SPSC Lecture Mathematics Past Paper

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SPSC lecturer mathematics past papers mcqs for jobs test preparation in Sindh Public Service Commission of Pakistan.

SPSC Lecturer Mathematics Past Papers MCQs

When she was in the university, she _______ wake up early in the morning.
  1. Should
  2. Would have
  3. Would
  4. Will
  5. Can
Antonym of ERUDITE
  1. Short
  2. Ignorant
  3. Professional
  4. None of these
The antonym of ‘Frugal’ is ?
  1. Rich
  2. Miserable
  3. Happy
  4. Extravagant
Solution of inequality x-3/x+7 < 0 is?
  1. [-7,3]
  2. (-7) < (3)
  3. (10-7)
  4. (-7,3)
3 < x < 7=>?
  1. |x-2|<5
  2. |x-5|-2
  3. |x|<7
  4. |x|<3
The c of Cauchy mean value theorem for the functions f(x)=x², g(x) = x² on [12] is?
  1. 14/9
  2. 1
  3. 0
  4. -1
If lim sin2x + asinx/x^3 exists, then the value of ‘a’ is?
  1. 2
  2. -2
  3. does not exist
  4. -1
If the radius of a circle increases from 10 cm to 10.1 cm, then the percentage change in its area is?
  1. 1%
  2. 2%
  3. 3%
  4. 4%
The series x- x^2/2 + x^3/3 – x^4/4 + …. is convergent for?
  1. |x1| < 1 only
  2. |x| ≤ 1
  3. -1 < x ≤ 1
  4. All real values of x
What is the value of the limit (x, y) –> (2, 1) of the expression: (x^3 + 2x^2y – xy – 2y^2) / (x + 2y)?
  1. 3
  2. 2
  3. 1
  4. 0
Degree of the function f(x,y)= √x+√y/x + y is?
  1. 1/2
  2. -1/2
  3. 1
  4. -1
If p: x + y = 3, then ¬p is?
  1. x + y ≠ 3
  2. x + y > 3
  3. x + y < 3
  4. x + y = 0
The synonym of METICULOUS is?
  1. Ridiculous
  2. Conscientious
  3. Mindless
  4. Strong
What is the opposite of “fragile”?
  1. Breakable
  2. Robust
  3. Strong
  4. Weak
What is a synonym of “elated”?
  1. Miserable
  2. Thrilled
  3. Depressed
  4. Unhappy
What is the opposite of “candid”?
  1. Forthright
  2. Frank
  3. Blunt
  4. Secretive
What is a synonym of “perplexed”?
  1. Lucid
  2. Clear
  3. Puzzle
  4. Unambiguous
What is a synonym of “brave”?
  1. Fearful
  2. Frightened
  3. Coward
  4. Fearless
p ∨ (p ∧ q) = ?
  1. p
  2. q
  3. p ∧ q
  4. p ∨ q
7 ∈ Sr (5) –>?
  1. d(5,7) < r
  2. d(5,7) ≠ r
  3. d(5,7) > r
  4. None
An open ball in a real line R is?
  1. An open-closed interval
  2. A closed-open interval
  3. A closed interval
  4. An open interval
What is Ext(A) equal to?
  1. Int(A°)
  2. X
  3. Int(A)
  4. None
The set of limit points of ] 0, 1 [ in real line R is?
  1. [ 0,1 ]
  2. ] 0,1 [
  3. [0,1 [
  4. ] 0,1]
A subset F of a metric space X is closed if and only if?
  1. F = F°
  2. F ∪ F = X
  3. F ∩ F´ = ∅
  4. F = F´
The solution of differential equation. day/dx = 1/√1+x^2 is y =?
  1. sinh^-1 x+c
  2. sech^-1x+c
  3. tanh^-1x+c
  4. cotx+c
If f(x,y) is a homogeneous function of degree zero in x and y, then f(x,y) is a function of ___ alone.
  1. y^2/x
  2. y/x^2
  3. y/x
  4. xy
In the first-order linear differential equation dy/dx + P(x)y = Q(x), the integrating factor is?
