अनुपातों a_1/a_2,b_1/b_2 और c_1/c_2की तुलना क्र ज्ञात कीजिए कि निम्न समीकरण युग्म द्वारा निरूपित...

In direct proportion a_1/b_1 = a_2/b_2

If (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) , then the equations a_1x + b_1y + c_1 =0 and a_2x + b_2y + c_2=0 are _________. (consistent/inconsistent)

Statement-1: If the equations ax^2 + bx + c = 0 (a, b, c in R and a != 0) and 2x^2 + 7x+10=0 have a common root, then (2a+c)/b =2. Statement-2: If both roots of a_1 x^2 + b_1 x+c_1 = 0 and a_2 x^2 + b_2x + c_2 = 0 are same, then a_1/a_2=b_1/b_2=c_1/c_2. Given a_1,b_1,c_1,a_2,b_2,c_2 in R and a_1 a_2 != 0. (i) Statement I is true , Statement II is also true and Statement II is correct explanation of Statement I (ii)Statement I is true , Statement II is also true and Statement II is not correct explanation of Statement I (iii) Statement I is true , Statement II is False (iv) Statement I is False, Statement II is True

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B

Let vec a=a_1 hat i+a_2 hat j+a_2 hat k , vec b=b_1 hat i+a_2 hat j+b_2 hat k ,a n d vec c=c_1 hat i+c_2 hat j+c_2 hat k , be three non-zero vectors such that vec c is a unit vector perpendicular to both vectors vec aa n d vec b . If the angle between aa n db is pi//6, then |a_1a_2a_3b_1b_2b_3c_1c_2c_3|^2 is equal to 0 1 1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2) 3/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)(c1 2+c2 2+c3 2)

if D_1=|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and D_2=|{:(a_1+2a_2+3a_3,2a_3,5a_2),(b_1+2b_2+3b_3,2b_3, 5b_2),(c_1+2c_2 + 3c_3 , 2c_3 , 5c_2):}| then D_2/D_1 is equal to :

Let b_i > 1 for i =1, 2,....,101. Suppose log_e b_1, log_e b_2,....,log_e b_101 are in Arithmetic Progression (A.P.) with the common difference log_e 2. Suppose a_1, a_2,...,a_101 are in A.P. such that a_1 = b_1 and a_51 = b_51. If t = b_1 + b_2+.....+b_51 and s = a_1+a_2+....+a_51 then