At what time, in minutes, between `3\ o^(prime)c loc k` and `4\ o^(prime)c loc k` , both the needles will coincide each other? `5 1/(11)^"p a s t` (b) `12 4/(11)^"\ p a s t` (c) `13 4/(11)^"\ p a s t` (d) `16 4/(11)^"\ p a s t`

At what time, (in minutes) between 3 O' clock and 4 O'clock both the needles will coincide with each other ?

At what time between 9 and 10 o^(prime)c loc k will the hands of a watch be together? (a) 45 min. past 9 (b) 50 min. past 9 (c) 49 1/(11) m indotp a s t 9 (d) 48 2/(11) m indotp a s t 9

At what time between 4 and 5 o^(prime)c loc k will the hands of a watch point in opposite directions? (a) 45 min. past 4 (b) 40 min. past 4 (c) 50 4/(11) m indotp a s t 4 (d) 54 6/(11) m indotp a s t 4

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o^(prime)c loc k , the true time is 59 7/(12) m indotp a s t 3 (b) 4 p.m. 58 7/(11)m indotp a s t 3 (d) 2 3/(11) m indotp a s t 4

At what time between 5.30 and 6 will the hands of a clock be at right angles? 43 5/(11) m indotp a s t 5 (b) 43 7/(11) m indotp a s t 5 (c) 40 min. past 5 (d) 45 min. past 5

Let P be the set of prime numbers and let S={t|2^(t)-1 is a prime }. Prove that S sub P.

Which of the following numbers are twin primes? 3,5 (b) 5,11 (c) 3,11 (d) 13,17

lf r, s, t are prime numbers and p, q are the positive integers such that their LCM of p,q is r^2 t^4 s^2, then the numbers of ordered pair of (p, q) is (A) 252 (B) 254 (C) 225 (D) 224

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s