Recently Active Mathematics Questions

ABCD is a square of side 1.P,Q lie on AB and R lies on CD.FInd all possible values of circumradius of triangel PQR ...

Find all roots of the polynomial 4x^6 - 6x^2+2\sqrt 2 = 0 ...

here's a simple one prove that a number with 3^m equal digits is divisible by 3^m ...

If x,y,z are positive reals satisfying x+y+z=1 , find the maximum value of (1-x)(2-y)(3-z) . ...

Solve this one Guys!!!!! The height of a parabolic arch is 18m.The span of the arch is 24m.Find the height of the arch 8m on each side from its central position? ...

The new coordinates of point (3,4) when it is rotated through an angle of \Pi /4 about the origin in anticlockwise direction Ans(-1/√2 , 7/√2) ...

Find the number of roots of the equation z^7+4z^2+11=0 satisfying 1<|z|<2 ...

if (1+x+3x^2)^{30}=a_0+a_1x+a_2x^2............a_{60}x^{60} then find the value of a_{5}+a_{7}+a_{9}+.........a_{59} ...

\frac{4}{19}+\frac{44}{19^2}+\frac{444}{19^3}..........\infty ...

i need the best and shortest methods to solve these in exma hall... Q1 Let P(x)=x^5+x^2+1 have roots x_1,x_2,x_3,x_4,x_5 and g(x)=x^2-2 then find value of g(x_1)g(x_2)g(x_3)g(x_4)g(x_5)-30g(x_1x_2x_3x_4x_5) Q2 Let \alpha =e^{ ...

find the average of numbers ksin(k) wer (k=2,4,6......180) ...

ABC is a right angled isosceles triangle, right angled at A(2,1).If the equation of side BC is 2x+y=3, then find the combined equation of lines AB and AC. Ans-- 3x2-3y2-8xy-4x+22y-7=0 ...

Q) The tangents that are parallel to the bisector of the first co-ordinate angle for the curve F(x)= ∫0x 2tdt are a) y=x- 1/4 b) y=x+ 1/4 c) y=x- 3/2 d) y=x+ 3/2 ...

Q1 \ \int \frac{dx}{x^{22}(x^7-6)} Q2 \ Let \ t(x)=u(x)-v(x) \ where \ u(x)=sin^62\pi x \ and \ v(x)=lnx Prove \ area \ enclosed \ by \ u(x) \ and \ v(x) \ is \sum_{r=0}^{n}{\int_{x_r}^{x_{r+1}}{(-1)^r.t(x)dx}} \ where \ x_0, ...

Integrate the foll. ∫ 12x12+5x9/x5+x3+1 dx ∫etanx(xsec2x + sin 2x )dx ∫e3x( 2+3sin2x/1+cosx )dx ...

If x-2y+4=0 and 2x+y-5=0 are sides of a isosceles triangle having area 10 sq. units.Find the equation of third side?(Note that its an right angled triangle) ...

(1) Various injective functions f are defined from set A≡ {1,2,3,4} to {1.2.3.4.5.6.7.8.9.10} and a function among them is choosen randomly. If it is found to be increasing , then the probability that f(4) = 8 is (A) 1/12 ( ...

Let a real function f(x) satisfy following conditions : 1)f(x+y+1)=(\sqrt{f(x)}+\sqrt{f(y)})^2 2)f(0)=1 3)f(x)\geq 0 \ \forall x\in R Find f(x) ...

1> \lim_{x\rightarrow 0}\frac{e^{-4x}-1}{e^{-2x}+e^{-x}-2} 2> \lim_{x\rightarrow -1^{+}}\frac{\sqrt{\pi}-\sqrt{cos^{-1}x}}{\sqrt{x+1}} 3> \lim_{x\rightarrow 1}(1-x)tan(\frac {\pi x}{2}) ...

z=\frac{3}{2+cos\theta + i \sin\theta } the locus of z is ? ...

f(x) = log { log|sin x|(x2-8x+23) - 3/log2|sin x| } Find the domain of this function. ...

if f'(x/y).f(y/x) = \frac{x^{2}+y^{2}}{xy} for all x,y belongs to positive R and f(1)= 1 then f2(x) is????????? ...

the number of ordered pair (a,b) such that (a + ib)^2010 = a - ib is??? ...

Could anyone post the questions please? I am told it was held today. ...

Let A= \begin{bmatrix} 3 & -4\\ 1 & -1 \end{bmatrix} if det. (A+A^2+A^3......A^n)=64, then what is the value of n??? ...

Q) Let S1 and S2 be foci of an ellipse of equation : (x^2/a^2)+(y^2/b^2)=1 Locus of reflection of S1 with respect to any tangent to the ellipse is : a) circle b) parabola c) ellipse d) hyperbola ...

1) ∫(tan(pi/4-∂))/sin∂cos∂√(1+tan∂+cot∂) d∂ = -2tan-1√f(∂) + c. Then Minimum value of f(∂) is Opts - 4, 2, 6, 3 2) f(x) and g(x) are two real valued functions. Find the no. of solutions of equation ∫f( ...

a bag contains 10 white and 10 black balls. a person draws 2 balls at a time without replacement and repeats the process till bag is empty. what is the probability that he draws the balls of same colour each time? ...

f:R→R be twice diff fn satisfying f"(x)-5f'(x)+6f(x)≥0 for all x≥0.If f(0)=1,f'(0)=0 and f(x) satisfies f(x)≥a.h(bx)-b.h(ax) for all x≥0,then find (a+b).h(0) i understood BT's soln...but i am looking for shorter met ...

Good an' simple --- try this one --- Given four distinct numbers in the interval (0,1) , show that there exists 2 numbers among them x and y , such that ------ 0 < x \sqrt{1 - y^{2}} - y \sqrt{1 - x^{2}} < \frac{1}{2} ...