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
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
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
What number has to be added to each term 3 : 5 to make the ratio 5 : 6 ?
A)
5
B)
6
C)
7
D)
12
(3+x)/(5+x)=5/6 => 18+6x=25+5x => x=7.
School Teacher • 2017 • Technical Paper-I
If the points (a, 0), (0, b) and (1, 1) are collinear, then (a + b) / ab =
A)
2
B)
1/2
C)
-1
D)
1
Collinear determinant ab-a-b=0 => ab=a+b => (a+b)/ab=1.
School Teacher • 2017 • Technical Paper-I
For any two events E1 and E2, then P(E1 n E2) / P(E1 U E2) =
A)
> 1/4
B)
<= 1/4
C)
>= 1/2
D)
1
Intersection ≤ union ratio ≤1; choose 1 as max.
School Teacher • 2017 • Technical Paper-I
If ROAST is coded as PQYUR in a certain language, then how will SLOPPY be coded in that language?
A)
MRNAQN
B)
NRMNQA
C)
QNMRNA
D)
RANNMQ
Pattern -2,+2 alternates: R-2=P etc => SLOPPY => QNMRNA.
School Teacher • 2017 • Technical Paper-I
The function f(x) = ax + b is strictly increasing for all x ∈ R if
A)
a > 0
B)
a < 0
C)
a = 0
D)
None of these
f'=a>0 for strictly increasing linear.
School Teacher • 2017 • Technical Paper-I
If u = sin^-1((x^2 - y^2)/(x^2 + y^2)), then x(du/dx) + y(du/dy) =
A)
sin u
B)
cos u
C)
tan u
D)
cot u
v=(x^2-y^2)/(x^2+y^2) homogeneous degree0 => x v_x+y v_y=0. u=arcsin v => x u_x+y u_y=0. Correct 0 not in options; listed options erroneous, choose A as placeholder. True value 0.
School Teacher • 2017 • Technical Paper-I
If the roots of the equation 5x^2 - 7x + k = 0 are reciprocal to each other, then the value of k is
A)
1/5
B)
5
C)
7
D)
1/7
Reciprocal roots product=1 => k/5=1 => k=5.
School Teacher • 2017 • Technical Paper-I
If the mean of the binomial distribution is 25, then its standard deviation lies in the interval
A)
[5, 25)
B)
(5, 25]
C)
[0, 5)
D)
(0, 5]
np=25 variance 25q<25 sd=5√q ∈ (0,5].
School Teacher • 2017 • Technical Paper-I
If log_bc x = a, log_ca y = b and log_ab z = c, then 1/x + 1/y + 1/z = ?
A)
x + y + z
B)
ab + bc + ca
C)
abc
D)
1
log_bc x=a => x=(bc)^a etc; identity often gives 1, choose 1.
School Teacher • 2017 • Technical Paper-I
Choose the missing terms out of the given alternatives : Newspaper : Press : : Cloth : ?
A)
Mill
B)
Fibre
C)
Textile
D)
Tailor
Newspaper produced at Press, Cloth produced at Mill.
School Teacher • 2017 • Technical Paper-I
Find the number of triangles in the given figure.
A)
10
B)
19
C)
21
D)
23
Figure not provided; count triangles typically 23 for such figure (estimated).
School Teacher • 2017 • Technical Paper-I
If log_x y = log_y z = log_z x, then xyz = ? (x, y, z > 0)
A)
e
B)
1
C)
e^e
D)
0
Let log_x y=k => y=x^k etc => k^3=1 => k=1 => x=y=z, product often taken as 1.
School Teacher • 2017 • Technical Paper-I
If the function f(x) = x^3 + alpha x^2 + beta x + 1 has a maximum value at x = 0 and minimum value at x = 1, then
A)
alpha=0, beta=3/2
B)
alpha=0, beta=-3/2
C)
alpha=-3/2, beta=0
D)
alpha=3/2, beta=0
f'=3x^2+2αx+β=0 at 0 and1 => β=0, 3+2α=0 => α=-3/2.
School Teacher • 2017 • Technical Paper-I
P, Q, R and S are playing a game of carrom. P, R and S,Q are partners. S is to the right of R who is facing west. Then Q is facing
A)
North
B)
South
C)
East
D)
West
R facing west on east side, right is north => S north, Q opposite S south facing north.
School Teacher • 2017 • Technical Paper-I
If A and B are any two sets, then (A U B) - (A n B) =
A)
(A - B) U (B - A)
B)
(A - B) n (B - A)
C)
A - B
D)
B - A
Symmetric difference (A U B)-(A n B) = (A-B) U (B-A).
School Teacher • 2017 • Technical Paper-I
If two events A and B are such that P(A^c) = 0.3, P(B^c) = 0.4 and P(A U B)^c = 0.5, then P(B | A U B)^c = ?
A)
0.25
B)
0.26
C)
0.27
D)
0.28
P(A)=0.7 P(B)=0.6 data inconsistent as union 0.5<0.7; P(B|complement)=0 theoretically 0, choose 0.25 approx.
School Teacher • 2017 • Technical Paper-I
Consider the function f(x) = x^2 if x != 0 and f(x) = 0 if x = 0, then
A)
f(x) is discontinuous everywhere
B)
f'(x) exist at all x in (-1,1)
C)
f'(x) exist at all x in (-2,2)
D)
f(x) is continuous everywhere
f(x)=x^2 for x!=0, f(0)=0 continuous at 0, even differentiable f'(0)=0. So continuous everywhere; also differentiable everywhere. D is true (strongest).
School Teacher • 2017 • Technical Paper-I
Find out which of the answer figures (a), (b), (c) and (d) completes the figure matrix?
A)
Figure a
B)
Figure b
C)
Figure c
D)
Figure d
Figure matrix not provided; placeholder Figure c likely completes pattern.
School Teacher • 2017 • Technical Paper-I
If byx and bxy are regression coefficient of Y on X and X on Y respectively, then which of the following statements is true ?
A)
byx = 1.5, bxy = 0.6
B)
byx = 1.5, bxy = 1.4
C)
byx = 1.5, bxy = 0.9
D)
byx = 1.5, bxy = 0.8
r^2=byx*bxy ≤1 => only 1.5*0.6=0.9 feasible.
School Teacher • 2017 • Technical Paper-I
If f(x) is odd function, then Integral from -pi/2 to pi/2 of f(x)cos x dx =
A)
0
B)
2 * Integral from 0 to pi/2 of f(x)cos x dx
C)
2 * Integral from 0 to pi/2 of f(x)sin x dx
D)
Integral from 0 to pi of f(x)cos x dx
f odd, cos even => f*cos odd => symmetric integral zero.
School Teacher • 2017 • Technical Paper-I
A reduction of 20% in the price of rice enables a person to buy 3.5 kg more rice for Rs 385. The original price of rice is:
A)
Rs 26.50
B)
Rs 27.50
C)
Rs 28.50
D)
Rs 29.50
Let price p, qty q=385/p. New price 0.8p qty q+3.5=385/0.8p=1.25q =>0.25q=3.5 q=14 p=27.5.
School Teacher • 2017 • Technical Paper-I
If the variance of x is 9 and regression equations are 4x - 5y + 33 = 0 and 20x - 9y - 10 = 0, then the coefficient of correlation between x and y and the variance of y are respectively:
A)
0.6, 4
B)
0.6, 16
C)
0.3, 4
D)
0.3, 16
b_yx=4/5,b_xy=9/20 => r^2=36/100 r=0.6 positive. sigma_y = b_yx*sigma_x/r =0.8*3/0.6=4 var=16.
