One-third of the boys and one-half of the girls of a college participated in a sport. If the number of participating students is 300, out of which 100 are boys. What is the total number of students in the college?

Number between 0 and 11 which are multiple of 2 or 3
= 11/2 + 11/3 - 11/6 = 5 + 3 - 1
= 7

Number between 0 and -11 which are multiple of 2 or 3
= 11/2 + 11/3 - 11/6 = 5 + 3 - 1
= 7

? Number be 15, including 0

Let the number be x.
44² < x < 45²
? 1936 < x < 2025 ...(i)

From equation (i), the required number will be any number between 1936 and 2025. Since one part of the number is the square of 6 means one factor is 36.

? L, C, M of 36 and 5 = 180
? Number will be multiple of 180 i,e.,
180 x 11 = 1980 the only value which satisfies the equation (i).

If A run 1000 meters then B runs 900 meters and C runs 800 meters.
? B runs 1350 meters while C will run 800 * 1350/ 900 = 1200 meters

Hence, B can beat C by (1350 ? 1200) = 150 m

S = {HH, HT, TT, TH}
and E = {HH, HT, TH }
? P(E) = n(E)/n(S) = 3/4

Exp. = 25 log₅4 = 5² log₅4
= 5 log₅ 4²
= 16

Area of square = 64 sq cm
(Side)² = 64
? Side = ?64 = 8 cm


According to the question,
? 2?r = 4 x 8
? r = (4 x 8)/2?
? r = 16/?

? Area of the circle
= ? x (16/?) x (16/?) sq cm
= 256/? sq cm.

? 5^5-x = 2^x-5
? 5^5-x = 2^-(5-x)
? (5-x)log 5 = -(5-x)log 2
? (5-x)log 5 + (5-x)log 2 = 0
? (5-x){log 5 + log 2 } = 0
? (5-x){log10/2 + log 2 } = 0
? (5-x){log10 - log 2 + log 2} = 0
? 5-x = 0
? x = 5

The HCF of m and n is 1, so m and n are prime number.
Let m = 7 and n = 5 ? m + n = 12
HCF of(m + n)and m = HCF of 12 and 7 = 1
Similarly, HCF of (m - n) and n = 1