Recently Active Mathematics Questions

limx→0 {(1+3x)1/3-1-x} / {(1+x)101- 1-101x} has the value equal to? ...

Why is the value of log-3-27 ≠3? Because... log-3-27 = log-3(-3 * 9)=log-3-3 + log-39 = 1 + 2 = 3 ...

A TRIANGLE ABC HAS AN ANGLE 60 DEGREE.AB=b & BC=C. FIND THE AREA OF THE TRIANGLE. ...

Suppose a,b,c are positive integers and f(x) = ax2-bx+c =0 has two distinct roots in (0,1) m then (a) a≥5 (b) b≥5 (c) abc≥25 (d) abc≥5 2 ...

Let f(x) = ax2+bx+c where a,b,c ε R. Suppose |f(x)| ≤ 1 for all x ε [0,1],then (a) |a|≤8 (b) |b|≤8 (C) |c|≤1 (d) |a|+|b|+|c|≤17 ...

A point moves such that the sum of squares of its distances from the four sides of a square is constant;prove that it always lies on a circle. ...

What is the minimum distance between any two curves?? ...

Let α be a repeated root of p(x) = X3+ 3ax2 +3bx+c =0 , then (a) α is a root of x2+2ax+b=0 (b) α =(c-ab)/2(a2-b) (c) α=(ab-c)/(a2 -b) (d) α is a root of ax2+2bx+c =0 ...

Let a,b,c,d be four integers such that ad is odd and bc is even,then ax3+bx2+cx+d = 0 has (a) at least one irrational roots (b) all three rational roots (c) all three integral roots (d) none of these ...

\hspace{-16}\bf{(1)\;\; \int\frac{x^2-1}{(x^2+1)\sqrt{1+x^4}}dx}$\\\\\\ $\bf{(2)\;\;\int\frac{x^2}{(x^4-1)\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(3)\;\;\int\frac{x-1}{(x+1)\sqrt{x^3+x+1}}dx}$ ...

\hspace{-16}\bf{\int_{0}^{\frac{\pi}{2}}\frac{\sin(2nx).\sin x}{\cos x}dx\;\;, }$ Where $\bf{n\in \mathbb{N}}$ ...

Let a,b,p,q ε Q and suppose that f(x) = x2 +ax+b=0 and g(x)= x3 + px + q = 0 have a common irrational root , then (a) f(x) divides g(x) (b) g(x) ≡ x f(x) (c) g(x) ≡ (x-b-q)f(x) (d) none ...

a ray of light is coming along the line y = b from the positive direction of the x-axis and strikes a concave mirror , whose intersection with the xy-plane is a parabola y2 = 4ax . find the equation of the reflected ray and s ...

The equation of common tangent to the circle {{x}^{2}}+{{y}^{2}}=2 and parabola {{y}^{2}}=8x is ...

The points on the parabola {{y}^{2}}=12x , whose focal distance is 4, are ...

The parametric representation (2+{{t}^{2}},2t+1) represents ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pεR,then the value of bc+ca+ab is? ...

Let f(x)= ax2+bx+c ,a,b,c ε R.If f(x)takes real values for real values of x and non real values for non real of x,then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a,b,c ...

If x is real,then the maximum value of y=2(a-x)[x+√(x2+b2] ...

Let a,b,c be non-zero real numbers such that 0 ∫ 1 (e-x +ex )(ax2+bx+c)dx = 0 ∫ 2 (e-x+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...

Let a,b,c be non-zero real numbers such that 0 ∫ 1 (e-x +ex )(ax2+bx+c)dx = 0 ∫ 2 (e-x+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...

If both the roots of the equation x2-6ax+2-2a+9a2=0 exceeds 3 then (a) a<1 (b) a>11/9 (c) a>3/2 (d) a<5/2 Please solve here ...

If both the roots of the equation x2-6ax+2-2a+9a2=0 exceeds 3 then (a) a<1 (b) a>11/9 (c) a>3/2 (d) a<5/2 Please solve here ...

If x is real,then the maximum value of y=2(a-x)(x+√(x2+b2) ...

If the radical axis of circles {{x}^{2}}+{{y}^{2}}-6x-8y+p=0 and {{x}^{2}}+{{y}^{2}}-8x-6y+14=0 passes through the point (1, – 1), then p is equal to ...

The locus of the centre of circle which cuts the circles {{x}^{2}}+{{y}^{2}}+4x-6y+9=0 and {{x}^{2}}+{{y}^{2}}-4x+6y+4=0 orthogonally is ...

[sin 75{}^circ =] ...

What is the product of roots? ...