Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is
Let f:R0,1 be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? ex−∫0xf(t)sintdt (b) f(x)+∫02πf(t)sintdt(c)x−∫02π−xf(t)costdt (d) x9−f(x)
Consider the cube in the first octant with sides OP,OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0,0,0) is the origin. Let S(21,21,21) be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If p=SP,q=SQ,r=SR and t=ST then the value of ∣(p×q)×(r×(t)∣is
Let Sbe the set of all non-zero real numbers such that the quadratic equation αx2−x+α=0has two distinct real roots x1andx2satisfying the inequality ∣x1−x2∣<1.Which of the following intervals is (are) a subset (s) of S?(21,51)b. (51,0)c. (0,51)d. (51,21)
Let P and Q be distinct points on the parabola y2=2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ΔOPQ is 32 , then which of the following is (are) the coordinates of P?
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
Let ωbe a complex cube root of unity with ω=1andP=[pij]be a n×nmatrix withe pij=ωi+j˙Then p2=O,whe∩=a.57b. 55c. 58d. 56