Recently Active Mathematics Questions

If a, b are roots of cos2x + acocx + b=0 as well as of sin2x + psinx + q, then a, b, p, q satisfy the relation 1)1 + b + a2 = p2 - q - 1 2)a2 + b2 = p2 + q2 3)b + q = a2 + p2 - 2 answer given is 3 ...

$\textbf{Calculate value of $\mathbf{m}$ for which the equation }$\\\\ \mathbf{\sqrt{x+1-2\sqrt{x}}+\sqrt{x+9-6\sqrt{x}}=m.}$ \textbf{has 2 Distinct Solution.} ...

'theorem on weighted means' is in iit jee syllabus ? If yes , where can i get some good problems to master that topic.....?? ...

$\textbf{No. of Real roots of the equation $\mathbf{|sin\;x|+sin\;|x|=2-\frac{x^2}{8}}$}$ ...

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The equation ∏/2∫x sin2y. dy= 0 has: A) NO SOLUTION B) ONE SOLUTION C) TWO SOLUTIONS D) THREE SOLUTIONS ...

A four-digit number has the following properties: (a) It is a perfect square; (b) Its first two digits are equal (c) Its last two digits are equal. Find all such four-digit numbers. (RMO '91) ...

1. Find the total number of terms in the expansion of (x + y + z + w)n , n ∈ N. 2. Find numerically greatest term in the expansion of (2 + 3x)9, when x = 3/2 ...

Solve the equation y3= x3 + 8x2 - 6x + 8 for positive integers. I have a method which is not very good. ...

1. Sum of the series : 1 + 3x + 5x2 + 7x3 + ......... 2. Sum the series : 1.2.3 + 2.3.4 + 3.4.5. + ......... + to n terms. 3. Sum the series : 12 + (12 + 22) + (12 + 22 + 32) + ........ to n terms. ...

On a chessboard, the positive real numbers are entered into the squares in such a way that every number is the arithmetic mean of its neighboring squares . Is this possible? If possible then prove it. ...

$\textbf{If $\mathbf{x=\left(\frac{\sqrt{\sqrt{2}+\frac{1}{8}}}{2}-\frac{\sqrt{2}}{8}\right)}$. Then Calculate value of $\mathbf{A=x^2+\sqrt{x^2+x+1}}$} ...

1. If α,β are the roots of x2+px+q=0 then express α5+β5 in terms of p and q. 2. \left|\left|x-1 \right|-x \right| \leq 4 ...

$\textbf{Find all Matrices $\mathbf{A}$ of order $\mathbf{2\times 2}$ that satisfies the equation}\\\\ \textbf{(i)}::$\mathbf{A^2=A}$\\\\ \textbf{(ii)}::$\mathbf{A^3=A}$\\\\ These are two different Questions. ...

\textbf{Solve system of equations }\textbf{\begin{cases} x^4+y^4+6x^2y^2=8 \\ x^3+3xy^2=x^2+y^2+2 \end{cases}} ...

In a certain test, there are n questions, In this test 2n-i students give wrong answers to atleast i questions (1 ≤ i ≤ n). If the total number of wrong answers given is 2047, find the value of n. ...

The equation A2/(x-a) + B2/(x-b) + C2/(x-c) + ..... + H2/(x-h) = k has 1) No real root 2) At most one real root 3) No complex root 4) At most two complex roots ...

$\textbf{If $\mathbf{\sqrt{9-8.sin\;50}=a+b.cosec\;50}$, Where $\mathbf{a,b\in\mathbb{Z}}$.Then find $\mathbf{ab=}$$} ...

If one root of ax^2+bx-2c=0 (a,b,c are real) is imaginary and 8a+2b>c , then a) a>0 and c<0 b)a>0 and c>0 c)a<0,c>0 d)a<0,c<0 ...

1/(1*4) +1/(4*7)+1/(7*10)+......................∞=? ...

1) x\sqrt{y}+y\sqrt{x}=20 x\sqrt{x}+y\sqrt{y}=65 2) 3x+4x+5x =6x 3) Find all the roots of the equation : 4x4 – 24x3 + 57x2 + 18x – 45 = 0 if one root is 3 + i 6 . ...

How to draw the graph of y≥x2-1? If x=1 then y≥0.So,where to find this point as y can be anywhere? ...

1. Find the real values of a so that a2+2a,a2+3a+8,2a+3 are the sides of a triangle. 2. If x=2+21/3+22/3 then the value of x3-6x^2+6x is ? 3. Find the eqn whose roots are two more than the roots of ax^2+bx+c=0 . ...

Problem 1: If a1,a2,.........an-1,an are in AP prove: 1/(a1an) + 1/(a2an-1)+1/(a3an-2)+..............+1/(ana1)=[2/(a1+an)][1/a1 + 1/a2+ 1/a3 +.........+ 1/an] ...

Evaluate : \int_{-1}^{1}{\frac{\ln(13-6\cos{x})dx}{\sqrt{1-x^2}}} ...

find the max value of (cos\,\, \alpha _{1}) (cos\,\, \alpha _{2}) ...... (cos\,\, \alpha _{n}) under the restrictions 0\leq \alpha _{i}\leq \Pi /2 and (cot\,\, \alpha _{1}) (cot\,\, \alpha _{2}) ...... (cot\,\, \alpha _{n}) = ...

If f(x)=\frac{ax}{x+1} , x\neq -1 then for what value of a is f(f(x))=x ? ...

Find 3-digit numbers that are divisible by 5 as well as 9 and whose consecutive digits are in A.P ...

A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the s ...

If ax+by+c=0 is a tangent to xy=4, then find the sign of a and c . ...