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For x belongs to G , define H _x = { g^(-1) x g | g belongs to G } . Under what condition on x will H_x <= G ? Further, if H _x <= G , will H _x ∆= G ? Give reason for your answer
State the following statement are True? 1. If G = <x> is of order 25 , then x^(alpha) generates G , where alpha is a factor of 25
Find the roots of the equation 2x^3 - x^2 - 22x - 24 = 0 .if two of them are in the ratio 3:4 .
Let x_i belongs to R such that 0 < x_1<= x_2 <= ...<= x_n , n>= 2 and (1/1+x_1)+(1/1+x_2)+...+(1/1+x_n) = 1 .Then show that √x_1 + √x_2 + ..+ √x_n >= (n-1) [( 1/√x_1)+...+(1/√x_n) .
how would the area be affected if the sides of rectangle are increased by a factor k?
A committee of three is chosen from a group of 20 people. How many different committees are possible, if
(a) the committee consists of a president, vice president, and treasurer?
(b) there is no distinction among the three members of the committee?
(a) the committee consists of a president, vice president, and treasurer?
(b) there is no distinction among the three members of the committee?
f(x,y)=5xy-ln(xy)-5,check whether there exists a continuously differentiable function g defined by f(x,y)=0 in the neighbourhood of x= 3,such that g(3)=1/3.find g'(3) if exists.
is cluster sampling sometimes always or never random?
Q. The hyperboloid of one sheet is S={(x,y,z)∈R^3 |x^2+y^2-z^2=1} show that for every θ,the straight line (x-z)cosθ=(1-y)sinθ,
(x+z)sinθ=(1+y)cosθ
Is contained in S and that every point of hyperboloid lies on one of these deduce that S can be covered by a single surface patch, and hence is a surface.
(x+z)sinθ=(1+y)cosθ
Is contained in S and that every point of hyperboloid lies on one of these deduce that S can be covered by a single surface patch, and hence is a surface.
Q. Show that the circular cylinder S={(x,y,z)∈R^3 |x^2+y^2=1} can be covered by a single surface patch and so a surface.
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#340153 on Dec 2023
#340153 on Dec 2023