Recently Active Mathematics Questions

For a positive integer n, the expression {(1 - i)^n}{left( {1 - frac{1}{i}} ight)^n} equals ...

int {frac{{dx}}{{sin x + sin 2x}}}Â = ...

int {frac{{dx}}{{{{(x - 1)}^2}(x - 2)}}}Â = ...

*Image* AB is a secant which intersects a circle with centre O at the points C and D such that AC=BD. From A, B two tangents AR and BS are drawn to meet the circle at the points P and Q respectively( as given in the diagram). ...

Find the next term: 3, 8, 15, 24, 35, ___ ...

The value of {i^{1 + 3 + 5 + ... + (2n + 1)}} is ...

int {frac{{dx}}{{4{{sin }^2}x + 5{{cos }^2}x}}} ...

The least positive integer n which will reduce {left( {frac{{i - 1}}{{i + 1}}} ight)^n} to a real number, is ...

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

{i^2} + {i^4} + {i^6} + ..... upto (2n+1) terms = ...

Solve the equation cos 4θ+sin5θ=2. (cos4θ=1....and sin5θ=1...using this i got θ= nπ/2 and θ= nπ/5 +(-1)n π/10 ....how should i proceed further??) ...

∫f(x)/f'(x) dx ...

The sum of 1+3+5+7+..... upto n terms is ...

If {left( {frac{{1 + i}}{{1 - i}}} ight)^m} = 1, then the least integral value of m is ...

The values of x and y satisfying the equation frac{{(1 + i),x - 2i}}{{3 + i}} + frac{{(2 - 3i),y + i}}{{3 - i}} = i, are ...

Find the next term: 521, 612, 343, 215, ____ ...

Find the next term: 0, 7, 26, 63, 124, _____ ...

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

If sin-1x + tan -1x = frac{pi }{2} , then 2x2 + 1= ...

For real values of x, range of the function y=frac{1}{2-sin 3x} is ...

suppose a,b,n are positive integers , all greater than 1. if an+bn is Prime then what can be said about n ? A) n must be 2 B) n need not be 2 but must be a power of 2 C) n need not be a power of 2 but must be even D) none of ...

\hspace{-16}$If $\bf{f:\mathbb{Z}\rightarrow \mathbb{Z}}$ and $\bf{m + f\big(m + f(n + f(m))\big) = n + f(m)}$\\\\ and $\bf{f(6)=6}$.\;Then $\bf{f(2012)=}$ ...

If 3+3alpha +3{{alpha }^{2}}+........infty =frac{45}{8}, then the value of alpha will be ...

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

The roots of the given equation (p-q){{x}^{2}}+(q-r)x+(r-p)=0 are ...

If the {{p}^{th}},,{{q}^{th}}, and {{r}^{th}} term of an arithmetic sequence are a, b and c respectively, then the value of [a (q – r)+b(r – p)+ c (p – q)]= ...

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} = ...

\hspace{-16}$If $\bf{f:(0,\infty)\rightarrow (1,\infty)}$ and $\bf{f(x)=x^4+x^2+x+1}$. Then $\bf{\frac{d}{dx}\left\{f^{-1}(4)\right\}=}$ ...

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