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Q. Two sides of a rhombus ABCD are parallel to y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at (1,2) and the vertex A is on the y axis, find the possible co-ordinates of A. My soln- let A be (0,h). Also ...
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Q what is the pH of a solution made by mixing 100 mL HCl and 200 mL aniline? Kb for aniline is 4.6 x 10^(-10) One can solve this prob after realising a buffer is formed. The ans given in the book is 4.89 which is what we get ...
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Here's the doubt When a fully charged capacitor is connected across an uncharged one, is total energy of the system of the two capacitors conserved? If no then where and how is it lost? Thanks for your replies. ...
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1. if a1 , a2 , a3 ... a7 are seven not necessarily distinct real numbers such that 1<ai<13 , prove that we can construct a triangle with its sides with length ai 2 If Nn denote the nth son square integer so that N1=2 , ...
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Let Xn be the n-th non square positive integer. Thus X1=2 , X2=3 , X3=5 , X4=6 , etc. For a positive number x, denote integer closest to it by <x> , if x = m + 0.5 where m is an integer then define <x> by m , for ...
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suppose a and b are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1 =0 are all positive real numbers. Prove that: (i) 0<3ab\le1 and (ii) b\ge \sqrt{3} ...
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i was unable to solve this one but wait till you see the solution given in the book!! if a,b,c,d are four non-negative reals and a+b+c+d=1, show that ab+bc+cd \le \frac{1}{4} ...
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prove that \sqrt{(x_1-x_2)^2+ (y_1-y_2)^2}\le \sqrt{x^2_1+y^2_1}+ \sqrt{x^2_2+y^2_2} for all real numbers x_1,y_1,x_2,y_2 HINT: proceed by forming a triangle with suitable coordinates ...
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if a+\frac{1}{a}=-1 find the value of (a^2+a+1)+(a^4+a^2+1)+(a^6+a^3+1)+(a^8+a^4+1)+...+(a^{2006}+a^{1003}+1) ...
