Recently Active Mathematics Questions

$If $\mathbf{a,b,c\in \mathbb{R^{+}}}$.Then prove that \\\\ $\mathbf{\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq 3.\left(\frac{a^2+b^2+c^2}{ab+bc+ca}\right)^{\frac{2}{3}}}$\\\\ ...

Let f(x) be a funcn. differentiable on [ 0 , a ] such that f(0) = 1 , f(a) = 31/6 . If f'(x) is greater than equal to [f(x)]4 + [f(x)]-2 , then the max. value of a is: (a) pi/6 (b) pi/12 (c) pi/24 (d) pi/36 ...

draw the graph of y=ax-(1/(bx)) where x=1/√(ab). ...

Which of these definitions is correct. ML khanna says a square matrix is called nilpotent matrix if Ak=O,where 'k' is a positive integer,smallest value of k is called index of nilpotent matrix SK goyal in Arihant algebra says ...

hello,im getting an old Arihant Integral Calculus of Amit M Agarwal for 70rs only :D should i buy it ,but its of 2002 edition! ...

The following Question is of Assertion and Reason type. Select the correct choice from the following options. Statement 1: The probability for the graph of 16x2 + 8(a+5)x -7 a - 5 in the interval is strictly above the x-axis ...

The probability that two integers chosen at random and their product will have the same last digit is? ...

I was going through Play with graphs. There the graph of \sin^{-1} sinx is given . Though the graph happens to be okay. I got one problem. IT SUGGESTS students to learn defination of it like x+2Î ; -5Î /2<= x<= -3Î /2 - ...

Let f(x) = x2 − 2x. How many distinct real numbers "c" satisfy f(f(f(f(c)))) = 3? ...

so i recently bought Arihant Algebra by SK goyal as many people recommended it as best book for algebra. I started doing matrices from it & what i find is,it has lot of mistakes in theory. Havent done any problem yet so cant ...

is 2.222...........= 10*(0.2222........) because 2.2222.... contains some infinite digits and 0.222.... contains another infinite digits also so, some infinite value = another infinite value ...

Integrate {0 to π} [cotx ]dx , where [ . ] denotes the greatest integer function, is equal to? ...

In an A.P. the fourth and the seventh terms are 17 and 23 respectively. Now find 'd' and 'a'. ...

Is 0 = 0? ...

if a continous function satisfies F(F(x))=1/F(x) and F(1000)=999, Find F(500) ...

Q-> 7+2 10 = A + B Find the value of A+B ...

*Image* i believe that answer is not given in options....all options are wrong i mean..or did they mean that "positive real number" rather than "real numbers"? ...

F(x) = (x3 + 3x - 14)(x2 + 3x - 10) , has a local maxima at ?? ...

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1. f(a-x) = f(a+x) and f(b-x) = f(b+x) for all Real x, where a and b are constants and a>b, then find the period. ?? My Ans: ?? I found 2(a-b), but a sir is saying it's not correct! ...

if a+b+c>0 is it possible to have (a-b)2+(b-c)2+(c-a)2 =0?if yes when? ...

for a function f(x) satisying f(0)=1,f'(0)=-1,f(x)>0 for all x,what can we say regarding f''(x) ...

12+22+32+..........+20032=2003*4007*334 1*2003+2.2002+3*2001+..........+2003*1=2003*334*x what is x? ...

1. \lim_{x\rightarrow 0^{-}} \frac{\sum_{r =1}^{2n+1}{[x^{r}]+(n+1)}}{1+[x]+|x|+2x} 2. \lim_{x\rightarrow 0} \left\{\lim_{n\rightarrow \infty } \left(\frac{[1 (sinx)^{x}]+[2^{2}(sinx)^{x}] + .....}{n^{3}} \right) \right\} ...

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for natural number n find Left Hand Derivative of f(x)=1-tannx ...

Evaluate the following expression : - *Image* ...