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Q) Find the maximum radius of a semi-circle that can be placed inside a square of side 'a' ...

Value of k for which 4x2+4x+1=0 has exactly one point of intersection with k-|x+(1/2)| is equal to: a) 1 b) 2 c) 3/2 d) 3/4? ...

Let P(x) = x^{6}-x^{5}-x^{3}-x^{2}-x Q(x) = x^{4}-x^{3}-x^{2}-1 If a,b,c,d are roots of q(x) then find the value of P(a)+P(b)+P(d) ? ...

\int (x^{3}-3x^{2}+2)^{2012}dx ...

Start with the set S - { 3 , 4 , 12 } . In each step , you may chose two numbers " a " and " b " from S and replace " ( . 6 a - . 8 b) " by " ( . 8 a + . 6 b ) " . Can you form a set P - { 4 , 6 , 12 } by finitely many steps ...

http://www.iapt.org.in/index.php?option=com_content&task=view&id=27&Itemid=53 see the official solutions ...

Can anyone explain reciprocal system of vectors? Its the only topic I am not understanding properly! :/ ...

This is my collection of brilliant tutorials papers. I couldnt use them to my fullest but i hope you will do and vasool my money. i m presently in nirma university, gujarat. Thanks once again to all tiitians and my friends Th ...

\int_{-10}^{10}{xe^{x[x+\frac{1}{2}]} dx} Where [.] is Floor function. ...

Please post your expected marks. mine- Physics: 140(objective)+ 0(subjective) Chemistry: 165 (as per resonance solutions) ...

*Image* What is the time period of small horizontal oscillation of the given block? ...

which is correct and why? *Image* ...

*Image* Now my doubt is, if we consider C as the origin then centre of mass comes on CD at a distance L/4 from C. i.e., F ≡ (0, L/4) But what if we consider A as the origin... *Image* In this case we get, F ≡ (L/2, L/4) C ...

I've got a problem which I am not sure of the method of solving. 3x + 36 x 2 = 37 3x + 729 x 2 = 36 x 3 3x + 1458 = 729 x 3 3x = 2187 - 1458 3x = 729 3x = (3)6 x = 6 But isnt there any other method of solving? Please help ...

Today is the birthday of theprophet sir wishing him many more happy years to come happy birthday sir ...

I have passed my 12th and wish to do IIT. And I have by now finished reading NCERT books and some of HCV. (Yes, I haven't done much of Chem. and Math yes) So, now I that I have gotten a hold of the required Syllabus, planning ...

This is a part of my initiative - Not A Doubt : A snowball is thrown against a wall . Where does its momentum go ? Where does its energy go ? Explain clearly . ...

1. A stone is dropped from top of a tower. When it crosses a point 5 m below the top , another stone is dropped from a point 25 m below the top. Both stones reach the bottom of the tower simultaneously. Find the height of the ...

How was NSEP for u guys (those who gave) ? ...

Hello, I am studying X standard. I want to write IIT-JEE (Just to test my skill level). Is being in the XII standard a requirement for writing IIT-JEE?! Thanks in advance. -Cheran ...

A typhoon originates in the Indian Ocean. Satellite imaging shows that the distance travelled by it are 105 and 95 kms in the first 2 hours after it originated. It is dangerous at speeds above 50 km/hr. Find the time for the ...

\left\{ \left( ^{n}C_{0}+^{n}C_{3}+...\right)-\frac{1}{2}\left(^{n}C_{1}+^{n}C_{2}+^{n}C_{4}+^{n}C_{5}+.... \right)\right\}^{2}+\\\frac{3}{4}\left(^{n}C_{1}-^{n}C_{2}+^{n}C_{4}-^{n}C_{5}+....\right)^{2} = ? ...

If z=log(tan\frac{x}{2}) and \frac{d^2y}{dx^2}+cotx\frac{dy}{dx}+4ycosec^{2}x =0 then show that \frac{d^2y}{dx^2}+4y=0 ...

\hspace{-16}$Prove that\\\\ $\mathbf{\binom{2n+1}{1}.\binom{2n+1}{3}.\binom{2n+1}{5}.......\binom{2n+1}{2n-1}.\binom{2n+1}{2n+1}<\left(\frac{4^n-1}{n}\right)^n} ...

\hspace{-16}\int\frac{1+\sin x}{x\cos x}dx ...

Find " m " such that (x^{2}-5x+4)^{2}+(2m+1)(x^{2}-5x+4)+3=0 has two distinct Real roots. ...

1. A projectile is fired at an angle 60â—¦ with some velocity u. If the angle is changed infinitesimally, let the corresponding fractional changes in the range and the time of flight be x and y, respectively, Then y is (A) 2/ ...

what is the usual cut-off in nsec? will 180 out of 240 be enough? ...

If h(x)= 10/x -2 find directly h-1(2) ...

find the equation to the circle which touches the y-axis at origin and passes through the point (a,b). ...