For the given compound X, the total number of optically active stereoisomers is ____.
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of nm is ____
Let fprime(x)=2+sin4πx192x3forallx∈Rwithf(21)=0.Ifm≤∫211f(x)dx≤M, then the possible values of mandM are (a)m=13,M=24 (b) m=41,M=21(c)m=−11,M=0 (d) m=1,M=12
The coefficients of three consecutive terms of (1+x)n+5are in the ratio 5:10:14. Then n=___________.
In a triangle PQR, P is the largest angle and cosP=31. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)
The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?
Suppose that p,qandr are three non-coplanar vectors in R3. Let the components of a vector s along p,qandr be 4, 3 and 5, respectively. If the components of this vector s along (−p+q+r),(p−q+r)and(−p−q+r) are x, y and z, respectively, then the value of 2x+y+z is
Three randomly chosen nonnegative integers x,yandzare found to satisfy the equation x+y+z=10.Then the probability that zis even, is:125 (b) 21 (c) 116 (d) 5536