Recently Active Mathematics Questions

Q1. y=sin^-^1(2x\sqrt{1-x^2}) then dy/dx = (Find answer by trigonometric substitution)? My attempt: Let x=sinθ Then the given expression translates to y=2θ = 2sin-1x So, dy/dx = 2/ 1-x2 Let x=cosθ Then the given expression ...

let a1,a2,......,an be a sequence of real numbers with an+1=an+(√1+an^2) and a0=0 find limit an/2^(n-1) n→∞ ...

A square has tens digit 7.Find its units digit I want to learn the basic concept of this question more than just the answer :-) ...

1) Find the minimum of (a+b)4+(b+c)4+(c+a)4- 4/7 (a4+b4+c4) a,b,c are reals. 2) Solve the Diophantine equation for integers x3+2y3+4z3-6xyz=1 Beleive me, number 2 is really hard... ...

Ques1) Show that one of the solution of the equation -x4+x2-P=0 where x belongs to (0,1) and P belongs to (0,1/4) is sin (1/2 sin - 1 2 √P). Ques2) Tangents are drawn to y = ax2+bx+c at (5,4) is parallel to x- axis. If a be ...

If x2-2xcosα +1=0 and y2-2ycosβ+1=0 then what is the value of 2cos(α+β) ...

If a<b<c<d , then the equation (x-a)(x-c) + 2(x-b)(x-d) = 0 has a)Imaginary roots b)equal roots c)distinst real roots d) none 2. If α is a root of a2x2 + bx + c=0 , β is a root of a2x2 -bx - c=0 and α<β , then ...

integrate: ∫1/1+x^n ...

Find equation of conjugate axis of hyperbola xy-3y-4x+7=0 ...

A right angle is divided in 3 parts, angles x,y,z..... Prove tanx+tany+tanz>1+tanxtanytanz..... ...

a,b,c are positive reals such that abc=1 prove *Image* ...

Let k and n be positive integers and put Sk=Σnk (n varies from 1 to n. show that m+1C1S1+m+1C2S2...............+m+1CmSm=(n+1)m+1-(n+1) ...

A triangle is inscribed in a circle of radius 1.The distance between orthocentre and circumcircle cannot be a)1 b)2 c)3/2 d)4 ...

Ques1) Show that the value of ∫ [(1 - cot n-2 x) / (tanx + cotx .cot n-2 x ) ]dx is equals to (1/n) log | sin n x + cos n x| + c. Ques2) If I1 =∫ sin -1 x dx and I 2 = ∫ sin -1 1-x 2 dx then show that I 1 +I 2 = pie x / ...

Q1. \int (cos2\theta )^3^/^2cos\theta d\theta Q2. \int \frac{cos8x-cos7x}{1+2cos5x}dx ...

If f(x+y)=f(x)+f(y) where x,yε R and ∫(0 to 1) f(x).dx=1 find f(1) ...

what is the reduction formula for ∫ 1/1+x^n ...

let ABC be a triangle with AB=AC=6. If the circumradius of the triangle equals 6, then BC equals: (a)25/3 (b)9 (c)48/5 (d)10 this is a sample question on the kvpy website. ...

f(x+y)=f(x)+f(y) where x,yεR Prove thta nf(x-\frac{a}{n})+f(a) is an odd functionm wheere nεI-{0} I am also givng ma soln...plz continue and finsh it off... nf(x-a/n)=+f(a) =>nf(x)-nf(a/n)+f(a) =>nf(x)-n(f(a/n)-1/nf(a ...

If a+b+c=0 and a,b,c are real, then prove that the eqn (b-x)2 - 4 (a-x)(c-x) = 0 has real roots and the roots will not be equal unless a=b=c. ...

Ques1) Prove that the sum of 1 st n odd natural numbers is n2 and hence or otherwise prove that the sum of next 'n' odd natural numbers is divisible by 3. Ques2) Show that the sum of 2/3 + 8/9 + 26/27 + 80/81 + .............u ...

If area bounded by y=logx,y=x ,x2+y2+2xy-k2=0 is a square units,then calculate area bounded by y=ex,y=logx ,x2+y2+2xy-k2=0 . ...

Find the minimum value of \frac{a^2}{cos^2x}+\frac{b^2}{sin^2x} ...

All points on the curve y2=4a(x+asin(x/a)) at which the tangents are parallel to the X axis lie on which curve ? I solved it and got x=aπ But answer is a parabola Please give the right solution :-) ...

I_1=\int_{0}^{1}{e^{-\frac{x^2}{2}}}dx I_2=\int_{0}^{1}{e^{-x^2}}dx I_3=\int_{0}^{1}{e^{-x^2}}cos^2xdx I_4=\int_{0}^{1}{e^{-x}}cos^2xdx ...

Let g'(x)>0 and f'(x)<0 for all x ε R then prove that g(f(x+1))<g(f(x-1)) ...

Ques1) The lengths of three unequal rectangular block arein G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2 . Show that the length of the longest edge is 12 cm. Ques2)Show that 11 2 + 12 2 +13 2 ...

One problem that has been troubling me for ages now.. anyone who can try and solve? ∫(tan x)1/6 dx ...

Q. Find the sum : 1 + 5 + 19 + 49 + 101 + 181 + 295 ................. ...

Evaluate the following limit: \lim_{x\to+\infty}\left(\sqrt[n]{(x+2)(x+4)\cdots(x+2n)}-\sqrt[2n]{(x+1)(x+2)\cdots(x+2n)}\right) where n is a positive integer. ...