x + c

A

Question 3: Order of differential equation x² (2y + 1) dy/dx – 1 = 0 is ?

- 3rd
- none
- 1st
- 2nd

C

Question 4: 3∫₀ dx/x² + 9 = ?

- π/6
- π/16
- π/12
- π/4

C

Question 5: The solution of differential equations x dy/dx = 1 + y is ?

- None
- y = cx – 1
- y = x – 1
- y = cx + 1

B

Question 6: The definite integral b∫af(x) dx represents the --------- above the x-axis and under the curve y = f(x) from x = a to x = b ?

- Area
- integral
- Function
- None

A

Question 7: If y = 1nx, then dy is equal to ?

- 1/x dx
- 1/x . 1/1n a
- xdx
- 1/x

A

Question 8: ∫ cosec²x/cotx dx = ?

- -ln(Cotx) + c
- -cotx + c
- ln |cotx| + c
- None of these

A

Question 9: ∫xex dx = ?

- ex + x + c
- Xex + ex + c
- xex + c
- xex – ex + c

D

Question 10: If ²∫₁(3x² + 2x + k) dx = 12 then k = ------- ?

- 0
- -1
- 2
- 1

A

Question 11: The conditions through which the orbitrary constants involving in the differential equation can be determined is called ?

- Initial value conditions
- Final value condition
- n-initial value conditions
- None

A

Question 12: To evaluate ∫ 1/√a²+x² dx, the best substitution is ?

- x = sin θ
- X = a cos θ
- x = a sec θ
- x = a tan θ

D

Question 13: ∫ex (1/x – 1/x²) dx = ----------- ?

- none
- lnx + c
- exl/x + c
- -ex l/x² + c

C

Question 14: ∫ x⁻¹ dx = ?

- ln|x| + c
- ln(lnx) + c
- l/x²
- x⁰/0

A

Question 15: ∫ dx/√a² - x² dx = -------- ?

- sin⁻¹ a/x + c
- cos⁻¹ x/c + c
- sin⁻¹ x/a + c
- sin⁻¹x + c

C

Question 16: ------ is inverse process of differentiation ?

- Limit
- Linear programming
- integration
- none

C

Question 17: ∞∫∞ dx/1 + x² = ?

- π/3
- π/4
- π/6
- π

D

Question 18: If ¹∫₋₂f(x)dx = 5,³∫₁f(x) dx = 3, then ³∫₋₂f(x)dx = ------- ?

- 8
- 5
- 3
- 1

A

Question 19: If a < c < b b∫af (x) dx = c∫af(x) dx + -------- ?

- c∫bf(x) dx
- b∫af(x)dx
- C
- b∫c f(x)dx

D

Question 20: ∫ sec5x tan5x dx = ?

- tan 5x/5 +c
- 5sec5x
- 1/5 sec 5x + c
- secx/5 +c

C

## 12th Class Math MCQs Chapter 4 Introduction to Analytical Geometry Punjab Board

Question 1: If the lines 3x + ky + 5 = 0 and 2x – y + 5 are parallel then value of k is ?

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

D

Question 2: Slope of y-axis is ?

- -1
- 1
- Undefined
- 0

C

Question 3: Equation of line through origin and parallel to x/a + y/b = 1 is ?

- x/a + y/b = 0
- x/a + y/b = 2
- x/b + y/a = 0
- x/a + y/b = 1

A

Question 4: Every homogenous equation of 2nd degree ax² + 2hxy + by² = 0 represents two straight lines ------- ?

- two parallel lines
- none of these
- Through origin
- not through origin

C

Question 5: If the distance of the point (5, b) from x – axis is 3 then b =---------- ?

- b – 3
- 5
- 3
- 0

C

Question 6: Two lines xy + x² + y² = 0 are -------- ?

- Real & distinct
- none of these
- imaginary
- real and coincident

C

Question 7: If α is the Inclination of a non-horizontal line than ?

- 0 ≤ α ≤ 180°
- 0 < α < 180°
- - 90° < α < 90°
- - 90° ≤ α ≤ 90°

B

Question 8: The point of concurrency of the medians of a triangle is called---------- ?

- Centroid
- circum centre
- orthocenter
- in centre

A

Question 9: The symmetric form of equation of line through point (x₁, y₁) and having Inclination α is ?

