Solved Past Paper
ELEMENTARY SCHOOL TEACHER (EST)
2024
3 < x < 7=>?
A. |x-2|<5
B. |x-5|-2
C. |x|<7
D. |x|<3
The c of Cauchy mean value theorem for the functions f(x)=x², g(x) = x² on [12] is?
A. 14/9
B. 1
C. 0
D. -1
If lim sin2x + asinx/x^3 exists, then the value of ‘a’ is?
A. 2
B. -2
C. does not exist
D. -1
If the radius of a circle increases from 10 cm to 10.1 cm, then the percentage change in its area is?
A. 1%
B. 2%
C. 3%
D. 4%
The series x- x^2/2 + x^3/3 – x^4/4 + …. is convergent for?
A. |x1| < 1 only
B. |x| ≤ 1
C. -1 < x ≤ 1
D. 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)?
A. 3
B. 2
C. 1
D. 0
Degree of the function f(x,y)= √x+√y/x + y is?
A. 1/2
B. -1/2
C. 1
D. -1
If p: x + y = 3, then ¬p is?
A. x + y ≠ 3
B. x + y > 3
C. x + y < 3
D. x + y = 0
The synonym of METICULOUS is?
A. Ridiculous
B. Conscientious
C. Mindless
D. Strong
What is the opposite of “fragile”?
A. Breakable
B. Robust
C. Strong
D. Weak
What is a synonym of “elated”?
A. Miserable
B. Thrilled
C. Depressed
D. Unhappy
What is the opposite of “candid”?
A. Forthright
B. Frank
C. Blunt
D. Secretive
What is a synonym of “perplexed”?
A. Lucid
B. Clear
C. Puzzle
D. Unambiguous
What is a synonym of “brave”?
A. Fearful
B. Frightened
C. Coward
D. Fearless
p ∨ (p ∧ q) = ?
A. p
B. q
C. p ∧ q
D. p ∨ q
7 ∈ Sr (5) –>?
A. d(5,7) < r
B. d(5,7) ≠ r
C. d(5,7) > r
D. None
An open ball in a real line R is?
A. An open-closed interval
B. A closed-open interval
C. A closed interval
D. An open interval
What is Ext(A) equal to?
A. Int(A°)
B. X
C. Int(A)
D. None
A subset F of a metric space X is closed if and only if?
A. F = F°
B. F ∪ F = X
C. F ∩ F´ = ∅
D. F = F´
If f(x,y) is a homogeneous function of degree zero in x and y, then f(x,y) is a function of____alone.
A. y^2/x
B. y/x^2
C. y/x
D. xy
In the first-order linear differential equation dy/dx + P(x)y = Q(x), the integrating factor is?
A. exp (∫P(x)dx)
B. exp (∫P(y)dy)
C. ∫P(x)dx
D. ∫P(y)dy
The differential form xdy – ydx/x^2 is equivalent to?
A. d[ln(y/x)]
B. d(y/x)
C. d(ln(x/y))
D. d(xy)
The equation of the form y’+P(x)y+Q(x)y² – R(x) is called the _____ equation.
A. Bernoulli
B. Ricatti
C. Clairaut
D. None
The differential form xdy + ydx/xy is equivalent to?
A. d(y²/x)
B. d(tan⁻¹(y/x))
C. d(ln(xy))
D. d(x^m/y^n)
The differential equation of the form y=x dy/dx +f (dy/dx) is known as _____ equation.
A. Bernoulli
B. Ricatti
C. Clairaut
D. None
The general solution of the differential equation d^2y/dx^2 – 4 dy/dx + 4y = 0 is?
A. (c1 + c2x)e^2x
B. c1e^2x + c2e^-2x
C. c1e^3x + c2e^-3x
D. c1e^4x + c2e^-4x
The solution of the differential equation ydx-2xdy=0 represents?
A. A family of straight lines
B. A family of parabolas
C. A family of hyperbolas
D. A family of circles
The order of differential equation x²dy + y²dx = 0 is?
A. 3
B. 2
C. 1
D. None
y= Asinx + Bcos x is the solution of the differential equation?
A. y” – y = 0
B. y” + y = 0
C. y” – 4y = 0
D. y” + 4y = 0
If S={1/n : ne ∈ N}, then inf S =?
A. 0
B. 1
C. 2
D. None
Which one of the following statement/s is true?
A. ∑1/n^p= converges if p ≤ 1
B. ∑1/n^p= diverges if p > 1
C. ∑1/n^p= converges if p > 1
D. ∑1/n^p= converges if 0 < p < 1
The identity element of a set X with respect to intersection in P(X) is?
A. X
B. does not exist
C. 0
D. None
In the group (G, *), A a,b ∈ G?
A. a + b ∈ G
B. ab ∈ G
C. a * b ∈ G
D. a – b ∈ G
The set of integers is an abelian group under?
A. Addition
B. Multiplication
C. Division
D. None
The set of all n, nth roots of unity forms a group under the ____ of complex numbers.
A. Addition
B. Multiplication
C. Division
D. 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?
A. a + b ∈ G
B. a – b ∈ H
C. a + (-b) ∈ H
D. ab ∈ G
Every cyclic group is?
A. Non abelian
B. Abelian
C. Non commutative
D. None
Every subgroup of a cyclic group is?
A. Non abelian
B. Non cyclic
C. Cyclic
D. None
