Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF5 is
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)
Let Xbe the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ,¨and Ybe the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, ¨. Then, the number of elements in the set X∪Yis _____.
Let a, b, cbe three non-zero real numbers such that the equation 3 acosx+2 bsinx=c, x∈[−2π,2π], has two distinct real roots αand βwith α+β=3π. Then, the value of abis _______.
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
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
For how many values, of p, the circle x2+y2+2x+4y−p=0and the coordinate axes have exactly three common points?
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)=