Three rectangles `A_1,\ A_2` and `A_3` have the same area. Their lengths `a_1,\ a_2` and `a_3` respectively are such that `a_1

For a post three person A_1, A_2, A_3 appear in the interview. The probability of A_1 being selected is twice as much as that of A_2 and the probability of A_2 being selected is three times as much as that of A_3 . What are the individual probabilities of A_1, A_2, A_3 being selected?

In the figure, blocks A, B and C of mass m each have acceleration a1, a2 and a3 respectively. F_(1) and F_(2) are external forces of magnitudes 2mg and mg respectively, then :

Three distinct numbers a_1 , a_2, a_3 are in increasing G.P. a_1^2 + a_2^2 + a_3^2 = 364 and a_1 + a_2 + a_3 = 26 then the value of a_10 if a_n is the n^(th) term of the given G.P. is:

If a_1 +a_2cos 2x + a_3sin^(2)x = 0 be true for all x then a_1, a_2 and a_3 can be uniquely determined. True or False ?

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these

The average of a_1, a_2, a_3, a_4 is 16. Half of the sum of a_2, a_3, a_4 is 23. What is the value of a_1

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0fora l lx in R , then (a)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=4 hat i+2 hat j+ hat k are perpendicular to each other (b)vector vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=- hat i+ hat j+2 hat k are parallel to each other (c)vector vec a=a_1 hat i+a_2 hat j+a_3 hat k is of lengthsqrt(6) units, then one of the ordered triple (a_1, a_2, a_3)=(1,-1,-2) (d)are perpendicular to each other if 2a_1+3a_2+6a_3=26 ,t h e n|a_1 hat i+a_2 hat j+a_3 hat k|i s2sqrt(6)

If Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]| and A_1,B_1,C_1 denote the co-factors of a_1, b_1, c_1 respectively, then the value of the determinant |[A_1,B_1,C_1],[A_2,B_2,C_2],[A_3,B_3,C_3]| is-

Three vessels containing same liquid, upto the same height h, then pressure at the bottom is ( A_1 > A_2 > A_3 )