  1. exp (∫P(x)dx)
  2. exp (∫P(y)dy)
  3. ∫P(x)dx
  4. ∫P(y)dy
The equation of the form y’+P(x)y+Q(x)y² – R(x) is called the ____ equation.
  1. Bernoulli
  2. Ricatti
  3. Clairaut
  4. None
The differential form xdy + ydx/xy is equivalent to?
  1. d(y²/x)
  2. d(tan⁻¹(y/x))
  3. d(ln(xy))
  4. d(x^m/y^n)
The differential equation of the form y=x dy/dx +f (dy/dx) is known as ___ equation.
  1. Bernoulli
  2. Ricatti
  3. Clairaut
  4. None
The general solution of the differential equation d^2y/dx^2 – 4 dy/dx + 4y = 0 is?
  1. (c1 + c2x)e^2x
  2. c1e^2x + c2e^-2x
  3. c1e^3x + c2e^-3x
  4. c1e^4x + c2e^-4x
The solution of the differential equation ydx-2xdy=0 represents?
  1. A family of straight lines
  2. A family of parabolas
  3. A family of hyperbolas
  4. A family of circles
The order of differential equation x²dy + y²dx = 0 is?
  1. 3
  2. 2
  3. 1
  4. None
Change the Voice “Lion does not eat grass, however hungry he may be”?
  1. Grass is not eaten by a lion, however hungry he may be
  2. Grass was being not eaten by a lion, however hungry he may be
  3. Grass is eaten not by a lion, however hungry he may be
  4. Grass is not being eaten by a lion, however hungry he may be
If one of the roots of the equation x^3−6x^2+11x−6=0 is 2, then the other two roots are?
  1. 1 and 3
  2. 0 and 4
  3. -1 and 5
  4. -2 and 6
In the three dimensions the equation x^2 – y^2 = a^2 represents?
  1. A pair of straight line
  2. A hyperbola
  3. A cylinder
  4. A cone
{1, i, -i, -1} is _____?
  1. Semi group
  2. Subgroup
  3. Cyclic group
  4. Abelian group
A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?
  1. y = vx, dy = vdx + xdv
  2. x + y = v, dy = dx + dy
  3. v = x – y, dy = dx – dy
  4. x + y = y, dy = dx + xdy
The mode of the numbers 7, 7, 7, 9, 10, 11, 11, 11, 12 is?
  1. 11
  2. 12
  3. 7
  4. 7 and 11
What is the area of the region bounded by the coordinate axes and the line tangent to the graph of y= 1/8x^2 +1/2x + 1 at the point (0,1)?
  1. 1/2
  2. 1
  3. 2
  4. 4
I hope everyone _____ learned something from this.
  1. Had
  2. Have
  3. Has
  4. Has to
Select the pair of words which are related in the same manner as the given words are related to each other: BIGOTRY : HATRED::?
  1. Sweetness : bitterness
  2. Sugar : Wheat
  3. Fanaticism : Intolerance
  4. Good : bed
If a line makes angles α, β, γ with coordinate axes, Find the value of sin^2 α + sin^2 β + sin^2 γ?
  1. 4
  2. 2
  3. 3
  4. 1
The Fourier series expansion of an even period function contains?
  1. Cosine terms
  2. Sine terms
  3. Odd Hormonics
  4. Even Hormonics
Which of the following is the greatest 3-digit prime?
  1. 96
  2. 97
  3. 98
  4. 99
(1 + i)^10 = ___?
  1. 1
  2. 32i
  3. 32
  4. i
Consider the point A(-1,2), B(6,2) and C(1,-20) in the plane. For how many different points D in the plane are A, B, C and D the vertices of Parallelogram?
  1. One
  2. Two
  3. Three
  4. Four
The package arrived _____ the expected delivery date.
  1. On
  2. In
  3. At
  4. Before
What type of word is “because” in the sentence: “She went to the store because she needed groceries”?
  1. Verb
  2. Adjective
  3. Conjunction
  4. Adverb
What will be the condition for L-Hospital’s Rule to work?
  1. The function must possess at least three non-zero derivatives
  2. The function must be determinate
  3. The function must be indeterminate
  4. The function must be inconsistent
Which is the synonym of “Admonish”?
