Class 11th

If the variance of the terms in an increasing A.P. b?,b?,b?,.,b? is 90, then the common difference of this A.P. is 

The set of all possible values of θ in the interval (0,π) for which the points (1,2) and (sinθ,cosθ) lie on the same side of the line x+y=1 is

Let f:R→R be a function which satisfies f(x+y)=f(x)+f(y) ∀x,y∈R. If f(1)=2 and g(n)=Σ?f(k), n∈N, then the value of n for which g(n)=20 is

A heat engine is involved with exchange of heat of 1915 J, –40 J, +125 J and –QJ, during one cycle achieving and efficiency of 50.0%. The value of Q is:

The area (in sq. units) of an equilateral triangle inscribed in the parabola y²=8x, with one of its vertices on the vertex of this parabola, is

The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?
(a) The force is zero at t = 3T/4
(b) The acceleration is maximum at t = T
(c) The speed is maximum at t = T/4
(d) The P.E. is equal to K.E. of the oscillation at t = T/2

A 10μF capacitor is fully charged to a potential difference of 50 V. After removing the source voltage, it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is: