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if x be real,prove that x^2 -2xcosA +1 x^2 -2xcosB +1 lies between sin^2(A/2)/sin^2(B/2) AND cos^2(A/2)/cos^2(B/2). ...
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The minimum are of triangle formed by any tangent to ellipse x2/a + y2/b =1 with the coordinate axes is : ...
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If we want to find out the the equation of the angle bisector of one of the angles of a triangle, how do we find out which sign(+/-) to take? Sir had told this in class but I can't remember now. ...
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A right angled triangle ABC having right angle at C.Ca=b and CB=a moves such that the angular points A and B slide along x-axis and y-axis respectively.Find the locus of C. ...
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\hspace{-16}$Let $\bf{(a,b,c)}$ be the real solution of the System of equations\\\\ $\bf{x^3-xyz=2}$\\\\ $\bf{y^3-xyz=6}$\\\\ $\bf{z^3-xyz=20}$\\\\ Then Greatest Possible value of $\bf{x^3+y^3+z^3}$ edited. ...
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\hspace{-16}\bf{(1)\;\; \mathbb{F}}$ind $\mathbb{L}$ast $\bf{2}$ Digit of $\bf{7^{7^{7^{7}}}}$\\\\\\ $\bf{(2)\;\; \mathbb{F}}$ind $\mathbb{R}$emainder When $\bf{2222^{5555}+5555^{2222}}$ is Divided by $\bf{7}$. ...
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Guys, how much are you scoring in IITJEE 2012 ? (the marks are available in respective iitjee websites from 5th May to 10th May 2012, check urs and post here ur marks ) ...
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how ∞/∞ indeterminate?? ...
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\hspace{-16}$If each side of Square $\mathbf{OABC}$ is $\mathbf{4}\;$unit\\\\ and There are $\mathbf{4}$ Quarter Circle Center at Corrosponding Vertex\\\\ Then Find Area of Region denoted by $\mathbf{\bold{\alpha}}$ and $\mat ...
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\hspace{-16}\mathbf{\int\frac{x.\sin^2 x}{\cos (2x).\cos^2 x}dx} ...
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1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...
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1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...
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1)Find the number of isosceles triangles with integer sides if no side exceeds 1994. ...
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\hspace{-16}\mathbf{\int\frac{x.\sin^2 x}{\cos (2x).\cos^2 x}dx} ...
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1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...
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nishant sir could you please provide some link or source from where we can study geometry which helps solve coordinate . ...
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In presence of external magnetic field d-orbitals are a)3-fold degenerate b)5-fold degenerate c)7-fold degenerate d)non-degenerate e)none of these answer in the key was (d) or (e) ..(i don't remember!!!) why is the answer not ...
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\hspace{-16}\mathbf{(1)::\int\frac{1}{x+\sqrt{x^2+x+1}}dx}\\\\\\ \mathbf{(2)::\int\frac{x^{2001}}{(1+x^2)^{1002}}dx}\\\\\\ \mathbf{(3)::\int\frac{x^3-x}{x^6+4x^4+4x^2+1}dx} ...
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In wolfram i read that 1 is a special case: It is neither prime nor composite. The fundamental theorem of arithmetic fails if we consider 1 to be a prime. But somewhere else i read that 1 is a prime. So, what's the truth? PS- ...
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Let f be twice differentiable in [0,2]. show that if f(0)=0,f(1)=2, f(2)=4, then there is an 'x' in (0,2) such that f''(x)=0 ...
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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 ...
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What is the nth term of 1,2,3,6,24,108 ......? ...
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If x,y,p satisfy x2+y2=p where p is a prime (4k+1) Then prove that the above equation has one and only one solution in Z ...
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If x,y,p satisfy x2+y2=p where p is a prime (4k+1) Then prove that the above equation has one and only one solution in Z ...
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1.Prove that the number between a pair of twin prime numbers is always divisible by 2. Twin prime numbers are prime numbers whose difference is 2. ...
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Dear friends The contest session of IMO 2011 starts tomorrow Lets root for our team. You can check them out http://official.imo2011.nl/year_reg_team.aspx?year=2011&code=IND. Its great to see a girl member, Mrudul Thatte on th ...
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1.Prove that the number between a pair of twin prime numbers is always divisible by 2. Twin prime numbers are prime numbers whose difference is 2. ...
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1 . What is a " convex " function ? 2 . Prove that " y = x 2 " is a convex function . 3 . Out of 15 persons , 6 are girls while 9 are boys . We want the boys to form a line with increasing heights , and also the girls , but t ...
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Let " x " and " y " be positive integers such that " xy " divides " x 2 + y 2 + 1 " . Prove that - x 2 + y 2 + 1/xy = 3 . I will add some more if I see that people are taking interest in this . ...
