IJSO Solutions 18-10-10

ISJO QUESTION WITHANSWER (18-10-10)

1.

Through a point on the hypotenuse of a right triangle, triangle , lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area a rea of the square. The ratio rat io of the area of the other small sm all right triangle to the area of the square is (A*)

Sol.

1 4m

(B)

1 2m  1

(C) m

(D)

1 8m2

A y D

E

a

a

a B

a

F

x

C

arEFC = m(a2) 1 × a × x = ma 2 2 x = 2am ADE ~ ABC y

a = ya a  2am

ya y =1+2m a 1+y =1+2m y=

a 2m

1 a a 2m = 1 Req. ratio  2 4m a2 2.

A ray of light falls on a prism having one silvered surface, at an incident angle of 45º as shown in figure. After refraction and reflection it retraces the path, then the refractive index of prism m aterial is (prism angle is 30º) :  /                 /                 /                 /                 /                 /                º /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                º  /                 /                 /                 /                 /                 /               

30

45º

(A*) Sol.

(B) 2 

2

90

(C)

1 2

Light retraces its path so QR ray falls normally on the side AC so,

AQR = 60º

(i.e. mirror)

(D) (D)

1 2

 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /                 /               

Hence r = 30º

Given i = 45º From snell s law : ’

=

3.

sin i sin 45 º 1 2     2 sin r sin 30 º 2 1

The highly unreactive metal gold can be dissolved in

Sol.

(A) Conc. H2SO4.

(B) Conc. HNO3.

(C) Conc. HCl.

(D*) aqua-regia.

Aqua-regia has maximum dissolving capacity and can dissolve almost everything. everything.

4.

Double fertilization is fusion of (A) Two eggs (B) Two eggs and polar nuclei with pollen nuclei (C) one male gamete game te with egg and other with synergid (D*) One male gamete with egg and other with secondary nucleus.