Recently Active Mathematics Questions

1) Evaluate the limit: \lim_{n\to\infty} |\sin (\pi\sqrt{n^2+n+1})| 2) Prove that \lim_{n\to \infty}n^2 \int_0^{1/n} x^{x+1}\ \mathrm dx=\dfrac{1}{2} 3) Find the real parameters m and n such that the graph of the function f(x ...

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2=4ax is another parabola with directrix? ...

Let f:[0,2]→R be defined by f(x)=\sqrt{x^3+2-2\sqrt{x^3+1}}+\sqrt{x^3+10-6\sqrt{x^3+1}} Find the indefinite integral of f w.r.t x. ...

Find the locus of the points of intersection of tangents drawn at the ends of all normal chords of the parabola y2=8(x-1). ...

Given that \int_{-\infty}^{\infty} e^{-x^2}\ \mathrm dx=\sqrt{\pi} evaluate the integral I=\int_0^\infty \dfrac{1}{\sqrt{x}}\ e^{-x}\ \mathrm dx ...

Find the remainder when 599 is divided by 13? ...

1) Prove: \left|\begin{array}{cccc} 1+a_1 & 1 & \cdots & 1\\1 & 1+a_2 & \cdots & 1\\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \cdots & 1+a_n\end{array}\right| = a_1a_2\cdots a_n \left(1+\dfrac{1}{a_1}+ \dfrac{1}{a_2}+\ldots ...

Nine gallons are drawn from a cask full of wine; it is then filled with water, then nine gallons of the mixture are drawn, and the cask is again filled with water. If the quantity of wine now in the cask be to the quantity of ...

*Image* whcih theorem to use for solving option c and d ...

*Image* which concept is involved here? ...

which concept is involved here? *Image* ...

*Image* In the soln its given that no three planes can meet at two distinct points. But we can have infinite number of planes through a given line. isnt it? Plese clarify ...

$ \displaystyle\prod_{n=1}^{15}cos\left(\frac{n\pi}{15}\right)=$\\\\ ...

In a triangle the lengths of two larger sides are 10 and 9 respectively.if the angles are in AP,then the length of third side can be:1.√91 2.3√3 3.5 4.none my query: sir this is a jee-87 question.i found the solution in a ...

*Image* explain ...

$Let $p(x)=x^n+a_{1}x^{n-1}+...............+a_{n-1}x+4$ be a polynomial with\\\\ non-negative coefficient has $n$ real roots.Then prove that $p(1)>2^{n+1}$ ...

If points x,y are choseaban for randomly from the interval [0,2] and [0,1] respectively then probabilty that y=<x2 is k/3 then k is ...

Q1)lim (x+2)tan-1(x+2) - x tan-1x (x→ ∞) Q2) lim ((1.5)n+ [(1+0.0001)10000]n)1/n (x→ ∞) Here[ ] is Greatest Integer Function (GIF) n Q3) lim Σ log( 1 +K/n)1/n (n→∞) k=1 Thnx in advance ...

pls answer *Image* ...

the area bounded by the curve {|x|, |y|}= 1/2 is ...

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Let f(x) be an increasing function defined on (0, ∞). If f(2a2 + a + 1) > f(3a2 – 4a + 1), then the number of integral values of a is/are (A)5 (B)4 (C)3 (D)6 ...

the eqn. of the plane passing through the intersection of the plane 2x-5y+z=3 and x+y+4z=5 and parallel to the plane x+3y+6z=1 is x+3y+6z=k where k is. ...

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solve it and find answer *Image* ...

1/1+ 2 + 1/ 2 + 3 + 1/ 3 + 4 + 1/ 4 + 5 +.........................till + 1/ 15 + 16 . simplify this problem. ...

2x2-7x+3=0 solve this quad. equation by completing the square method ...

Help me prove that a} xo=1 b}If two triangles are equiangular ,then their corresponding sides are proportional. ...

Find the eqn of the circle on the other side of the line x+y=2 similarly situated as the circle x2+y2-2x=0. ...

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