Recently Active Mathematics Questions

x \int \frac{\sqrt{2sin ( x ^ 2-1 ) - sin 2( x^2 -1 )}}{ \sqrt{2sin ( x^2 -1)+ sin2 ( x^2 -1 )} }where x^2 -1 \neq n\pi ans is log \mid \left( sec \frac{ x^2 -1 }{2} \right) \mid + c for practice ...

\int \frac{dx}{(1+\sqrt{x})(\sqrt{x + x^{2}})} ans is. \sqrt{2}log tan \left\{\frac{1}{2}(tan^{-1}\sqrt{x})+\frac{\pi }{8} \right\} + c ...

let α & β be the roots of the equation ax^2+bx+c=0,a≠0,then the sum of the series (α+β)^(2 )+(α^2+β^2 )+(α-β)^2+⋯upto n terms is equal to A)(n(a^2+(n-1)ac))/a^2 B)(n(a^2-(n-1)bc))/b^2 C)(n(b^2+(n-1)ac))/a^2 D)(n(b ...

Q1 A bag contains 10 white and 10 black balls.A perosn draws two balls at a time without replacementand rpeleats till bag is empty.The probablity tha the draws the balls of same color each time Q2 The number of ordered pairs ...

the sum of solution of the equation sinπx=x2-7x+12 is k which can be expressed as the prouct of two prime numbers.the sum of the primes= ...

Find the modulus and argument of the complex number z1=z2-z if z=cos θ + i sin θ ...

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The smaller area enclosed by y = f(x) when f(x) is polynomial of least degree satisfying *Image* 1/x = e and the circle x2 + y2 = 2 above the x axis is a) \pi / 2 b) 3/5 c) \pi /2 - 3/5 d) \pi /2 + 3/5 ...

1..if f:R→R be a differential finction such that that f(2-x)=f(x) and f(5-x)=f(5+x) then 1.f'(-3)=0 2..f'(9)=0 . 3.if \int_{3}^{5}{f(x)dx=k},then \int_{11}^{15}{f(x) dx} wil l be k ...

Prove that (\sin \gamma + a \cos \gamma)(\sin \gamma + b \cos \gamma) \le 1 + \left( \frac{a+b}{2} \right)^2 for reals a,b ...

A non-zero vector a i s parallel to the line of intersection of plane P1 determined by i+j , i - 2j and plane P2 determined by vector 2i + j ,3i + 2k , then angle between a and vector i - 2j +2k is (A)Î /4 (B) Î /2 (C) Î /3 ( ...

area of the region bounded by the curve *Image* is A) 3 sq . unit B) 4 sq . unit C) 1 sq . unit D) 2 sq . unit ...

Prove (1 - cos A) /(sin A) tan(A/2) ...

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q.If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectum of the given ellipse at the points A) \left(\pm \frac{3\ ...

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how to draw graph of x^(something in fraction) say x2/3 ...

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f(x)=a_0+a_1cosx+a_2cos2x+a_3cos3x+...+a_ncosnx g(x)=b_1sinx+b_2sn2x+b_3sin3x+..+b_nsinnx Q1 If br= 1/r+1 ,then \lim_{n\rightarrow \infty} \int_{0}^{\pi }{g(x)dx} Q2 \sum_{k=0}^{n}{\int_{0}^{2\pi }{f(x).(cos kx)dx}} Q3 \sum_{ ...

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\int {e^{x\sin x+\cos x}}\left(\frac{x^4\cos^3x-x\sin x +\cos x}{x^2\cos^2 x} \right)dx ...

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A(z1), B(z2), C(z3), D(z4), E(z5) are the vertices of a regular polygon ABCDE in anti clockwise order whose centre is at the origin O and M(z) is point inside the polygon. 1) If |arg(z4-z5/z-z5)| = |arg(z-z3/z4-z3)| = θ then ...

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if x^{5}-x^{3}+x=k then prove that x^{6}≥ 2k-1 ...