- x - x₁/Cosα = y - y₁/Sinα
- x + x₁/Sinα = y - y₁/Cosα
- x - x₁/Sinα = y - y₁/Cosα
- x + x₁/Cosα = y - y₁/Sinα

A

Question 10: If (2,2) is the mid point of the segment joining points (4,6) and (a,b) then ?

- a = 2, b = 1
- a = 0, b = -2
- A = 0, b = 0
- a = -2, b = 0

B

Question 11: In translation of axes, origin is shifted but axes remain --------- to the old axes ?

- Co-planer
- Perpendicular
- Parallel
- Collinear

C

Question 12: If slope of l₁ ⊥ to l₂, then slope of l₂ is ?

- -1
- 0
- -2
- 2

D

Question 13: The distance of point (1/2, -√3/2) from origin ?

- √3/2
- √3/4
- 1/2
- 1

D

Question 14: The point P(x₁, y₁) lies ---- the line ax + by + c = 0 if ax₁ + by₁ + c < 0 ?

- below
- Above
- none of these
- on

A

Question 15: If m is slope of line passing through origin then its equation is ---------- ?

- y = mx + c
- Y = mx
- Y=x
- y = - x

B

Question 16: General form of equation of line is---------- ?

- ax + y = c
- none
- ax + by + c = 0
- X + y + c = 0

C

Question 17: If a ≠ 0, b ≠ 0 then slope of line ax + by + c = 0 is ?

- - b/c
- c/b
- b/a
- - a/b

D

Question 18: The two lines a₁x + b₁y + c₁ = 0 & a₂x + b₂y + c₂ = 0 are parallel if ?

- a₁/a₂ = b₁/b₂
- b₁/c₂ = b₂/c₂
- a₁/c₁ = a₂/c₂
- a₁/b₁ = -a₂/b₂

A

Question 19: If (3, 1) & (5, 1) are the end points of diameter of a circle then coordinates of its center are -------- ?

- (0, 0)
- (-2, 1)
- (4, 1)
- (8, 2)

C

Question 20: The points A (7, 9), B (3, -7) and c (-3, 3) are the vertices of ?

- A right angle isosceles triangle
- An equilateral triangle
- An isosceles triangle
- A right triangle

A

## 12th Class Math MCQs Chapter 5 Math Online Test Linear Inequalities and Linear Programming Punjab Board

Question 1: Most general form of 2nd degree ax² + 2hxy + by² + 2gx + 2fy + c = 0 form a circle if ------ ?

- h² - ab < 0
- h² - ab = 0
- none of these
- h² - ab > 0

A

Question 2: The equation of circle whose center is g & f radius is ---- ?

- √g² - f² - c
- √g² + f² + c
- √g² + f² - c
- √g² - f² + c

C

Question 3: The equation of conjugate axis of x²/16 -y²/9 = 1 is ?

- Y = 0
- y = 9
- x = 16
- x = 0

D

Question 4: If a plane passes through the vertex of cone then the intersection is ?

- A point circle
- Parabola
- Ellipse
- Hyperbola

A

Question 5: The points where the hyperbola meets the focal axis are called its ?

- co-vertices
- Foci
- vertices
- Directrices

C

Question 6: The eccentricity of ellipse x²/16 + y²/9 = 1 is ?

- 16
- 9
- 7/4
- √7/4

D

Question 7: The equation of asymptotes of x²/16 - y²/25 = 1 are ?

- y = ± 5/4 x
- y = ± x
- Y = ± 4/5 x
- y = ± 3/5 x

A

Question 8: The focus of parabola y² = -8x is ?

- (0, 2)
- (2, 0)
- (0, 0)
- (-2, 0)

D

Question 9: If e = o, then conic is called -------- ?

- Circle
- Hyperbola
- Parabola
- Ellipse

A

Question 10: The line through focus and perpendicular to directrix of parabola is called ?

- Vertex Parabola
- Latusrectum Parabola
- Axis of Parabola
- None of these

C

Question 11: If r = 0 then x² + y² = r² is called ----------- circle ?

- large
- small
- Point
- Zero

C

Question 12: The end points of major axis of ellipse are called ?

- Co-vertices
- Foci
- Vertices
- Directrices

C

Question 13: The vertex of parabola x² - 4x – 8y + 4 = 0 is ?

