Parallel rays of light of intensity I=912Wm−2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan - Boltzmann constant σ=5.7×10−8Wm−2K−4 and assume that the energy exchange with the surroundingsis only through radiation. The final steady state temperature of the black body is close to .
If a chord, which is not a tangent of the parabola y2=16xhas the equation 2x+y=p,and midpoint (h,k),then which of the following is(are) possible values (s) of p,handk?p=−1,h=1,k=−3 p=2,h=3,k=−4 p=−2,h=2,k=−4 p=5,h=4,k=−3
Let −61<θ<−12π Suppose α1andβ1, are the roots of the equation x2−2xsecθ+1=0 and α2andβ2 are the roots of the equation x2+2xtanθ−1=0. If α1>β1 and α2>β2, then α1+β2 equals
Let Tbe the line passing through the points P(−2,7)and Q(2,−5). Let F1be the set of all pairs of circles (S1,S2)such that Tis tangent to S1at Pand tangent to S2at Q, and also such that S1and S2touch each other at a point, say, M. Let E1be the set representing the locus of Mas the pair (S1,S2)varies in F1. Let the set of all straight lines segments joining a pair of distinct points of E1and passing through the point R(1,1)be F2. Let E2be the set of the mid-points of the line segments in the set F2. Then, which of the following statement(s) is (are) TRUE?The point (−2,7)lies in E1(b) The point (54,57)does NOT lie in E2(c) The point (21,1)lies in E2(d) The point (0,23)does NOT lie in E1
Let f:R→Rbe a differentiable function with f(0)=1and satisfying the equation f(x+y)=f(x)fprime(y)+fprime(x)f(y)for all x, y∈R. Then, the value of (log)e(f(4))is _______
The total number of ways in which 5 balls of differert colours can be distributed among 3 persons so thai each person gets at least one ball is
Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, x2+y2=a, (i), my=m2x+a, (P), (m2a,m2a)II, x2+a2y2=a, (ii), y=mx+am2+1, (Q), (m2+1−ma,m2+1a)III, y2=4ax, (iii), y=mx+a2m2−1, (R), (a2m2+1−a2m,a2m2+11)IV, x2−a2y2=a2, (iv), y=mx+a2m2+1, (S), (a2m2+1−a2m,a2m2+1−1)The tangent to a suitable conic (Column 1) at (3,21)is found to be 3x+2y=4,then which of the following options is the only CORRECT combination?(IV) (iii) (S) (b) (II) (iii) (R)(II) (iv) (R) (d) (IV) (iv) (S)
The option(s) with the values of a and L that satisfy the following equation is (are) ∫0πet(sin6at+cos4at)dt∫04πet(sin6at+cos4at)dt=L