Electrons with de- Broglie wavelength λ fall on the target in an X -ray tube. The cut- off wavelength of the emitted X-rays is
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)=
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)If a tangent to a suitable conic (Column 1) is found to be y=x+8and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)
Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that x1+x2+x3 is odd isThe probability that x1,x2,x3 are in an aritmetic progression is
In R', consider the planes P1,y=0 and P2:x+z=1. Let P3, be a plane, different from P1, and P2, which passes through the intersection of P1, and P2. If the distance of the point (0,1,0) from P3, is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relation is (are) true ?
A line l passing through the origin is perpendicular to the lines l1:(3+t)i^+(−1+2t)j^+(4+2t)k^,∞<t<∞,l2:(3+s)i^+(3+2s)j^+(2+s)k^,∞<t<∞ then the coordinates of the point on l2 at a distance of 17 from the point of intersection of
The coefficients of three consecutive terms of (1+x)n+5are in the ratio 5:10:14. Then n=___________.
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.264 b. 265 c. 53 d. 67