The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C4H6 is
Let f[0,1]→R (the set of all real numbers be a function.Suppose the function f is twice differentiable, f(0)=f(1)=0,and satisfies f′(x)–2f′(x)+f(x)≤ex,x∈[0,1].Which of the following is true for 0<x<1?
The coefficients of three consecutive terms of (1+x)n+5are in the ratio 5:10:14. Then n=___________.
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
Ifα=∫01(e9x+3tan(−1)x)(1+x212+9x2)dxwherηn−1takes only principal values, then the value of ((log)e∣1+α∣−43π)is
The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots
For a∈R (the set of all real numbers), a=−1),(lim)n→∞((n+1)a−1[(na+1)+(na+2)+……(na+n)]1a+2a++na=60.1Then a=(a)5 (b) 7 (c) 2−15 (d) 2−17
Let f:RRbe a differentiable function such that f(0),f(2π)=3andfprime(0)=1.If g(x)=∫x2π[fprime(t)cosect−cottcosectf(t)]dtforx(0,2π],then (lim)x0g(x)=
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 of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is