Begin to Be Now What You Will Be Here After

D.A.V. CENTENARY PUBLIC SCHOOL, ROHTAK HOLIDAYS HOME WORK (2011-12)
CLASS - XI : SUBJECT - MATHS
* ** Do all questions of Assignment-1. Revise Chapter 'Sets', 'Complex Number and Quadratic Equation' and 'Straight lines' from N.C.E.R.T. Book and Elements of Mathematics for Class XI. Assignment No. 1 (Ch. 1,5,10) Write in roster form G = {x : x2=9, xEZ} What is a Power Set ? Write the Power set of A = {5,0,7} Distinguish between equivalent and equal sets. Explain by taking examples. If A and B are two sets, then prove that A-B=A if and only if A∩B=φ Prove that in + in+1 + in+2 + in+3 = 0, nEN. If Z = x+ iy and 2 =a+ib and a,b,x,y are real, then show that 2x2=√a2+b2+a z 3+2 i Sinθ Find real θ such that is (i) real (ii) Purely imaginary. 1–2 i Sinθ If a2+b2=1, then show that x will have a real value which satisfies the relation 1– i x = a–ib. 1+ i x (a2+i)2 (a+i)2 If x + i y = then prove that x2+y2 = 4a2+1 2a–i Evaluate x4+4x3+6x2+4x+9 if x = –1+√–2 Solve the quadratic equation 2x2 – (3+7i)x + 9i-3=0. 1+i Find the modulus and argument of 1-i What is the slope of the line perpendicular to the line 3x+4y–11=0. For what value of a, the lines ax+3y=7 and 3x–4y=11 are perpendicular Find the disance between the lines y=mx+c and y=mx+d. Find the values of a and b so that the equations 8x–9y–16=0 and bx+3y–4=0 are dependent. Find the length of perpendicular segment from the origin to the line x–√3y–4=0. Find the equation fo a line through the point (-4, -3) and parallel to the line 3x–5y+11=0. Find the length of the perpendicular and the coordinates of the foot of the perpendicular from the point (-3, -5) on the line x+y+6=0. If a,b,c are in A.P. then show that ax+2y+1=0 and bx+3y+1=0 and cx+4y+1=0 are concurrent. Find a point on the line x+2y=3, whose distance from the line 3x+4y=2 is 2 units. Find the coordinates of points at unit distance from the lines 3x–4y+1=0 and 8x+6y+1=0. Find the distance of the point (2,3) from he line 2x-3y+9=0 measured along a line which makes...