দুটি সংখ্যার যোগফল x & y হল 36 এবং TheirHCF এবং LCM যথাক্রমে 3 এবং 105৷ তারপর frac(1)...

The sum of two numbers x & y is 36 and Their HCF and LCM are 3 and 105 respectively. then frac(1)(x)+frac(1)(y) is equal to (A) 35 (B) frac(3)(5) (C) frac(4)(35) (D) frac(1)(35)

It is given that, y = frac(1)(x^3 -x) , If x =2, , then the value of y is (A) 6 (B) frac(1)(6) (C) frac(1)(4) (D) frac(1)(8)

Let (alpha, beta, gamma) be the foot of perpendicular from the point (1, 2, 3,) on the line frac{x 3}{5} = frac{y - 1}{2} = frac{z 4}{3} then 19 (alpha beta gamma)

Let y = y(x) be the solution of the differential equation frac{dy}{dx} = 2x (x y)^3 – x (x y) – 1, y(0) = 1 , Then (frac{1}{sqrt 2} y (frac{1}{sqrt 2}))^2 equals.

Find the LCM of the following: ( 1.) x^(3)y^(2),xyz

If the shortest distance between the lines frac{x - lambda} {-2} = frac{y - 2} {1} = frac{z - 1} {1} and frac{x - sqrt 3}{1} = frac{y-1}{-2} = frac{z-2}{1} is 1, then the sum of all possible values of lambda is :

Let O be the origin, and M and N be the points on the lines frac{x-5}{4} = frac{y-4}{1}=frac{z-5}{3} and frac{x+8}{12} = frac{y-2}{5}=frac{z+11}{9} respectively such that MN is the shortest distance between the given lines. Then vec (OM). vec (ON) is equal to _____.

Let a unit vector hat u = x hat i y hat j z hat k make angles (pi)2, (pi)/3 and (2 pi)/3 with the vectors frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat k , frac{1}{sqrt 2} hat j frac{1}{sqrt 2} hat k and frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat j respectively. If vec v = frac{1}{sqrt 2} hat i frac{1}{sqrt 2} hat j frac{1}{sqrt 2} hat k , then |hat u - vec v|^2

If R = {(x', y): x in W, Y in W and (x + 2y)^(2) = 36} then R^(-1) is__________. (a) {(0, 3), (2,3), (1,4), (0, 6)} (b) {(0,6),(0,3),(2,2), (4,1)} (c) {(3,0), (2,2), (1,4), (0,6)} (d) {(3,0), (2,2),(1,4), (6,0)}

Silver (atomic weight 108 g mol^(-1)) has a density of 10.5 g cm^(-3) . The number of silver atoms on a surfaces of area 10^(-12) m^(2) can be expressed in scientific notation as Y xx 10^(-x) , The value of x is …….