  1. Defeat
  2. Defend
  3. Destroy
  4. Counsel
Change the capital letters word without changing the meaning: He enjoys VICARIOUS authority?
  1. Tenuous
  2. Limited
  3. Delegated
  4. Wide
At the time of its establishment, Pakistan became the ____ of Muslim States.
  1. Great
  2. Greater
  3. Greatest
  4. Greatly
y= Asinx + Bcos x is the solution of the differential equation?
  1. y” – y = 0
  2. y” + y = 0
  3. y” – 4y = 0
  4. y” + 4y = 0
If S={1/n : ne ∈ N}, then inf S =?
  1. 0
  2. 1
  3. 2
  4. None
Which one of the following statement/s is true?
  1. ∑1/n^p= converges if p ≤ 1
  2. ∑1/n^p= diverges if p > 1
  3. ∑1/n^p= converges if p > 1
  4. ∑1/n^p= converges if 0 < p < 1
The identity element of a set X with respect to intersection in P(X) is?
  1. X
  2. does not exist
  3. 0
  4. None
In the group (G, *), A a,b ∈ G?
  1. a + b ∈ G
  2. ab ∈ G
  3. a * b ∈ G
  4. a – b ∈ G
The set of integers is an abelian group under?
  1. Addition
  2. Multiplication
  3. Division
  4. None
The set of all n, nth roots of unity forms a group under the ___ of complex numbers.
  1. Addition
  2. Multiplication
  3. Division
  4. None
Let (G,+) be a group. A nonempty subset H of G is a subgroup of G if and only if for all a, b ∈ H, the element?
  1. a + b ∈ G
  2. a – b ∈ H
  3. a + (-b) ∈ H
  4. ab ∈ G
Every cyclic group is?
  1. Non abelian
  2. Abelian
  3. Non commutative
  4. None
Every subgroup of a cyclic group is?
  1. Non abelian
  2. Non cyclic
  3. Cyclic
  4. None
Let H be a subgroup of a group G, then the number of left cosets is _____ the number of right cosets of H in G.
  1. Less than
  2. Equal to
  3. Greater than
  4. None
In the group G = (-1,1,-i,i), the order of -i is?
  1. -1
  2. 1
  3. 2
  4. 4
If X has n elements, then ____ permutations can be taken on X.
  1. n
  2. n!
  3. (n – 1)!
  4. (n + 1)!
The order of a cyclic permutation of length n is?
  1. n
  2. n!
  3. (n – 1)!
  4. (n + 1)!
A cycle of length _____ is called the transposition.
  1. Two
  2. Three
  3. Four
  4. None
Every group of prime order is?
  1. Cyclic group
  2. Non-abelian group
  3. Not cyclic
  4. Abelian but not cyclic group
A subset F of a topological space X is closed if and only if F = ?
  1. Int(F)
  2. Cl(F)
  3. Bd(F)
  4. X
Ext(A) =?
  1. X
  2. Int(A)
  3. Int(A^c)
  4. None
Power set of a nonempty set X is?
  1. A topology on X
  2. An empty set
  3. Not topology on X
  4. An infinite set
A sequence (Xn) in a metric space X is said to be strictly increasing if for all n?
  1. Xn ≤ X(n+1)
  2. Xn ≥ X(n+1)
  3. Xn < X(n+1)
  4. Xn > X(n+1)
A convergent sequence in a metric space is?
  1. Bounded
  2. Not constant
  3. Unbounded
  4. None of these
The value of the solid of revolution when rotating around the x-axis is given by?
  1. π ∫[a, b] (f(x))^2 dx
  2. 2π ∫[a, b] (f(x))^2 dx
  3. π ∫[a, b] (f(x)) dx
  4. 2π ∫[a, b] (f(x)) dx
The series is convergent if?
  1. P
  2. p
  3. p>1
  4. 0<p<1
Which one of the following is a unary operation?
  1. Addition
  2. Multiplication
  3. Square root
  4. None
Z is a group under?
  1. Subtraction
  2. Addition
  3. Multiplication
  4. Division
In the group (G, *), where a, b ∈ G, which of the following is always true?
