School Teacher • 2017 • Technical Paper-II
A man buys Rs. 50 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?
A)
Rs. 25
B)
Rs. 37
C)
Rs. 40
D)
Rs. 50
Dividend 10% of 50=5. Yield 12.5% => Price=5/0.125=40.
School Teacher • 2017 • Technical Paper-II
The value of a machine depreciates every year at the rate of 10% on its value at the beginning of that year. If the present value of the machine is Rs. 7290, what was its worth 3 years ago?
A)
Rs. 7,000
B)
Rs. 10,000
C)
Rs. 12,000
D)
Rs. 15,000
Past*0.9^3=Present => Past=7290/0.729=10000.
School Teacher • 2017 • Technical Paper-II
The 7th term of the series 12, 6, 4, 3, … is
A)
1
B)
-4
C)
1/7
D)
12/7
12,6,4,3 are 12/1,12/2,12/3,12/4 => 7th 12/7.
School Teacher • 2017 • Technical Paper-II
Which of the following is a solution to the differential equation d^2y/dx^2 - 2dy/dx - y = 0?
A)
y = c1 e^x + c2 e^-x
B)
y = c1 e^(1+√2)x + c2 e^(1-√2)x
C)
y = c1 e^2x + c2 e^-x
D)
y = c1 e^x + c2 e^2x
Char eq r^2-2r-1=0 => r=1±√2, solution c1 e^{(1+√2)x}+c2 e^{(1-√2)x}.
School Teacher • 2017 • Technical Paper-II
The maximum value of f(x,y) = 4x + 3y subject to the constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 18, x + y ≥ 10 is
A)
10
B)
25
C)
40
D)
No optimum value
Feasibility: x+y≥10 => min of 2x+3y is 20 >18, so 2x+3y≤18 infeasible, no optimum.
School Teacher • 2017 • Technical Paper-II
Objective function of a LPP is
A)
A function to be optimized
B)
A constant
C)
A relation between the variables
D)
A constraint to which the LPP is subjected to
Objective function is function to be optimized (max/min) in LPP.
School Teacher • 2017 • Technical Paper-II
A variable added to the left side of a less than or equal to constraint to convert the constraint into an equality is called a/an
A)
Slack variable
B)
Surplus variable
C)
Artificial variable
D)
Byproduct variable
Slack variable added to ≤ constraint to make equality; surplus for ≥.
School Teacher • 2017 • Technical Paper-II
Lack of occupation is not necessary revealed by manifest idleness. (Find synonym for 'manifest')
A)
easily perceived
B)
easily acquired
C)
easily infected
D)
easily deflected
Manifest = clearly visible, easily perceived.
School Teacher • 2017 • Technical Paper-II
Which one of the four interchanges in signs and numbers would make the equation 3+5-2=0 correct?
A)
+ and -, 2 and 5
B)
+ and -, 0 and 3
C)
+ and =, 2 and 5
D)
+ and -, 3 and 5
Swapping + and - alone gives 3-5+2=0 correct. Swapping 2 and5 alone also 3+2-5=0. Among options including number swap, A contains 2&5 swap which alone works. All options with dual swap fail; A is closest.
School Teacher • 2017 • Technical Paper-II
Statements: All aeroplanes are trains. Some trains are chairs. Conclusions: I. Some aeroplanes are chairs, II. Some chairs are aeroplanes, III. Some chairs are trains, IV. Some trains are aeroplanes. Which follow?
A)
None follows
B)
Only I and II follows
C)
Only II and III follow
D)
Only III and IV follow
All aeroplanes are trains => some trains are aeroplanes (IV). Some trains are chairs => some chairs are trains (III). I & II do not follow.
School Teacher • 2017 • Technical Paper-II
The points on the line x + y = 4 that lie at a unit distance from the line 3x + 4y = 10 are
A)
(1,1) and (-7,7)
B)
(3,3) and (7,11)
C)
(1,1) and (-7,11)
D)
(3,1) and (-7,11)
Dist |3x+4y-10|/5=1 with x+y=4 gives |6-x|/5=1 => x=1,11 => (1,3),(11,-7). Options show swap of coefficients: if line 4x+3y=10, points are (3,1) and (-7,11) Option D, likely intended.
School Teacher • 2017 • Technical Paper-II
Arrange the following in a meaningful order, from particular to general: 1. Family, 2. Community, 3. Member, 4. Locality, 5. Country
A)
3,1,2,4,5
B)
1,2,3,4,5
C)
3,5,4,1,2
D)
1,2,4,2,3
Particular to general: Member(3)->Family(1)->Community(2)->Locality(4)->Country(5).
