[" Check whether "(1+m+n)" is a factor of the "],[" determinant "|[1+m,m+n,n+1],[n,1,m],[2,2,2]|" or not.Give reason."]

Check whether (l+m+n) is a factor of the determinant |{:(1+m,m+n,n+1),(" "n," "1," "m),(" "2," "2," "2):}| or not. Give reason.

Check whether (l+m+n) is a factor of the determinant |{:(1+m,m+n,n+1),(" "n," "1," "m),(" "2," "2," "2):}| or not. Give reason.

Find the value of the products: (3m-2n)(2m-3n) at m=1,n=-1

If m, n be natural numbers and (x^(2)-n) be a factor of the polynomial (ax^(2m)+bx^(2m+1)-1) , then prove that a=(1/n)^(m)andb=0 .

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

Let T_r a n dS_r be the rth term and sum up to rth term of a series, respectively. If for an odd number n ,S_n=na n dT_n=(T_n-1)/(n^2),t h e nT_m ( m being even)is 2/(1+m^2) b. (2m^2)/(1+m^2) c. ((m+1)^2)/(2+(m+1)^2) d. (2(m+1)^2)/(1+(m+1)^2)

Let T_r a n dS_r be the rth term and sum up to rth term of a series, respectively. If for an odd number n ,S_n=na n dT_n=(T_n-1)/(n^2),t h e nT_m ( m being even)is 2/(1+m^2) b. (2m^2)/(1+m^2) c. ((m+1)^2)/(2+(m+1)^2) d. (2(m+1)^2)/(1+(m+1)^2)

Let T_r a n dS_r be the rth term and sum up to rth term of a series, respectively. If for an odd number n ,S_n=na n dT_n=(T_n-1)/(n^2),t h e nT_m ( m being even)is a. 2/(1+m^2) b. (2m^2)/(1+m^2) c. ((m+1)^2)/(2+(m+1)^2) d. (2(m+1)^2)/(1+(m+1)^2)