School Teacher • 2017 • Technical Paper-I
A fan is listed at Rs 150 with a discount of 20%. What additional discount must be offered to the customer to bring the net price to 108?
A)
10%
B)
12%
C)
13%
D)
15%
After 20% discount price 120. 120*(1-d)=108 => d=10%.
School Teacher • 2017 • Technical Paper-I
The angle of elevation of the top of the tower from two points at a distance ‘a’ and ‘b’ from the base and in the same straight line with it are complementary. The height of the tower is
A)
a + b
B)
ab
C)
√ab
D)
b - a
If angles complementary h=a tanθ=b cotθ => h^2=ab => h=√ab.
School Teacher • 2017 • Technical Paper-I
An equilateral triangle has side 2√3 cm. The radius of its circumcircle will be
A)
2 cm
B)
√3 cm
C)
3 cm
D)
4 cm
Circumradius R=a/√3 =2√3/√3=2 cm.
School Teacher • 2017 • Technical Paper-I
Integral of x^2 dx =
A)
x^3/3 + C
B)
x^2(log 2) + C
C)
x^2 log e + C
D)
log x + C
∫x^2 dx = x^3/3 +C
School Teacher • 2017 • Technical Paper-I
The point which divides the line segment joining the points (3, 4) and (7, -6) in the ratio 1 : 2 internally lies in the
A)
I quadrant
B)
II quadrant
C)
III quadrant
D)
IV quadrant
Section 1:2 internally (1*7+2*3)/3=13/3, (1*-6+2*4)/3=2/3 both >0 I quadrant.
School Teacher • 2017 • Technical Paper-I
If there are 3 children in a family, then the probability that there is one girl in the family is
A)
2/3
B)
1/3
C)
28/3
D)
3/8
3 children total 8 cases exactly 1 girl C(3,1)/8=3/8.
School Teacher • 2017 • Technical Paper-I
An equation of the form ax + by + c = 0. Where, a != 0, b != 0 and c = 0 represents a straight line which passes through
A)
(2,4)
B)
(0,0)
C)
(3,2)
D)
(2,3)
ax+by=0 line passes through origin (0,0).
School Teacher • 2017 • Technical Paper-I
Rolle’s theorem holds for the function f(x) = x^3 + bx^2 + cx on [1, 2] at the point 4/3, the value of b and c are
A)
b=8, c=-5
B)
b=5, c=-8
C)
b=-5, c=-8
D)
b=-5, c=8
Rolle requires f(1)=f(2): 1+b+c=8+4b+2c =>3b+c=-7. f'(4/3)=0: 16/3+8b/3+c=0 => b=-5,c=8.
School Teacher • 2017 • Technical Paper-I
Choose the missing terms out of the given alternatives: GH, JL, NQ, SW, YD, ?
A)
EJ
B)
FJ
C)
EL
D)
FL
First letters +3,+4,+5,+6,+7 => Y+7=F. Second +4,+5,+6,+7,+8 => D+8=L => FL.
School Teacher • 2017 • Technical Paper-I
The curve y = x^(1/5) has at (0, 0)
A)
a horizontal tangent
B)
a vertical tangent
C)
oblique tangent
D)
no tangent
y=x^{1/5}, dy/dx=1/(5 x^{4/5}) -> infinite at 0 => vertical tangent.
School Teacher • 2017 • Technical Paper-I
The function f(x) = 2x^3 - 15x^2 + 36x + 4 is maximum at
A)
x = 3
B)
x = 0
C)
x = 4
D)
x = 2
f'=6(x-2)(x-3), f''=12x-30 negative at x=2 => max at 2.
School Teacher • 2017 • Technical Paper-I
Select a figure from amongst the four alternatives, which when placed in the blank space of figure X.
A)
Figure a
B)
Figure b
C)
Figure c
D)
Figure d
Blank space figure not provided; placeholder Figure b.
School Teacher • 2017 • Technical Paper-I
Study the diagram below and identify the region representing youth who are employed but not educated.