- (-2, 1)
- (2, 0)
- (1, -2)
- (-1, 2)

B

Question 14: Ax² + By² + Gx + Fy + C = 0 form ellipse if ?

- None of these
- A ≠ B, both have same signs
- A ≠ B, both have opposite signs
- A = B

B

Question 15: Ax ² + By² + Gx + Fy + C = 0 form hyperbola if ------ ?

- None of these
- A ≠ B, both have opposite signs
- A ≠ B, both have same signs
- A = B

B

Question 16: The condition that line y = mx + c may touch the circle x² + y² = a² is ?

- c = ±m√1 - a²
- c = ±a√1 + m²
- c = ±m√1 + a²
- c = ±a√1 - m²

B

Question 17: The centre of the circle (x - 5)² + (y - 3)² = 8 is ?

- (-5, 3)
- (5, 3)
- (-5, -3)
- (5, -3)

B

Question 18: The parabola y² = 4ax passes through the point (2, 3) then the value of “a” is ?

- -1/3
- 9/8
- 8/9
- 1/3

B

Question 19: Then length of latusrectum of ellipse x²/9 + y²/16 is ?

- 9/2
- 2/9
- 1/9
- 9

A

Question 20: The length of latusrectum of ellipse x²/a² + y²/b² = 1 is ?

- 2ab
- 2b²/a
- a²/2b
- a/2b²

B

## 12th Class Math MCQs Chapter 6 Math Online Test Conic Sections Punjab Board

Question 1: If θ is angle between two vectors u & v then u . v ≥ 0 only for ?

- π/2 ≤ θ ≤ π
- O ≤ θ ≤ π
- O ≤ θ ≤ π/2
- O < θ < π/2

C

Question 2: The work done by a force 2i – i – k in moving on object through a displacement 3i + 2i – 5k is ------- ?

- 5
- 9
- 7
- 3

B

Question 3: If ⊻ = I – 3 j + 4k and w = ai + 9 j – 12k are parallel then the value of a is ?

- 1
- 3
- -1
- -3

D

Question 4: If the vectors 2i + α j + 5k and 3i + j + α k are perpendicular then value of α is ?

- None of these
- 0
- -1
- 1

C

Question 5: Explicit form of y - x² - 2x + 1 = 0 is -------- ?

- Y = x² + 2x – 1
- 2x + x² = y + 1
- y – x² = 2x – 1
- None

A

Question 6: If 4i + 0i – 3k be a vector them cos γ = ----------- ?

- 1/5
- 2/5
- 4/5
- -3/5

D

Question 7: If 2 and 2 are x and y-components of a vector then its angle with x-axis ?

- 45°
- 60°
- 30°
- 90°

D

Question 8: The norm of non zero vector u is --------- ?

- |u| < 0
- |u| ≥ 0
- |u|= 0
- |u| > 0

D

Question 9: The vectors u 2i + 3 j + k and w = - 6i – 9 j – 3 k are ?

- Parallel but have opposite direction
- Perpendicular
- Neither parallel nor perpendicular
- Parallel and have same direction

A

Question 10: The projection of – 2i + 3 j + 7k on 2 j + k ?

- 13/5
- 13
- 13/4
- 13/√5

A

Question 11: If u . i = -2, u . i = 3 then u = ---------- ?

- 3i – 2i
- -2i + 3i
- 2i – 3i
- 3i + 2i

B

Question 12: A vector parallel and perpendicular to every vector is -------- ?

- negative vector
- zero vector
- unit
- Position vector

B

Question 13: Two vectors u & v, written as pu + qv = 0 are collinear if ?

- p = 0 , q ≠ 0
- p = 0 = q
- p ≠ 0 , q = 0
- p ≠ 0 , q ≠ 0

D

Question 14: A vector whose magnitude is 2 and is in the direction of 5i + 3i + 2k is ?

- 10i/√38 + 6j/√38+4k/√38
- 5/√38 i + 3/√38 i 2/√38 k
- 10i + 6i + 4k
- -10i – 6i -4k

A

Question 15: A unit vector in the direction of ⊻ = [3, -4] is ?

- [3/5, +4/5]
- [3/5, -4/5]
- none of these
- [-3/5, 4/5]

B

Question 16: If the magnitude of dot product and cross product of two vectors are 6√3 and 6 respectively then the angle between vectors is ?

