Match the crystal system/unit cells mentioned in column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4×4 matrix given in the ORS.
Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let xbe the number of such words where no letter is repeated; and let ybe the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, 9xy=
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
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
Let f1:R→R, f2:(−2π,2π)→R f3:(−1, e2π−2)→Rand f4:R→Rbe functions defined by
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)=
There are five students S1, S2, S3, S4and S5in a music class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, i=1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is403(b) 81(c) 407(d) 51
The function y=f(x) is the solution of the differential equation dxdy+x2−1xy=1−x2x4+2x in (−1,1) satisfying f(0)=0. Then ∫2323f(x)dx is