Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :
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
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
Let f:(0,∞)→R be a differentiable function such that f′(x)=2−xf(x) for all x∈(0,∞) and f(1)=1, then
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 ?
Let a and b be two unit vectors such that a.b=0 For some x,y∈R, let c=xa+yb+(a×b If (∣c∣=2 and the vector c is inclined at same angle α to both a and b then the value of 8cos2α is
If w=α+iβ,where β=0and z=1, satisfies the condition that (1−zw−wz)is a purely real, then the set of values of zis ∣z∣=1,z=2 (b) ∣z∣=1andz=1z=z (d) None of these
Let Mbe a 2×2symmetric matrix with integer entries. Then Mis invertible ifThe first column of Mis the transpose of the second row of MThe second row of Mis the transpose of the first column of MMis a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of Mis not the square of an integer