  1. a + b ∈ G
  2. ab ∈ G
  3. a * b ∈ G
  4. a – b ∈ G
The action of wearing of sock and shoes?
  1. Does not commute
  2. Commute
  3. Does not exist
  4. Associative
ax(bxc) is a vector lying in the plane containing vectors?
  1. a and b
  2. a and c
  3. b and c
  4. a and axb
When is z = a + 2by + 2bxy true?
  1. When x = 0
  2. When y = 0
  3. When b = 0
  4. When a = 0
When she was in the university, she ___ wake up early in the morning.
  1. Should
  2. Would have
  3. Would
  4. Will
  5. Can
Antonym of ERUDITE
  1. Short
  2. Ignorant
  3. Professional
  4. None of these
Change the Voice “Lion does not eat grass, however hungry he may be”?
  1. Grass is not eaten by a lion, however hungry he may be
  2. Grass was being not eaten by a lion, however hungry he may be
  3. Grass is eaten not by a lion, however hungry he may be
  4. Grass is not being eaten by a lion, however hungry he may be
If one of the roots of the equation x^3−6x^2+11x−6=0 is 2, then the other two roots are?
  1. 1 and 3
  2. 0 and 4
  3. -1 and 5
  4. -2 and 6
In the three dimensions the equation x^2 – y^2 = a^2 represents?
  1. A pair of straight line
  2. A hyperbola
  3. A cylinder
  4. A cone
{1, i, -i, -1} is ____?
  1. Semi group
  2. Subgroup
  3. Cyclic group
  4. Abelian group
A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?
  1. y = vx, dy = vdx + xdv
  2. x + y = v, dy = dx + dy
  3. v = x – y, dy = dx – dy
  4. x + y = y, dy = dx + xdy
The mode of the numbers 7, 7, 7, 9, 10, 11, 11, 11, 12 is?
  1. 11
  2. 12
  3. 7
  4. 7 and 11
What is the area of the region bounded by the coordinate axes and the line tangent to the graph of y= 1/8x^2 +1/2x + 1 at the point (0,1)?
  1. 1/2
  2. 1
  3. 2
  4. 4
I hope everyone _____ learned something from this.
  1. Had
  2. Have
  3. Has
  4. Has to
Select the pair of words which are related in the same manner as the given words are related to each other: BIGOTRY : HATRED::?
  1. Sweetness : bitterness
  2. Sugar : Wheat
  3. Fanaticism : Intolerance
  4. Good : bed
If a line makes angles α, β, γ with coordinate axes, Find the value of sin^2 α + sin^2 β + sin^2 γ?
  1. 4
  2. 2
  3. 3
  4. 1
The Fourier series expansion of an even period function contains?
  1. Cosine terms
  2. Sine terms
  3. Odd Hormonics
  4. Even Hormonics
Which of the following is the greatest 3-digit prime?
  1. 96
  2. 97
  3. 98
  4. 99
(1 + i)^10 = ____?
  1. 1
  2. 32i
  3. 32
  4. i
Consider the point A(-1,2), B(6,2) and C(1,-20) in the plane. For how many different points D in the plane are A, B, C and D the vertices of Parallelogram?
  1. One
  2. Two
  3. Three
  4. Four
The package arrived ____ the expected delivery date.
  1. On
  2. In
  3. At
  4. Before
What type of word is “because” in the sentence: “She went to the store because she needed groceries”?
  1. Verb
  2. Adjective
  3. Conjunction
  4. Adverb
What will be the condition for L-Hospital’s Rule to work?
  1. The function must possess at least three non-zero derivatives
  2. The function must be determinate
  3. The function must be indeterminate
  4. The function must be inconsistent
Which is the synonym of “Admonish”?
  1. Defeat
  2. Defend
  3. Destroy
  4. Counsel
Change the capital letters word without changing the meaning: He enjoys VICARIOUS authority?
  1. Tenuous
  2. Limited
  3. Delegated
  4. Wide
At the time of its establishment, Pakistan became the_____of Muslim States.
  1. Great
  2. Greater
  3. Greatest
  4. Greatly

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