Four numbers `n_1,n_2,n_3a n dn_4` are given as `n_1=sin15^0-cos15^0,n_2=cos93^0+sin93^0,n_3=tan27^0-cot27^0, n_4=cot127^0+tan127^0dot` `n_1<0` (b) `n_2<0` (c) `n_3<0` (d) `n_4<0`

Prove that: t a n 720^0-cos 270^0-sin 150^0cos 120^0=1/4

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

The number of real negative terms in the binomial expansion of (1+ix)^(4n-2), n in N, x gt 0 is

Eliminate theta each of the following : l_1cos theta+m_1sin theta+n_1=0,l_2cos theta+m_2sin theta+n_2=0

The number of diagonal matrix, A of order n which A^3=A is a. 1 b. 0 c. 2^n d. 3^n

For non-negative integers ma n dn a function is defined as follows: f(m ,n)={n+1ifm=0 f(m-1,1)ifm!=0,n=0 f(m-1,f(m ,n-1))ifm!=0,n!=0} Then the value of f(1,1) is a. 1 b. 12 c. 3 d. 4

Explain, given reasons, which of the following sets of quantum numbers are not possible. (1) n=0,l=0,m_(l)=0,m_(S)+(1)/(2) (2) n=1,l=0,m_(l)=0,m_(S)=-(1)/(2) (3) n=1,l=1,m_(l)=0,m_(S)=+(1)/(2) (4) n=2, l=1, m_(1)=0,m_(S)=-(1)/(2) (5) n=3, l=3, m_(l)=-3,m_(S)=+(1)/(2) (6) n=4, l=1, m_(l)=0,m_(S)=+(1)/(2) .

Prove that ^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2-=(-1)^ndot

The number of diagonal matrix, A or order n which A^3=A is a. is a a. 1 b. 0 c. 2^n d. 3^n

If x in (0,pi//2)a n dcosx=1//3 , then prove that sum_(n=0)^oo(cosn x)/(3^n)=(3(3-cosx))/(10-6cosx+cos^2x)