B.Sc.B.Ed. 1st Semester Maths Exam 2021-22 (PDF)

Roll No. Total No. of Questions: 5] [Total No.of Printed Pages : 4 RA-19 B.Sc.B.Ed. - I Semester Examination, 2021-22 Mathematics (1.1 Algebra Trigonometry & Vector Analysis) Time: 3 Hours)...

Roll No. Total No. of Questions: 5] [Total No.of Printed Pages : 4 RA-19 B.Sc.B.Ed. - I Semester Examination, 2021-22 Mathematics (1.1 Algebra Trigonometry & Vector Analysis) Time: 3 Hours) [Maximum Marks :30 Note: -Al questions carry equal marks. Attempt any two parts from each questions. 1, (A) Find the rank of the following matrices RA-19 (1) PT.O. (I)  RA-19 2. (B) (A) (C) (B) x+x-3x'-x+2=0 Find H5( 81=0 One A=-2 3 vector ofthe Determine State A=|2 12 the root |2 -13 6 and 3 |3 is equation 2x-3x$ J2+i. 0 1 the of 21 -2 matrix the proof eigen 0 -1 -1 the whose +Fiequation nd 3 0 0] (2) 5x4+ Cayley-Hamiltian values each rootsare all the 6x'-27 2x-3x+ and diminished roots. the equal x corresponding +8l=0% Sx+6x-27x+ theorem. by theto 3. roots (F eigen of A¢ RA-19 4. 3. Prove that(B) (A) (C) (B) If (A) (C) Show Resolve nearly. 4°24' Statex'-27x Solve Log(1+i)=log sin 9 sin that and the Cosech(a-ip) 1014 1013 proof'D e +following 54 1014 1013 2 1 =0 prove moivre's equation (3) +i(2t 2 that intoreal 9 +) is theorem. by the Cardon's and number imaginary ofradians method PT.O. parts. in  Logos(x -iy) cos(x-iy) = 2iTan (tan x+tany) cos(x + iy) (C) Prove that 2a cos =2a cos+2a sin 20 -2a cos 30 1-2a sin 0+a -2a sine+. 5. (A) Sum the series 1 1 sin a +-sin 2a+ -sin 3a +...... 2 22 (B) Define Gradient, Divergence and curl. (C) If yf V= Xty, +4 show that ifgy f +y'+z vV=2/N[*+y'+z] and otr VxV=0 +++ RA-19 (4) Copies 400