Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4×4 matrix given in the ORS.
Let u^=u1i^+u2j^+u3k^ be a unit vector in be a unit vector in R3andw^=61(i^+j^+2k^).Given that there exists vector v^ in R3 such that ∣u^×v∣=1andw^.(u^×v)=1. Which of the following statement(s) is(are) correct?
A solution curve of the differential equation (x2+xy+4x+2y+4)(dxdy)−y2=0 passes through the point (1,3) Then the solution curve is
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 [x] be the greatest integer less than or equal to x˙ Then, at which of the following point (s) function f(x)=xcos(π(x+[x])) is discontinuous? (a)x=1 (b) x=−1 (c) x=0 (d) x=2
Let F(x)=∫xx2+6π[2cos2t.dt] for all x∈R and f:[0,21]→[0,∞) be a continuous function.For a∈[0,21], if F'(a)+2 is the area of the region bounded by x=0,y=0,y=f(x) and x=a, then f(0) is
Let XandYbe two arbitrary, 3×3, non-zero, skew-symmetric matrices and Zbe an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?a.Y3Z4Z4Y3b. x44+Y44c. X4Z3−Z3X4d. X23+Y23
Ifα=∫01(e9x+3tan(−1)x)(1+x212+9x2)dxwherηn−1takes only principal values, then the value of ((log)e∣1+α∣−43π)is