- 60°
- 90°
- 30°
- 45°

A

Question 17: If P = (2, 3) and Q = (6 , -2), then PQ = ?

- -4i + 5j
- 4i – 5 j
- 4i + 5j
- 5i - 4j

B

Question 18: (i - i) . (i - k) x (k - i) = ------- ?

- -1
- 2
- 1
- 0

D

Question 19: Angle between √3 i + j with x-axis is ?

- 90°
- 45°
- 30°
- 60°

C

Question 20: If A, B, C, D are vertices of parallelepiped, its volume = ------- ?

- [AB→BC→ CD→]

D

## 12th Class Math MCQs Chapter 7 Math Online Conic Vectors Punjab Board

Question 1: Explicit form of y - x² - 2x + 1 = 0 is -------- ?

- 2x + x² = y + 1
- Y = x² + 2x – 1
- y – x² = 2x – 1
- None

B

Question 2: A vector whose magnitude is 2 and is in the direction of 5i + 3i + 2k is ?

- 5/√38 i + 3/√38 i 2/√38 k
- -10i – 6i -4k
- 10i + 6i + 4k
- 10i/√38 + 6j/√38+4k/√38

D

Question 3: Angle between √3 i + j with x-axis is ?

- 60°
- 30°
- 90°
- 45°

B

Question 4: If 2 and 2 are x and y-components of a vector then its angle with x-axis ?

- 45°
- 60°
- 90°
- 30°

C

Question 5: The projection of – 2i + 3 j + 7k on 2 j + k ?

- 13/5
- 13/4
- 13
- 13/√5

A

Question 6: The work done by a force 2i – i – k in moving on object through a displacement 3i + 2i – 5k is -------- ?

- 9
- 3
- 7
- 5

A

Question 7: If A, B, C, D are vertices of parallelepiped, its volume = ------- ?

- [AB→AC→ AD→]
- [AB→BC→ CD→]
- [AB→AC→ BD→]
- [BC→BD→ AD→]

A

Question 8: If θ is angle between two vectors u & v then u . v ≥ 0 only for ?

- O < θ < π/2
- O ≤ θ ≤ π/2
- π/2 ≤ θ ≤ π
- O ≤ θ ≤ π

B

Question 9: Two vectors u & v, written as pu + qv = 0 are collinear if ?

- p = 0 = q
- p ≠ 0 , q = 0
- p ≠ 0 , q ≠ 0
- p = 0 , q ≠ 0

C

Question 10: If ⊻ = I – 3 j + 4k and w = ai + 9 j – 12k are parallel then the value of a is ?

- 1
- -1
- -3
- 3

C

Question 11: If u . i = -2, u . i = 3 then u = ---------- ?

- 3i + 2i
- -2i + 3i
- 2i – 3i
- 3i – 2i

B

Question 12: (i - i) . (i - k) x (k - i) = ------- ?

- 0
- -1
- 1
- 2

A

Question 13: A vector parallel and perpendicular to every vector is -------- ?

- zero vector
- unit
- Position vector
- negative vector

A

Question 14: If the vectors 2i + α j + 5k and 3i + j + α k are perpendicular then value of α is ?

- 0
- -1
- 1
- None of these

B

Question 15: The norm of non zero vector u is --------- ?

- |u|= 0
- |u| > 0
- |u| ≥ 0
- |u| < 0

B

Question 16: A unit vector in the direction of ⊻ = [3, -4] is ?

- [3/5, +4/5]
- [-3/5, 4/5]
- none of these
- [3/5, -4/5]

D

Question 17: The vectors u 2i + 3 j + k and w = - 6i – 9 j – 3 k are ?

- Perpendicular
- Neither parallel nor perpendicular
- Parallel and have same direction
- Parallel but have opposite direction

D

Question 18: If 4i + 0i – 3k be a vector them cos γ = ---------- ?

- 4/5
- 1/5
- 2/5
- -3/5

D

Question 19: If the magnitude of dot product and cross product of two vectors are 6√3 and 6 respectively then the angle between vectors is ?

- 45°
- 90°
- 30°
- 60°

D

Question 20: If P = (2, 3) and Q = (6 , -2), then PQ = ?

- 4i + 5j
- 4i – 5 j
- -4i + 5j
- 5i - 4j

B