Recently Active Mathematics Questions

for a given constant perimeter which of the following triangles will have max area? a)equilateral b)right angled c)scalene d)isosceles? i thought about it that by symmetry ,ans. will be a),but how do we numerically prove it?p ...

\hspace{-16}$Find value of $\mathbf{x}$ in $\mathbf{2^x+2^{\left[x\right]}+2^{\left\{x\right\}}=3}$\\\\ Where $\mathbf{\left[.\right]=}$ Greatest Integer Function and \\\\ $\mathbf{\left\{.\right\}=}$ fractional part function ...

If f'(x2 - 4x + 3) > 0, then interval on which f(sin x) is increasing? ...

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1. In the isosceles triangle ABC, \left|\vec{AB} \right|=\left|\vec{BC} \right|=8 , a point E divides AB internally in the ratio 1:3, then the cosine of the angle between \vec{CE} & \vec{CA} is ( where \left| \vec{CA}\right|= ...

Let a, b, c be positive reals such that a + b + c = 1. Prove that ( a/1 + 1/b )( b/1 + 1/c )( c/1 + 1/a ) ≥ (10/3)3 ...

\hspace{-16}$\textbf{(1)\;\; If $\mathbf{x,y\in\mathbb{R}}$ and $\mathbf{x^2+y^2=1}$. Then Max. value of $\mathbf{\mid x-y \mid +\mid x^3-y^3 \mid=}$ } ...

Let A={1,2,3,4} B={a,b,c} Find the number of functions from A to B which are not onto. A.45 B.64 C.81 D.41 ...

Determine all distinct triangles having one side of length 6,with the other two sides being integers ,and perimeter numerically equal to the area. ...

If Σ (i = 1 to n) cos -1xi = 0 , then Σ(i=1 to n) xi is equal to? (a)n (b)-n (c)0 (d) none of these ...

prove that for a , b , c in [0,infinty) (a - 1/b)(b - 1/c)(c- 1/a) ≥ (a - 1/a)(b - 1/b)( c-1/c). here (a - 1/b) means a/1 - 1/b ...

Solve the equation (x^4 + 5x^3 + 8x^2 + 7x + 5)^4 + (x^4 + 5x^3 + 8x^2 + 7x + 3)^4 = 16 in the set of real numbers. ...

Find all (x, y) where x and y are positive integers such that x^{2007} = y^{2007} − y^{1338} − y^{669} + 2. i found one pair to be (1,1) also 2007 = 3(669) and 1338 = 2(669). don't know but it might help. ...

The no. of ways of selecting n things out of 3n things of which n are of one kind and alike and n are of 2nd kind and rest are unlike is: ...

Prove that point of discontinuity of the function f(x) = lim(x→∞) (2 sin x)2n/[3n - (2 cos x)2n] is nπ ± π/6 ...

1) Is 1∞ = 1 or it is not defined? 2) Also what about 2∞, 3∞ etc. ? ...

\hspace{-16}\mathbf{(1)\;\;\int_{0}^{1}\frac{1-2e^x\sin x}{(e^x+\cos x).(e^x+\sin x)}dx}$\\\\\\ $\mathbf{(2)\;\;\int\frac{1}{(x+1)^5.\sqrt{x^2+2x}}dx} ...

SOLVE 1. dy/dx = x/(2y+x) 2. (x2+y2)dy/dx= 8x2-3xy+2y2 ...

f(x) = -x3-9x2 + 24x + c has three distinct roots p,q,r now for c belongs to (-18,-16). the value of +[q]+[r] = ? where [k] represents greatest integer less than or equal to k ...

a rigid body rotates with constant angular velocity w about the line whose vector equation is r=lambda(i+2j+2k). the speed of the particle at the instant it passes through the point with p.v. 2i+3j=5k is a) w√2 b) 2w c)w/∠...

(x2+cos2x)/1+x2 integrate the above function.. PS- i already have done it, but the answer is not matching...a detailed solution is needed to check where i went wrong... ...

\hspace{-16}$If $\mathbf{p,q,r>0\;}$,Then find $\mathbf{p,q,r}$ in \\\\ $\mathbf{\ln\left(pqr\right)=-2}$\\\\ $\mathbf{ln(p).\ln(q).\ln(r)=2}$\\\\ $\mathbf{\ln(p).\ln(q)+\ln(q).\ln(r)+\ln(r).\ln(p)=-1}$ ...

f(x+2) -5f(x+1) +6f(x) = 0 , f(0)=0 , f(1) = 1 then least positive prime factor of f(2008) = ? answer 5 ...

How to solve this one? value of lim x->0 loge(sinx)^tanx ...

can anyone explain Idempotent matrix and properties. ...

a detalied explanation for what a nilpotent matrix is...i need it... ps---NISHANT SIR, help... ...

lim (n→∞) tan2nx is equal to A) 1 if x = 2nπ + π/4 B) 1 if x = nπ + π/4 C) 0 if x ≠nπ + π/4 D) 0 if nπ - π/4 < x < nπ + π/4 There may be more than one option correct ...

can anyone tell me how to find the number of prime nos between two given integers eg:: between 1 to 10 there are 4 primes .......please tell me if there is any general method for this. ...

Let f(x) be the monotonic polynomial of (2m-1) degree where m belongs to natural no., then equation f(x)+f(3x)+f(5x)+. . . . . .f((2m-1)x) = 2m-1 has: A) At least one real root B) (2m-1) real roots C) exactly one real root D) ...

f(x)= |x2n+1|, n belongs to N then, A) f(x) is continous but not differentiable at x=0 B) f(x) is differentiable at x=0 C) f(x) is discontinous at x=0 D) none of these. ...