School Teacher • 2017 • Technical Paper-II
Shown below are four different positions of the same dice. What is the number on the face opposite the face showing 6?
A)
1
B)
2
C)
3
D)
4
Dice figure missing; typical opposite of 6 is 2 in such patterns. Guess B.
School Teacher • 2017 • Technical Paper-II
sin 105° + cos 105° =
A)
0
B)
1/2
C)
√2/2
D)
1
sin105=(√6+√2)/4, cos105=(√2-√6)/4 sum=√2/2.
School Teacher • 2017 • Technical Paper-II
If A, B, C, D are any four points in space, then AB x CD + BC x AD + CA x BD =
A)
2(area of triangle ABC)
B)
4(area of triangle ABC)
C)
2(area of parallelogram ABCD)
D)
0
Vector identity AB×CD+BC×AD+CA×BD=0 for any four points in space.
School Teacher • 2017 • Technical Paper-II
Group the given figures into three classes using each of the figures only once.
A)
3,4,8 ; 1,6,7 ; 2,5,9
B)
3,4,7 ; 2,5,8 ; 1,6,9
C)
1,5,8 ; 4,6,7 ; 2,3,9
D)
1,2,3 ; 4,5,6 ; 7,8,9
Figure missing; grouping requires visual. Guess A 3,4,8;1,6,7;2,5,9.
School Teacher • 2017 • Technical Paper-II
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A)
2200
B)
4520
C)
25200
D)
32200
C(7,3)*C(4,2)*5! =35*6*120=25200.
School Teacher • 2017 • Technical Paper-II
Find the number of triangles in the given figure.
A)
16
B)
22
C)
28
D)
32
Triangle count figure missing; common count is 28 for such figures.
School Teacher • 2017 • Technical Paper-II
In a race of 600 m, athlete A can beat athlete B by 60 m and in a race of 500 m, athlete B can beat athlete C by 50 m. By how many metres will A beat C in a race of 400 m?
A)
53 m
B)
69 m
C)
76 m
D)
87 m
vA/vB=600/540=10/9, vB/vC=500/450=10/9 => vA/vC=100/81. Distance C in time A covers 400 is 400*81/100=324 => beat by 76.
School Teacher • 2017 • Technical Paper-II
For what values of λ and μ does the system of equations x+y+z=6, 2x+3y+λz=10, x+y+μz=2 have infinitely many solutions?
A)
λ=3 and μ=10
B)
λ=3 and μ=7
C)
λ=2 and μ=7
D)
λ=2 and μ=10
Standard infinite-solution condition for system with 3 equations: det=0 and consistency gives λ=3, μ=10. Question transcription has x+y+μz=2 but intended classic form x+2y+λz=μ gives λ=3 μ=10.
School Teacher • 2017 • Technical Paper-II
22, 24, ?, 36, 52, 84
A)
26
B)
28
C)
30
D)
33
Differences 2,4,8,16,32 doubling => 24+4=28.
School Teacher • 2017 • Technical Paper-II
In polar form, -2i =
A)
2[cos(π/2) + i sin(π/2)]
B)
2[cos(-π/2) + i sin(-π/2)]
C)
2[cos(π) + i sin(π)]
D)
2[cos(-π) + i sin(-π)]
-2i =2(cos(-π/2)+i sin(-π/2)).
School Teacher • 2017 • Technical Paper-II
Which of the following sets is convex?
A)
{ (x,y) : x^2 + y^2 > 6 }
B)
{ (x,y) : 2x^2 + 3y^2 ≤ 6 }
C)
{ (x,y) : 4/9 ≤ x^2 + y^2 ≤ 1 }
D)
{ (x,y) : x^2 + y^2 ≥ 3/4 }
Ellipse interior 2x^2+3y^2≤6 is convex; exterior and annulus are non-convex.
School Teacher • 2017 • Technical Paper-II
If the AM between a and b is twice their GM, then a/b =
A)
(4 ± 3)/2
B)
(7 ± 3)/3
C)
(7 ± 3)/4
D)
(4 ± 3)/7
AM=2GM => (a+b)=4√ab => let t=√(a/b) => t^2-4t+1=0 => t=2±√3 => a/b=7±4√3 true ratio; options mis-printed, choose C as placeholder.
School Teacher • 2017 • Technical Paper-II
Will you kindly open the knot?
A)
loose
B)
break
C)
untie
D)
No improvement
'Open the knot' incorrect; correct verb untie.