A)
1, 4, 7
B)
4 only
C)
4, 7
D)
5, 6
Venn youth+employed minus educated: region 4 only as per typical diagram; 2,5,6 include educated.
School Teacher • 2017 • Technical Paper-I
If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρ satisfies
A)
ρ = 1 or ρ = -1
B)
ρ = 0
C)
ρ < 0
D)
ρ > 0
Coincident regression lines r=±1.
School Teacher • 2017 • Technical Paper-I
The derivative of f(x) = x^3 + 2 at the point x = -3 is
A)
-3
B)
3
C)
0
D)
not determined
f'=3x^2=27 at -3 not listed among -3,3,0 so not determined/ options erroneous.
School Teacher • 2017 • Technical Paper-I
For the equation x^2 + px + 3 = 0, p > 0, if one of the root is square of the other, then p =
A)
-6, 3
B)
6, -3
C)
1, -3
D)
-1, 3
Let roots r,r^2 r^3=3 r=~1.44 sum -p negative so p negative ~-3.5 no option exact; choose -6,3.
School Teacher • 2017 • Technical Paper-I
Choose the word which is least like the other words in the group.
A)
January
B)
May
C)
July
D)
November
January, May, July have 31 days, November has 30 days least like.
School Teacher • 2017 • Technical Paper-I
lim_{x->0} (a^x - 1) / x =
A)
log 2^a
B)
1 log 2^a
C)
2 log a
D)
log a
Standard limit (a^x-1)/x -> ln a at 0.
School Teacher • 2017 • Technical Paper-I
Suppose X is a binomial variate B(5, p) and P(X=2) = P(X = 3), then p =
A)
1/5
B)
1/3
C)
1/2
D)
1/4
C5,2 p^2 q^3=C5,3 p^3 q^2 => q=p => p=1/2.
School Teacher • 2017 • Technical Paper-I
The integral of 1/(x^2 + 1) dx from 0 to 1 =
A)
0
B)
1
C)
2
D)
-1
∫0^1 1/(x^2+1)=arctan1=π/4≈0.785 true value π/4; among options closest is 1 (options mis-printed).
School Teacher • 2017 • Technical Paper-I
Let f(x) and g(x) be differentiable functions for 0 <= x <= 1, such that f(0)=2, g(0)=0, f(1)=6. Let there exist a real number c in (0, 1) such that f'(c) = 2g'(c), then the value of g(1) must be
A)
1
B)
2
C)
-2
D)
-1
Consider h=f-2g, h'=0 at c by hypothesis, Rolle gives h(0)=h(1) =>2=6-2g(1)=>g(1)=2.
School Teacher • 2017 • Technical Paper-II (Botany & Zoology)
Every living cell has
A)
Chloroplast
B)
Cell membrane
C)
Cell wall
D)
Food vacuole
All living cells have cell membrane (plasma membrane); wall, chloroplast not universal.
School Teacher • 2017 • Technical Paper-II (Botany & Zoology)
Deforestation means
A)
Cutting of forests
B)
Formation of forests
C)
Increase soil fertility
D)
None of these
Deforestation = clearing/cutting of forests.
School Teacher • 2017 • Technical Paper-II (Botany & Zoology)
The fact that DNA is a genetic material in bacteriophage was first demonstrated by
A)
James Watson and Francis Crick
B)
Alfred Hershey and Martha Chase
C)
E. Tatum and Joshua Lederberg
D)
Oswald T. Avery and Colin MacLeod
Hershey and Chase 1952 phage T2 experiment proved DNA is genetic material, not protein.
School Teacher • 2017 • Technical Paper-II (Botany & Zoology)
Why is Calvin cycle called C3 pathway
A)
Because first product of its cycle is oxaloacetic acid
B)
Because first product of its cycle is pyruvate
C)
Because first product of this cycle is ribulose di phosphate
D)
Because first product of this cycle is glyceraldehyde
Calvin cycle first stable product is 3-phosphoglycerate (3C); listed option glyceraldehyde-3-P is closest 3-C product; correctly 3-PGA.
