The greatest number of four digits which when divided by 3, 5, 7, 9 leaves remainders 1, 3, 5, 7 respectively is

Solution
The difference between divisor and the corresponding remainder is equal.
LCM of 3, 5,7 and 9 = 315
Largest 4digit number = 9999
315)9999(31\(underline{945}\)
549
\(underline{315}\)
234
∴ Number divisible by 315 = 9999234 = 9765
Required number = 9765  2 = 9763
The radii of two circles are 5cm and 12cm. The area of a third circle is equal to the sum of the areas of the two circles. The radius of the third circle is

Solution
πr^{2} = π × 5^{2} + π × 12^{2}
⇒ r^{2} = 25 + 144 = 169 ⇔r=\(sqrt{169}\)= 13cm
Pis thrice as good a workman as Q and therefore became able to finish a job in 48 days less. than Q. Working together, they can do it in

Solution
Time taken by P = x days
∴ Time taken by Q = 3x days
Now, according to the question,
3x  x = 48 ⇒ x = 24
∴ Q willfinish the work in 3x days
= (3 x 24 =) 72 days
∴(P + Q)'s 1 day's work\(=frac{1}{24}+frac{1}{27}=frac{3+1}{72}=frac{1}{18}\)
∴ Required time = 18 days
If a^{3} – b^{3}= 56 and a – b = 2, then value of a^{2} + b^{2} will be

Solution
a^{3} b^{3} = 56
⇒ (a b) (a^{2} + ab + b^{2}) = 56
⇒ a^{2} + ab + b^{2} = 28 ⇔(a  b)^{2}+ 3ab = 28
⇒ 4 + 3ab = 28 ⇔3ab = 28  4 = 24
⇒ab=8
∴ a^{2}+b^{2}(ab)^{2}+2ab=4+ 16=20
Two candidates contested in an election. One got 60% of the votes and won by 1600 votes. What is the number of votes polled ?

Solution
If the number of votes polled be x, then
\(frac{xtimes 20}{100}=1600\)
\(Rightarrow x=frac{1600 times 100}{20}=8000\)
India has the monopoly in the International market in the supply of
The sea which existed in the place of the Himalayas was
Which of the following is not the “Tri Ratna” of Jainism?
Who proposed the Preamble before the drafting committee of the Constitution?
“Not to destroy the Government property” is a