
The roots of the equation {7^{{{log }_7}}}^{({x^2}  4x + 5)} = x  1 are ...

If {a^x} = bc,{b^y} = ca,,{c^z} = ab, then xyz = ...

If {9^x}  4 imes {3^{x + 2}} + {3^5} = 0, then the solution pair is ...

If x = sqrt {7 + 4sqrt 3 } , then x + frac{1}{x} = ...

If {log _{12}}27 = a, then {log _6}16 = ...

The set of values of x which satisfy 5x + 2 < 3x + 8 and frac{{x + 2}}{{x  1}} < 4 , is ...

\hspace{16}$4 balls are to be selected from a group of 11 bolls. 5 of them are of type A,\\\\ 2 of them are type B, 2 are of type R, one of type K and one of type D.\\\\ Q.In how many ways we can arrange 4 balls out of these ...

\hspace{16}$Find real values of $\bf{x}$ in $\bf{ {5}^{1+x}+{5}^{1x}={2}^{1+x}+{2}^{1x}+{3}^{1+x}+{3}^{1x}}$ ...

In a third order determinant, each element of the first column consists of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of four terms. Then it can b ...

in how many ways can a number whose no of factors is N be divided into product of three factors... ...

suppose f:R>R is a differentiable function and f(1) = 4, then find the value of lim ∫(frm 0 to 4){ 2t/x1 dt}. x>1 ...

The value of lim (n > ∞) [sum (r varies 1 to n) {1/2r}], where [.] > G.I.F is ................ ...

Prove that f(x) = [x2]  [x]2 is discontinuous for all integral values of x except only at x = 1. ...

find domain of sin1 { x2 + 1/2x } m not able to find it... please help me...!! ...

while solving a question i got stuck here..!! (a0xn + a1x(n1) + a2x(n2) + ............... + an)(a0/xn + a1/x(n1) + a2/x(n2) + ............... + an) = (a0xn + a1x(n1) + a2x(n2) + ............... + an) + (a0/xn + a1/x(n1 ...

The inequation is (2x + 3) ( x  1) / ( x  2) ≤ 0 The critical points are 3/2 , 1 ,2 . I know how to locate them on the number line and I also know how to write the signs. But I don't know how to go about in writing the s ...

Mathematics for IITJEE 20122013: Algebra http://goo.gl/jVO7E Is it good enough? ...

If the pth, qth, rth terms of GP are a , b , c respectively prove that aqrbrpcpq = 1 How to proceed? ...

\hspace{16}$If $\bf{p(x)}$ is a Quadratic Polynomial with Real Coeff. satisfying\\\\ $\bf{x^22x+2\leq p(x)\leq 2x^24x+3\;\forall x\in \mathbb{R}}$ and $\bf{p(11)=181}$\\\\ Then $\bf{p(2012)=}$ ...

If z=(3+7i)(p+iq) where p,q E I{0}' is purely imaginary ,then minimum value of z^2 is? Ans 3364 please explain how you have solved it ...

\hspace{16}$For a $\mathbb{C}$omplex no. $\bf{z}$ find Area enclosed by the curve\\\\ $\bf{\mid z \mid+\mid z1 \mid+\mid z2 \mid+\mid z3 \mid = 4}$ ...

\hspace{16}$If $\bf{\log_{6}(30)=a}$ and $\bf{\log_{15}(24)=b}$. Then $\bf{\log_{12}(60)}$\\\\ In terms of $\bf{a}$ and $\bf{b}$ is... ...

\hspace{16}$The Set of Real no.$\bf{x}$ for which $\bf{\frac{1}{x2012}+\frac{1}{x2013}+\frac{1}{x2014}\geq 1}$ is \\\\ The Union of the form $\bf{a<x\leq b}$.\; Then What is the Length of Sum of\\\\ that Interval. ...

Let a1,a2,a3......,a10 be a permutation of the set {1,2,3......,10} such that the sequence ai decreases first and then increases like 8,6,4,1,2,3,5,7,9,10.If N is the number of such permutations,then the sum of digits of N is ...

\hspace{16}$Let $\bf{(a,b,c)}$ be the real solution of the System of equations\\\\ $\bf{x^3xyz=2}$\\\\ $\bf{y^3xyz=6}$\\\\ $\bf{z^3xyz=20}$\\\\ Then Greatest Possible value of $\bf{x^3+y^3+z^3}$ edited. ...

\hspace{16}$ Let $\bf{\omega}$ be a cube root of unity which is not equal to $1$.\\\\ Then the number of distinct elements in the set $\bf{{(1+\omega+\omega^2+\omega^3+...+\omega^n)^m}$\\\\ Where $\bf{m,n=\left\{1,2,3,...\ri ...

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\hspace{16}\mathbb{I}$f $\bf{a_{0}=0}$ and $\bf{a_{n}=3\left(a_{n1}+1\right)\forall n>1}$\\\\\\ Then Remainder when $\bf{a_{2010}}$ is Divided by $\bf{11}$ ...

came across a interesting questin...not hard but... if 60a=3 and 60b=5 find the value of 12x where x= 1ab/2(1b) ? ...

find the no. of real solutions of exx=0 please solve graphically.. ...