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Prove that among the +ve numbers a,2a,3a,...,(n-1)a, there is one that differs by an integer by at most 1/n ...

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 ...

0∫∞ 1/(1+xn)n = 1 find n . ...

Let p(x) = x2+ax+b be a quadratic polynomial. 'a' and 'b' belongs to integers. Prove that for any integer 'n' ,there is some 'm' such that P(n)P(n+1) = P(m) Does this question have any good solution? one can show that m = an ...

is f(x)=x+sinx a strictly increasing or only increasing function ...

Nishant , why do u hate engineering? ...

∫(1+sinx)/(1+cosx)ex/2dx ...

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 ...

$\textbf{Determine all function $\mathbf{f:\mathbb{R}\rightarrow\mathbb{R}}$ such that\\\\ $\mathbf{f(x+y)f(x-y)=\left(f(x)+f(y)\right)^2-4x^2f(y)}$,each x,y\in \mathbb{R}$}\\ I have got a quadratic expression. ...

A sample of wusite Fe.93O1.00..find the % of Fe(III)in the sample... ...

1. A bulb is placed at a depth of 2 7 m in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. What is the minimum diameter of the disc? 2. A fish rising vertically to th ...

Q- lim [ -2x/tanx ] x→ 0 where [.]=greatest integer function. why isn't the answer -3 ??? ans given is -2 i'm confused at this...... as x→0 tanx/x →1 so x→0 x/tanx →1+ but buk says as x→0 x/tanx < 1 ...

a stone is thrown horizontally with velocity of 10 m/s. the radius of curvature at the end of 3 seconds is ??? ...

Can anyone tell me what is the Content Management System(CMS) of this site. ...

We know that a energy of a electron shell is given by E= 2pi2z2e4m/n2h2 But then according to aufbau principal lower the shell number lower is the energy but according to formula e is inversely proportional to n2??? ...

*Image* The equivalent resistance between P and Q is ...

1. If p,q,r are real nos. a. max(p,q)<max(p,q,r) b. min(p,q)=1/2{p+q-mod(p-q)}....mod stands for modulus c. max(p,q)<min(p,q,r) d. none of the above 2.f(x)= cos(x) +cos(√2x) ['x' is not within root] Find the no. of va ...

A particle is moving along x - axis whose acceleration is given by a = 3 x - 4 , where x is the location of the particle. At t = 0, the particle is at rest at x = 4/3. Find the distance travelled by the particle in 5 s. ...

f(x)=x2,find {f(1.1)-f(1)}/(1.1-1) ...

i came across a statement in ncert: "Since N is the smallest subset of R which is an inductive set,it follows that any subset of R that is an inductive set must contain N" could somebody plz elaborate what this means? ...

Let \, \, y= f(x)\, \, \textrm{be continous ,positive,and increasing over the interval [a,b] } Show \,\, that\, \,\rightarrow \boxed{\, \, \int_{a}^{b}f(x)dx+\int_{f(a)}^{f(b)}f^{-1}(y)dy=bf(b)-af(a)} ...

Can anyone tell my mistake i am making in the general solution of following equation; I am getting different answers. Solve - 4sin2x + 3cos 2x = 5 My answer- 4(2sinxcosx) + 3 ( 2cos2x - 1) = 5 → 8 sinx cosx + 6 cos2x = 8 ↠...

A dumb bell consists of a light rod of length ' r ' and two small masses ' m ' attached to it. The dumb bell stands vertically in the corner formed by two frictionless surfaces. After the bottom end is moved slight towards ri ...

*Image* calculate the equivalent resistance across A B of this infinitely long ladder ...

If S=.99999999.......∞ then 10S=9.9999999.....∞ then 9S=9 then S=1 ????? ...

1.\lim_{x\rightarrow \infty} \frac{\left(\ln x \right)^{2}}{x} NOTE: Without L' Hospital Rule 2.\lim_{x\rightarrow \infty} \left(1+\frac{1}{x} +\frac{1}{x^{2}}\right)^{2x} 3.\lim_{x\rightarrow 1} \left(\frac{x}{x-1} -\frac{1} ...

can some one help me in drawing equivalent circuit (with some explaination pls) in these type of questions.. *Image* ...

in which case condensation is favoured? a) CH3NO2+CH3CHO B) CH3CHO+CH3CH2CHO C) CH3CHO+C6H5CHO D) CH3COCH3+CH3CHO With explanation! please answer if sure ...

*Image* *Image* *Image* ...

1. *Image* Unlike other aromatic amines, why is this amine strongly basic? 2. Compare the dipole moments of the following compounds: *Image* 3. What is the major elimination product? *Image* 4.Identify the bond which will und ...