‘a’ divides 228 leaving a remainder 18. The biggest twodigit value of ‘a’ is

Solution
228 = 70 × 3 + 18
Clearly, the biggest twodigit number is 70
Find the value of \(3 + \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3} + 3} + \frac{1}{\sqrt{3} – 3}\).

Solution
\(3 + frac{1}{sqrt{3}} + frac{1}{sqrt{3} + 3} + frac{1}{sqrt{3}  3}\)
= \(3 + frac{1}{sqrt{3}} + left (frac{sqrt{3}  3 + sqrt{3} + 3}{left (sqrt{3} + 3 right )left (sqrt{3}  3 right )} right )\)
= \(3 + frac{1}{sqrt{3}} + frac{2sqrt{3}}{3  9}\)
= \(3 + frac{1}{sqrt{3}}  frac{sqrt{3}}{3}\)
= \(3 + frac{1}{sqrt{3}}  frac{1}{sqrt{3}} = 3\)
Electrostatic precipitator is used to control
Which of the following contains high content of lead?
Which of the toxic heavy metals is found in modern tannery industries?
Uranium eventually decays into a stable isotope of
Glass is a
Rusting of iron requires
Xrays were discovered by
A parallel port is most often used by a
A new technology which provides the ability to create an artificial world and have people interact with it is called
Birds which swim in water have
Directions : From the given alternative words, select the word which can be formed using the letters of the given word.
MANUFACTURE
From the given alternative words, select the word which cannot be formed using the letters of the given word:
REFORMATION

Solution
There is no C in the given word.
A and B are standing at a distance of 20 km from each other on a straight EastWest road. A and B start walking simultaneously eastwards and westwards respectively and both cover a distance of 5 km. Then A turns to his left and walks 10 km. B turns to his right and walks 10 km at the same speed. Then both turn to their left and cover a distance of 5 km at the same speed. What will be the distance between them?

Solution
A = 20km
GH = (5 + 5) = 10 km
The value of (X+Y+Z)^{3} – (y+ZX )^{3} – (Z+Xy)^{3} – (X+yZ)^{3} is

Solution
If x = y = z = 1, then expression
= (3)^{3} (1)^{3} (1)^{3} (1)^{3}
= 27  3 = 24 = 24 xyz
94 is divided into two parts in such a way that the fifth part of the first and the eight part of the second are in the ratio 3 : 4. The first part is

Solution
Let the first part be x and the second part be
(94 x).
Now; according to the question,\(frac{frac{x}{5}}{frac{94x}{8}}=frac{3}{4}\)
\(frac{x}{5}times frac{8}{(94x)}=frac{3}{4}Rightarrow 32x = 15 times 94  15x\)
\(Rightarrow 47x = 15 times 94 Leftrightarrow x =frac{15times 94}{47}= 30\)
If the population of a town is 64000 and its annual increase is 10%, then its correct population at the end of 3 years will be

Solution
Population of town =\(pleft ( 1+frac{R}{100} right )T\)
\(=64000left ( 1+frac{10}{100} right )^{3}= 64000times frac{11}{10}times frac{11}{10}times frac{11}{10}\)
= 85184
There are two temples, one on each bank of a river, just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. The length of the temple is

Solution
AB = temple = 54 metres
CD = temple = h metres
BC = width of river = x metres
From ΔABC,\(tan60^{circ}=frac{AB}{BC}\)
\(Rightarrow sqrt{3}=frac{AB}{BC}Rightarrow x=frac{54}{sqrt{3}}: metres\)
From ΔADE, tan 30° =\(frac{AE}{BD}\)
\(Rightarrow frac{1}{sqrt{3}}=frac{54h}{18sqrt{3}}\)
⇒ 54  h= 18
⇒ h = (54  8 =) 36 metres
Which of the following can be used for biological control of mosquitoes?

Solution
Biological control is the USE of natural enemies to manage the mosquito population.Effective biocontrol agents include predatory fish that feed on mosquito larvae such as Gambusia affinis (mosquitofish) and some cyprinids (Carps and minnows).