Recently Active Mathematics Questions

number of points having integral co-ordinates and satisfying x2+y2≤5 is 1. 14 2. 21 3. 20 4. none of these please give a detailed solution. P.S.- nishant sir, i want a solution to this asap. ...

Solve for x. 1+ \frac{1}{2\sin(30^0+ x)}= \frac{\sin(\frac{x}{2})}{\sin(\frac{x}{2}+ 60^0)}+ \frac{\sqrt{3}}{2\sin(\frac{x}{2}+ 60^0)} ...

\hspace{-16}\mathbf{\lim_{x\rightarrow 0}\left[\frac{(1+4x)^{\frac{1}{x}}}{e^4}\right]^{\frac{1}{x}}} ...

\hspace{-16}$Prove That\\\\ $\mathbf{(1)::\log_{2}{3}>\log_{3}{4}}$\\\\ $\mathbf{(2)::\log_{2}{3}>\log_{3}{11}}$\\\\ $\mathbf{(3)::\log_{3}{5}>\log_{2}{3}}$\\\\ without Using properties of Logarithms ...

\{a_n\} is a sequence of real numbers such that |a_n- a_{n+1}| \le 1 \ \forall \ n \in \mathbb{N} Define b_n = \frac{a_1+a_2+...+a_n}{n} Prove that |b_n-b_{n+1}| \le \frac{1}{2} ...

Q. If y=\frac{1}{1+x^{n-m}+x^{p-m}}+\frac{1}{1+x^{m-n}+x^{p-n}}+\frac{1}{1+x^{m-p}+x^{n-p}} , then \frac{dy}{dx} at e^{m^{n^{p}}} \text{(a) }e^{mnp} \text{(b) }e^{\frac{mn}{p}} \text{(c) }e^{\frac{np}{m}} \text{(d) } none ...

Consider the cubic equation given by x3+ax2+bx+c = 0 , where a, b, c are real numbers. Which of the following is correct : A. If a2-2b < 0, then the equation has one real and two imaginary roots B. If a2-2b ≥ 0, then the ...

Q> Find the value of 'a' for which ax2 + (a - 3)x + 1 < 0 for at aleast one positive real x. ...

\hspace{-16}$Which one is Greater $\mathbf{2011^{2012}}$ OR $\mathbf{2012^{2011}}$ ...

Let tn be the no. of triangles with integral sides out of the side lengths {1,2,3,....n} . Then t20-t19 = ? ...

The condition that x4 + ax3 + bx2 + cx + d is a perfect square, is (A) c2 = ad (B) c2 = ad2 (C) c2 = a2d2 (D) c2 = a2d ???????????????? ...

find the factors of the no. 123456789 such that they have the minimum difference between them. ...

\hspace{-16}$If $\mathbf{x\;,y>0}$ and $\mathbf{xy+x+y=3}\;$.Then find Min. of \\\\\\ $\mathbf{P=\frac{x^2}{y+1}+\frac{y^2}{x+1}+\frac{xy}{x+y}}$ ...

\hspace{-16}$If $\mathbf{f(x)=x^3+x^2-4x+1}$ and If $\mathbf{\alpha}$ be a root of $\mathbf{f(x)=0}.\;$ Then Prove\\\\ that $\mathbf{\alpha^2+\alpha-3}$ is also root of $\mathbf{f(x)=0}$ ...

if the equation ax2 + bx + c = 0 does not have 2 distinct real roots and a + b > c, then prove that f(x) ≥ 0, for all x E R. ...

$\textbf{Solve system of equations:}\\\\ $\mathbf{x+y-z=7}$\\\\ $\mathbf{x^2+y^2-z^2=37}$\\\\ $\mathbf{x^3+y^3-z^3=1}$ ...

\hspace{-16}$If $\mathbf{\alpha\in \mathbb{R}}\;,$ Then Prove That\\\\\\ $\mathbf{\sqrt{17}\leq\sqrt{\cos^2 \alpha+4\cos \alpha +6}+\sqrt{\cos^2 \alpha-2\cos \alpha +3}\leq \sqrt{2}+\sqrt{11}}$ ...

if x2 + ax + 3/x2 + x + a takes all real values for possible real values of x then prove that 4a3 + 39 < 0. ...

\hspace{-16}\mathbf{\displaystyle \sum_{k=0}^{1004} \frac{2008!}{k!\times k!\times (1004-k)!\times (1004-k)!}} ...

\hspace{-16}$Solve $\mathbf{\sin^8 x+\cos^8 x=\frac{17}{32}}$ ...

Tangent lines to the curve : y=∫2|t|dt (limit from 0 to x) whch are parallel to the bisector of the first cordinate angle is given by? ...

\hspace{-16}\mathbf{\int_{1}^{\infty}\frac{x^2-3}{x.(x+1).(x^2+1)}dx} ...

\hspace{-16}(1)\;\;\mathbf{\int_{0}^{\pi}\frac{x^2\cos^2 x-x\sin x-\cos x-1}{(1+x\sin x)^2}dx}\\\\\\ (2)\;\; \mathbf{\int\frac{1}{x^n+x}dx}\\\\\\ (3)\;\;\mathbf{\int\frac{1}{1+\sqrt{x}+\sqrt{x+1}}dx} ...

Find the values of 'a' for which the equation (x2 + x + 2)2 - (a - 3)(x2 + x + 2)(x2 + x + 1) + (a - 4)(x2 + x + 1)2 = 0 has atleast one real root. ...

How will you arrange all the digits from 1to9 forming different digits such that they form an A.P.? For example,consider 147,258,369. They form an A.P. with common difference 111,and all the digits from 1 to 9 are used . form ...

we have to calculate the value of 1/x in a calculator, but the key of 1/x function is broken and we can only use the functions sinx , cosx. tanx. sin-1x ,cos-1x ,and tan-1x.how itz possible? ...

Someone please try to solve this problem. Two players A & B play a game of chess. Whoever wins first a total of two games wins. A's probability of winning,drawing or losing are p,q,r respectively. prove that the probability t ...

*Image* \hspace{-16} $The aera of an equilateral triangle $\mathbf{OPQ}$ is bisceted by a curve $\mathbf{AB}$ of\\\\ minimal length. What is the equation of the curve with respect to\\\\ the given axes? ...

Q. Use the fact that e^x>1+x to prove that e^\pi>\pi^e . ...

Can someone tell me that... Is there any other congruency criteria for triangles other than SAS SSS AAS ASA RHS ?????? ...